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This article is part of the series Radio Propagation, Channel Modeling and Wireless Channel Simulation tools for Heterogeneous Networking Evaluation .

Open Access Research

Performance of MUTP-aided MIMO systems over correlated frequency-selective wireless communication channels: a multi-cell perspective

Prabagarane Nagaradjane1*, Sabarish Karthik Vivek Sarathy2, Prasaanth Muralidharan4 and Yuvika Ashwina Rajan3

Author Affiliations

1 Department of ECE, SSN Institutions, Chennai, India

2 Department of ECE, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA

3 Department of ECE, Georgia Institute of Technology, Atlanta, GA, USA

4 QUALCOMM Inc. San Diego CA, USA

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EURASIP Journal on Wireless Communications and Networking 2012, 2012:194  doi:10.1186/1687-1499-2012-194

The electronic version of this article is the complete one and can be found online at: http://jwcn.eurasipjournals.com/content/2012/1/194


Received:6 April 2011
Accepted:11 June 2012
Published:11 June 2012

© 2012 Nagaradjane et al; licensee Springer.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this article, we investigate the performance of multiuser transmitter preprocessing (MUTP)-aided multiple-input multiple-output (MIMO) systems in a multi-cell multiuser setting where co-channel interference (CCI) is the major channel impairment, for both uplink (UL) and downlink (DL) transmissions. CCI can considerably reduce data rates resulting in outages in cellular systems, particularly at the cell edges in DL transmission. The MUTP considered in this article is based on singular value decomposition (SVD), which exploits the channel state information (CSI) of all the users at the base stations (BSs) with the aid of BS cooperation, and only the individual users' CSI at the mobile stations (MSs) for both UL and DL transmissions. In particular, in this article, we study the effects of three types of delay spread distributions coupled with different interferer configurations over correlated and uncorrelated frequency-selective channels. Our simulation study shows that SVD-aided MUTP perfectly eliminates CCI with lesser detection complexity under perfect CSI. Also, we provide performance comparisons of SVD-aided MUTP with various precoding techniques widely addressed in literature, and the results show that it provides better achievable symbol error rate (SER) by mitigating multi-stream interference (MSI) and CCI. Further, simulation results demonstrate that compared to equal CCI, the presence of a dominant interferer can lead to more degradation in the system performance in terms of achievable SER while, further degradation results when noise is dominant. Furthermore, this study confirms that imperfect CSI as well as imperfect power control can lead to degradation in the system performance.

Keywords:
multiple-input multiple-output (MIMO); preprocessing; post-processing; multiuser transmitter preprocessing (MUTP); singular value decomposition (SVD); co-channel interference (CCI); multiuser interference (MUI); multi-stream interference (MSI)

1. Introduction

Information theoretic results have shown that significant increase in the capacity of wireless communication systems can be achieved with the aid of multiple antennas at both the transmitters and receivers. The capacity of these multiple antenna systems, also called as multiple-input multiple-output (MIMO) systems, has been shown to grow linearly with small increase in the number of transmit and receive antennas in rich scattering environments, and at sufficiently high signal-to-noise (SNR) ratios [1]. MIMO systems can provide high data rates through spatial multiplexing (invoking Vertical Bell Laboratories layered space-time architecture (VBLAST) type processing) or considerable diversity using transmit diversity (by exploiting space-time block code type processing) [2]. Much of the research focus has been in the design of single user MIMO systems [3,4], where only multi-stream interference (MSI) is the major channel impairment. In single-cell multiuser MIMO systems, in addition to MSI, multiuser interference (MUI) becomes the dominating channel impairment. In the case of multiuser multi-cell MIMO systems, owing to frequency reuse, co-channel interference (CCI) from other cells becomes the domineering channel impairment. Further, next generation cellular standards like the 3GPP (Third generation partnership project) Long Term Evolution Advanced (LTE-A) aim at exploiting universal frequency reuse in order to maximize the area spectral efficiency. However, this could result in high levels of CCI as simultaneous transmission takes place on the same frequency band in the adjacent cells. In this context, the users may synchronously receive their own signals from the serving base station (BS) as well as signals from adjacent co-channel BSs. The signals from the adjacent BSs, namely CCI, can greatly reduce the achievable data rates leading to outages in cellular systems mainly at the cell edges [5-8]. This CCI is asynchronous and is a critical issue that requires serious attention. Hence, disregarding CCI would result in significant degradation in the system performance in terms of achievable symbol error rate (SER). To deal with this interference, multiuser detection (MUD) can be invoked both at the mobile station (MS) and BS [9], but its complexity increases excessively, thus making it impractical for implementation even at the BS, where complexity is acceptable. An alternate way to combat interference is to exploit multiuser transmitter preprocessing (MUTP) at the BS as well as at the MS [3,4,10].

Recently, MUTP that mitigates MUI and CCI has received considerable attention as it facilitates the implementation of less complex and more power efficient MSs. MUTP has been proposed to keep the receiver design simple by moving the required signal processing to the transmitter [10], i.e., signal processing at the BS in the case of DL transmission and at the MS in the case of UL transmission [4]. A comprehensive treatment on transmitter preprocessing, such as transmitter MUD, multiuser transmission (MUT), etc., has been addressed in [10]. As a design choice, in [11] maximum ratio UL transmission scheme was analyzed, by considering the dominant right-hand side (RHS) and left-hand side (LHS) singular eigenvectors for the preprocessing and postprocessing vectors, respectively, to increase the achievable diversity gain. In [3], the multiuser transmission schemes invoke the block diagonalization (BD) method. In some proposed schemes [12,13], it has been demonstrated that dirty paper (DP) precoding could approach the achievable system capacity in various joint transmissions for DL. Furthermore, singular value decomposition (SVD)-assisted space time block coding (STBC) for point-to-point transmission has found many applications [14], while in [4], SVD based MUTP is investigated for flat fading channels. Of late, BS cooperation aided multi-cell multiuser systems have received widespread attention [5-7,12]. The study of [15] presents a detailed survey on multi-cell MIMO cooperation aided wireless networks in the context of inter-cell interference mitigation. The main difference between MUTP aided single cell transmission and multi-cell transmission is that, in the former case BS cooperation is not needed to remove MUI, while in the latter full BS cooperation is required to completely eliminate CCI. The first work in the context of full BS cooperation was investigated by Hanly as stated in [15], for uplink transmission for a MIMO multiple access channel. In this publication, it was shown that the BSs cooperate to decode each user's symbols. Also, Hanly has shown that, by exploiting interference with the aid of global receivers, interference can be completely eliminated and thus all received signals carry useful information for the global decoder [15]. Further in [15], it is addressed that Hanly et al. have shown that BS cooperation eliminates CCI by invoking optimal power control. In other words, a network of interfering cells has the same per-cell capacity (in numbers of users) as a single, isolated cell. In [16] it is shown in the context of multi-cell MIMO systems, that significant performance gain can be achieved by grouping adjacent cells and by solving the optimal beamforming and power splitting problem jointly. It is demonstrated in [8] that in addition to pairing the adjacent BSs [16], a remarkable improvement in data rates can be achieved if the BSs are synchronized. In [17], BS cooperation approach is proposed to enhance the downlink sum capacity (throughput) with single-input single-output (SISO) systems employed in each cell, by implementing the DP coding (DPC). Also, these cooperative BS-assisted systems have been demonstrated to provide substantial gain in the form of system performance for a multi-cell MIMO system [12]. In [4,18], the performance of MUTP-aided multiuser MIMO systems has primarily been investigated in the context of single cell for DL and UL transmissions in flat-fading channels, respectively.

For cellular systems, two performance metrics namely average cell throughput and user throughput at the cell edges are vital. Improving these measures becomes indispensable in the context of next generation cellular networks. Average cell throughput can be improved by employing relatively simple methods (increasing transmission power), but improving the throughput of the users at cell edges is quite challenging. Furthermore, users at the cell edges experience strong CCI and any increase in the transmission power to improve average cell throughput further creates CCI for cell edge users. Besides this, frequency-selectivity of the channels will severely degrade the system performance resulting in an irreducible bit error rate, thus imposing a limit on the achievable data rates. Thus, improving cell edge throughput becomes imperative in such frequency-selective CCI environments, and that is why interference mitigation techniques have received wide spread attention among research communities in the context of next generation cellular standards.

Hence, in this correspondence, we will be investigating the performance of MUTP-aided MIMO systems in terms of achievable SER in such CCI limited environments with multi-cell cooperation (also called BS cooperation). Specifically, in this contribution we present the performance of joint VBLAST/STBC aided DL and STBC processing aided UL MIMO systems with MUTP in the context of multi-cell multiuser setting with BS cooperation over correlated and uncorrelated frequency-selective fading for three different delay spread distributions pertaining to LTE standard [19] and flat fading channels.

The rest of the article is organized as follows: Section 2 describes the system model of VBLAST/STBC-aided MIMO system with MUTP for DL and STBC-aided MIMO system with MUTP for UL communications. Section 3 elucidates the performance results of our analysis and in Section 4 conclusions are drawn.

Notations: The following notations are adopted for remaining of the article. All boldface capital letters represent a matrix while a lowercase boldface letter denotes a vector. (.)H denotes Hermitian transpose while (.)* refers to the complex conjugate. Additionally, (·;·) is used to denote row wise concatenation. (.)+ refers to the Moore-Penrose matrix (pseudo-inverse), while ε{·} gives the expectation of the argument. Trace{.} represents the trace of the argument, Q(.) specifies quantization and ∥.∥ denotes the norm operation.

2. System configuration

2.1 Downlink transmission

Let us consider an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M93','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M93">View MathML</a> cell downlink communication system supporting <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94">View MathML</a> users. Figure 1 elucidates a multi-cell MIMO DL communication system with MUTP. Here, the BS employs <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95">View MathML</a> transmit antennas and each of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94">View MathML</a> users' MS uses <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M96','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M96">View MathML</a> receive antennas. In multi-cell MIMO transmission, the users conflict CCI, as well as MSI and there will be <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M97','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M97">View MathML</a> interfering signals arriving at each of the mobile stations (MSs). Though the maximum-likelihood (ML) detector employed at the MS or at the BS offers optimum performance by mitigating the CCI, MUI, and MSI, it often imposes too much computational complexity. To reduce the complexity MUTP can be employed at the BSs [3,4] as well as at the MSs.

thumbnailFigure 1. Schematic illustrating a typical multi-cell downlink communication.

In DL transmission, we assume that the BS supports joint VBLAST/STBC processing architecture with MUTP based on SVD technique. The joint VBLAST/STBC technique can be described as follows:

Let <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M98','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M98">View MathML</a>, and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M99','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M99">View MathML</a> represent a group of the six symbols in the input data stream to be transmitted. Assuming <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M100','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M100">View MathML</a> and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M101','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M101">View MathML</a> and invoking joint VBLAST/STBC (STBC is based on Alamouti code [20]) processing, the received matrix after two symbol durations can be described as follows:

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M1">View MathML</a>

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M73','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M73">View MathML</a> is an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102">View MathML</a> component received matrix, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M2">View MathML</a> is an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103">View MathML</a> small-scale fading channel matrix, and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M74','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M74">View MathML</a> is an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M104','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M104">View MathML</a> symbol matrix. <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M75','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M75">View MathML</a> is the noise matrix, which is assumed to be Gaussian distributed with zero mean and covariance matrix given by <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M3">View MathML</a>. In this contribution, we evaluate the performance of MUTP-assisted VBLAST/STBC system in frequency-selective fading channels using LTE channel models for pedestrian (PED), vehicular (VEH), and typical urban (TU) propagation. The channel profiles are detailed in Table 1[19].

Table 1. Path delays and relative power levels

Using the parameters defined in Table 1, the channel impulse response from the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105">View MathML</a> transmit antenna to the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M106','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M106">View MathML</a> receive antenna can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M4">View MathML</a>

(1)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M5">View MathML</a> is a complex zero-mean Gaussian random process with variance <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M78','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M78">View MathML</a> and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M5">View MathML</a> is uncorrelated with other paths and channels. <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M107','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M107">View MathML</a> is the total number of paths between the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105">View MathML</a> transmit and the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M106','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M106">View MathML</a> receive antenna.

In the case of single cell, let <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M79','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M79">View MathML</a> be the signal transmitted to the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS which is given by

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M6">View MathML</a>

(2)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M80','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M80">View MathML</a> is an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M109','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M109">View MathML</a> component symbol matrix preprocessed before transmission by <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M110','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M110">View MathML</a> preprocessing matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M7">View MathML</a>[4], constituting the signal space component of the decomposed correlated channel matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8">View MathML</a>of size <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103">View MathML</a>, which can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M9">View MathML</a>

(3)

where

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M10">View MathML</a> denotes the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103">View MathML</a> uncorrelated fading co-efficient matrix and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M11">View MathML</a>, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M12">View MathML</a> are <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M111','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M111">View MathML</a> receive and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112">View MathML</a> transmit correlation matrices, respectively. <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M90','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M90">View MathML</a> denotes the large-scale fading co-efficient, that takes into account the effects of path loss and shadowing. Further, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M81','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M81">View MathML</a> is an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M111','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M111">View MathML</a> component diagonal matrix formulating the power normalization co-efficients for normalizing the transmit power associated with the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS. Here, exponential correlation model is considered as this model is reasonable in the case of uniform linear array [2]. Furthermore, in the case of multi-cell, let the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M113','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M113">View MathML</a> component DL symbol matrix transmitted to the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS after two symbol durations by all the BSs be denoted by <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M74','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M74">View MathML</a>. This is pre-multiplied by an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M114','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M114">View MathML</a> component preprocessing matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M13','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M13">View MathML</a> of all the users [4] formulated with the aid of BS cooperation, where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M14','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M14">View MathML</a> represents the signal space of the decomposed channel matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8">View MathML</a> of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user given by

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M15','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M15">View MathML</a>

(4)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M16','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M16">View MathML</a> denotes the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103">View MathML</a> correlated fading co-efficient matrix that connects the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M115','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M115">View MathML</a> BS and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS. Upon BS cooperation, the transmitted component symbol matrix to the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user will be as follows

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M17','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M17">View MathML</a>

(5)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M18','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M18">View MathML</a> constitutes the overall preprocessing matrix. <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M82','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M82">View MathML</a> denotes the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M113','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M113">View MathML</a> component transmitted symbol matrix, transmitted to the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS after two symbol durations. Here, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M83','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M83">View MathML</a> represents the power control coefficient matrix formulated for imposing the transmission power constraint. The received signal matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M84','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M84">View MathML</a> at the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M19','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M19">View MathML</a>

(6)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M85','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M85">View MathML</a> represents the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102">View MathML</a> noise matrix having zero mean and covariance matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M3">View MathML</a>.

Upon carrying out SVD on <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8">View MathML</a>, we arrive at

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M20','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M20">View MathML</a>

(7)

where

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M21','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M21">View MathML</a> unitary matrix,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M22','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M22">View MathML</a> unitary matrix,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M86','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M86">View MathML</a> diagonal matrix containing the non-zero eigenvalues of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23">View MathML</a>,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M24','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M24">View MathML</a> matrix, constituting the eigenvectors corresponding to the non-zero eigenvalues of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M25','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M25">View MathML</a>,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M26','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M26">View MathML</a> matrix, constituting the eigenvectors corresponding to the zero eigenvalues of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M25','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M25">View MathML</a>.

Substituting (7) into (6), the received DL signal <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M84','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M84">View MathML</a> of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M27','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M27">View MathML</a>

(8)

The BS transmitter preprocessing matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M18','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M18">View MathML</a> is designed so as to effectively mitigate CCI, but there exists MSI, and the post processing matrix that completely mitigates the MSI is formulated as [4]

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M28','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M28">View MathML</a>

(9)

Applying this postprocessing matrix to the received matrix yields

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M29','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M29">View MathML</a>

(10)

Substituting the value for <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30">View MathML</a> from (9), the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user's observation matrix can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M31','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M31">View MathML</a>

(11)

Thus the postprocessing matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30">View MathML</a> mitigates MSI.

In the context of multi-cell DL transmission, power constraints should be considered per BS basis [6] in contrast to single cell DL transmission. If the average transmit power of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M115','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M115">View MathML</a> BS is <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M116','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M116">View MathML</a>, then in order to satisfy the power constraint on per BS basis, we need to have <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M32','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M32">View MathML</a> Here, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M33','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M33">View MathML</a> formulates the preprocessing matrix for transmission from the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M115','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M115">View MathML</a> BS to all the MSs. The elements of the received matrix are combined to get the estimates of the transmitted symbols as given below

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M34','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M34">View MathML</a>

(12)

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M35','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M35">View MathML</a>, denotes the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105">View MathML</a> estimated symbol of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M36','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M36">View MathML</a>, designates the element in the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M105">View MathML</a> row and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M106','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M106">View MathML</a> column of the received matrix of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user. Collecting all the estimates of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user symbols, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M37','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M37">View MathML</a> can be given by

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M38','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M38">View MathML</a>

(13)

For BPSK modulation, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M39','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M39">View MathML</a> gives the detected symbols and, for QAM modulation <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M37','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M37">View MathML</a> for the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user is given by

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M40','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M40">View MathML</a>

(14)

Symbols are then detected by <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M39','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M39">View MathML</a>.

2.2 Uplink transmission

Figure 2 illustrates a multi-cell MIMO UL communication system with MUTP. Here, we assume that each of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94">View MathML</a> users' MS is equipped with <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95">View MathML</a> transmit antennas and the BS with <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M117','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M117">View MathML</a> receive antennas. Also, in the context of UL transmission, we assume that MS supports STBC processing [20]. Let <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M41','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M41">View MathML</a> denote the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95">View MathML</a> length data symbol vector of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user. Then, by invoking Alamouti code [20] the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M104','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M104">View MathML</a> component symbol matrix denoted by <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M42','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M42">View MathML</a> will be transmitted to the BS from the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS after two symbol durations. It is premultiplied with an <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112">View MathML</a> component unitary matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M43','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M43">View MathML</a> of the decomposed correlated channel matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8">View MathML</a>, which is expressed as

thumbnailFigure 2. Schematic illustrating a typical multi-cell uplink communication.

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M44','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M44">View MathML</a>

(15)

where

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M45','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M45">View MathML</a> denotes the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M103">View MathML</a> uncorrelated fading co-efficient matrix and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M11">View MathML</a>, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M12">View MathML</a> are <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M111','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M111">View MathML</a> receive and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112">View MathML</a> transmit correlation matrices, respectively. After transmitter preprocessing, the signal transmitted by the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS is given by

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M46','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M46">View MathML</a>

(16)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M47','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M47">View MathML</a> formulates the preprocessing matrix [18] for the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user. The <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M112">View MathML</a> component diagonal matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M81','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M81">View MathML</a> constitute the power control co-efficients employed for normalizing the transmission power associated with the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS.

The <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102">View MathML</a> component UL received matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M87','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M87">View MathML</a> at the desired BS can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M48','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M48">View MathML</a>

(17)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M75','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M75">View MathML</a> is <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M102">View MathML</a> noise matrix which is assumed to be zero mean with covariance matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M3">View MathML</a>. In this article, we assume that the number of receive antenna at the BS is greater than or equal to the total number of antennas employed by all the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94">View MathML</a> MSs, i.e., <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M118','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M118">View MathML</a>. Upon carrying out the SVD on <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M8">View MathML</a>, we arrive at

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M49','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M49">View MathML</a>

(18)

where

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M21','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M21">View MathML</a> unitary matrix,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M50','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M50">View MathML</a> unitary matrix,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M88','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M88">View MathML</a> diagonal matrix containing the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M95">View MathML</a> non-zero eigenvalues of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23">View MathML</a>,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M51','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M51">View MathML</a> matrix, denoting the eigenvectors corresponding to the non-zero eigenvalues of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23">View MathML</a>,

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M52','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M52">View MathML</a> matrix, denoting the eigenvectors corresponding to the zero eigenvalues of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M23">View MathML</a>.

Upon substituting (18) into (17), the received UL matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M87','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M87">View MathML</a> at the desired BS can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M53','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M53">View MathML</a>

(19)

Substituting for <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54">View MathML</a> and exploiting the property <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M55','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M55">View MathML</a>, the UL received signal matrix can be simplified as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M56','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M56">View MathML</a>

(20)

From the above expression, it can be discerned that the UL transmitter preprocessing matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54">View MathML</a> decouples each of the antenna specific transmitted data symbols of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> MS from those of its other antennas. With the aid of BS cooperation, now let us define

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M57','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M57">View MathML</a>

(21)

Using (21) in (20), the received UL matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M87','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M87">View MathML</a> can be expressed as

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M58','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M58">View MathML</a>

(22)

where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M74','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M74">View MathML</a> denotes the overall data of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94">View MathML</a> UL users given by <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M89','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M89">View MathML</a>. Although, the columns of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M59','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M59">View MathML</a> are orthogonal, suggesting that there is no inter antenna interference or MSI, the columns of <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M60','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M60">View MathML</a> corresponding to the different UL MSs are not orthogonal and hence there exists CCI. The postprocessing matrix that completely removes the CCI is formulated as [18]

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M61','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M61">View MathML</a>

(23)

Let <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M62','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M62">View MathML</a> denote the estimates of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M94">View MathML</a> UL users. Substituting (22) into <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M63','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M63">View MathML</a> we have

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M64','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M64">View MathML</a>

(24)

Substituting the value for <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30">View MathML</a> from (23), the overall data estimates of all the MSs can be simplified to

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M65','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M65">View MathML</a>

(25)

Thus the SVD-based matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M30">View MathML</a> removes CCI. To be specific, the estimates of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user's signal is given by

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M66','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M66">View MathML</a>

(26)

An important constraint for transmitter preprocessing in UL transmission is to maintain the transmit power of the <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M108">View MathML</a> user before and after preprocessing unaltered. Hence, in order to maintain a constant transmission power, <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54">View MathML</a> should be normalized to satisfy

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M67','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M67">View MathML</a>

(27)

Alternatively, we can normalize <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M54">View MathML</a> to satisfy

<a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M68','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M68">View MathML</a>

(28)

The normalization in (28) is based on the assumption <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M69','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M69">View MathML</a>.

3. Performance results

In this section, the simulation results for characterizing the achievable performance of MUTP-assisted MIMO system with joint VBLAST/STBC processing for DL transmission for a multi-cell scenario are presented. Also, the performance results of MUTP-assisted MIMO system with STBC processing for UL transmission are presented. In order to provide a generic framework to deal with MUTP in the context of multi-cell setting, whilst remaining simple enough for analysis and simulation, we assume a model which is characterized by an array of cells. Here, we have taken into account the interference from the first tier. Further, we assume universal frequency reuse. Also, as a first approximation, considering worst case scenario, we deem interference to be Gaussian and hence, interference can be treated as equivalent noise, and the signal-to-interference-plus-noise ratio (SINR) takes the same value as SNR [21]. Furthermore, we assume that all the BSs transmit at the same power. The channel models considered here are based on LTE specifications and the performance is assessed for both correlated and uncorrelated fading channels. Tables 1 and 2 summarize the channel models and simulation parameters, respectively. The transmitted signals from the BSs (DL) and MSs (UL) experience free-space path loss, and then undergo path loss according to a power law with path loss exponent 3.7. The multipath propagation is modeled as zero mean complex Gaussian random variable with variance 1/2 per dimension. The standard deviation of log-normal shadow fading is assumed to be 8 dB. The MSs are arbitrarily distributed following a uniform distribution. The modulation technique considered in this study is 64QAM. Further, for transmitter preprocessing to be enabled in the context of multi-cell DL scenario, perfect channel state information (CSI) is assumed to be present at the transmitter with the aid of BS cooperation. Besides, open-loop power control is employed.

Table 2. Simulation parameters

Figure 3 illustrates the performance of MUTP-assisted VBLAST/STBC system for extended pedestrian channel model based on LTE specifications for DL transmission. Here, comparisons have been provided for flat fading, uncorrelated frequency-selective, and correlated frequency-selective fading with transmitter preprocessing (TP). We have assumed correlation ρ = 0.7 and a Doppler shift of 5 Hz. For comparison, we have assumed uncorrelated frequency-selective fading without MUTP. Monte Carlo simulation trials were carried out so as to evaluate the performance of the system and also for each SNR value, 10,000 channel realizations were employed. It is observed that to achieve a SER of 10-1, a system without TP (zero forcing) over uncorrelated channel requires 25 dB SNR as against the scheme with TP, which requires less than 3 dB in uncorrelated frequency-selective channel.

thumbnailFigure 3. Symbol error rate performance of MUTP-assisted VBLAST/STBC system for flat fading, uncorrelated, and correlated frequency-selective fading (LTE Pedestrian channel model) and uncorrelated frequency-selective fading without MUTP with 64 QAM modulation (downlink communication).

Figures 4 and 5 elucidate the SER performance of MUTP-assisted MIMO system with VBLAST/STBC processing for typical urban and extended vehicular channel models based on LTE specifications for DL transmission. For typical urban, Doppler frequency of 70 Hz and for vehicular, 300 Hz is assumed with the MS moving at a speed of 40.8 and 162 km/h respectively. MIMO channel models are assumed to be of high correlation with ρ = 0.7. Our simulation study shows that the system employing TP results in better performance in terms of achievable SER compared to an uncorrelated system without TP. Also, in all the three types of delay spread distributions, system operating over uncorrelated frequency-selective channel with MUTP outperforms the system over correlated channel with MUTP. Furthermore, in the context of multi-cell MIMO, a system operating over correlated frequency-selective fading with MUTP outperforms a system operating over uncorrelated frequency-selective fading without MUTP by completely mitigating CCI and MSI.

thumbnailFigure 4. SER performance of MUTP-assisted VBLAST/STBC system for flat fading, uncorrelated, and correlated frequency-selective fading (LTE Typical Urban channel model) and uncorrelated frequency-selective fading without MUTP with 64 QAM modulation (downlink communication).

thumbnailFigure 5. SER performance of MUTP-assisted VBLAST/STBC system for flat fading, uncorrelated, and correlated frequency-selective fading (LTE Vehicular channel model) and uncorrelated frequency-selective fading without MUTP with 64 QAM modulation (downlink communication).

Figure 6 illustrates the performance of MUTP-assisted MIMO system with STBC support for extended pedestrian channel model based on LTE specifications for UL transmission. It is seen that to achieve a SER of 10-3, system operating over uncorrelated frequency-selective channel requires 5 dB less than the correlated frequency-selective fading channel.

thumbnailFigure 6. SER performance of MUTP-assisted STBC system for flat fading, uncorrelated, and correlated frequency-selective fading (LTE Pedestrian channel model) and uncorrelated frequency-selective fading without MUTP with 64 QAM modulation (uplink communication).

Figures 7 and 8 show the performance of MUTP-assisted MIMO system for typical urban and extended vehicular channel model for UL transmission. It is discerned from simulation results that for a target SER of 10-3, system over uncorrelated frequency-selective fading channel performs better than the system over correlated frequency-selective fading channel, requiring 5 dB lesser SNR. Furthermore, in the context of multi-cell MIMO systems, MUTP based on SVD perfectly eliminates CCI and MSI. Also, MUTP-aided system outperforms system without MUTP. In Figures 9 and 10, we plot the average SER versus SINR for DL and UL transmissions, respectively, assuming different interferer configurations. Here, the simulation results correspond to equal power interferers' scenario [21]. The plots illustrate the performance comparison of SVD-aided MUTP MIMO systems with THP, DPC, ZF, BD, and geometric mean decomposition for DL transmission and THP, ZF, and DPC for UL transmission in uncorrelated frequency-selective channels. It is observed that SVD-based MUTP outperforms other precoding techniques in terms of achievable SER. Further, it can be discerned that performance of the system degrades when equal CCI is considered in contrast to our initial assumption that interference is Gaussian. This can readily be noticed by comparing SVD-aided systems in Figures 5 and 9 for DL and Figures 8 and 10 for UL transmission in the context of uncorrelated vehicular channel model. Figure 11 illustrates the influence of equal CCI, dominant CCI, and dominant noise on the SER performance. For the case of dominant interferes, we assumed two interferers to be dominant and the rest with equal power. Simulation results show that the existence of highly dominant interferers causes degradation in the system performance compared to low power interferers (equal CCI case). This follows from the fact that a single dominant interferer can have more variations in terms of interference power and therefore, can impact further on the average achievable SER. Furthermore, it is seen that dominant noise results in worst case performance compared to equal and dominant CCI case in the context of MUTP-aided multi-cell MIMO systems.

thumbnailFigure 7. SER performance of MUTP-assisted STBC system for flat fading, uncorrelated, and correlated frequency-selective fading (LTE Typical Urban channel model) and uncorrelated frequency-selective fading without MUTP with 64 QAM modulation (uplink communication).

thumbnailFigure 8. SER performance of MUTP-assisted STBC system for flat fading, uncorrelated, and correlated frequency-selective fading (LTE Vehicular channel model) and uncorrelated frequency-selective fading without MUTP with 64 QAM modulation (uplink communication).

thumbnailFigure 9. Performance comparison of MUTP-assisted MIMO system (LTE Vehicular channel model) for downlink communication.

thumbnailFigure 10. Performance comparison of MUTP-assisted MIMO system (LTE Vehicular channel model) for uplink communication.

thumbnailFigure 11. Average SER versus SINR for different interferers' configurations as well as dominant noise configuration for SVD-aided MUTP MIMO system (LTE Vehicular channel model) for both DL and UL communications.

In Figure 12, in contrast to our initial assumption of perfect CSI (PCSI), we demonstrate the impact of imperfect CSI (ICSI) on the performance of MUTP-aided MIMO systems. The channel estimation employed in this study is based on the MIMO pilot-assisted symbol modulation [22]. It follows then the channel matrix <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M2">View MathML</a> can be expressed as <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M70','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M70">View MathML</a>, where <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M71','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M71">View MathML</a> is the predicted channel matrix with zero mean and variance <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M91','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M91">View MathML</a> and <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M72','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M72">View MathML</a> is the CSI error matrix with zero mean and mean square error <a onClick="popup('http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M92','MathML',630,470);return false;" target="_blank" href="http://jwcn.eurasipjournals.com/content/2012/1/194/mathml/M92">View MathML</a>. As it can be seen from the plot that to achieve a target error rate of 10-4, PCSI results in SINR gains of 6 and 7 dB for DL and UL transmissions, respectively, compared to ICSI. This is due to the fact that ICSI results in perturbation in the eigenvalues contributing to imperfect removal of CCI and MSI in the context of both DL and UL transmissions. Figure 13 shows the impact of power control (PC) on the MUTP-aided MIMO system for both the DL and UL transmissions. We can see from the figure that SINR gains of approximately 3 and 5 dB are achieved for a target SER of 10-3 for DL and UL, respectively, when power control is invoked.

thumbnailFigure 12. Average SER versus SINR performance of SVD-aided MUTP MIMO system under perfect CSI (PCSI) and imperfect CSI (ICSI) (LTE Vehicular channel model) for both DL and UL communications.

thumbnailFigure 13. Average SER versus SINR performance of SVD-aided MUTP MIMO system with and without PC under perfect CSI (PCSI) (LTE Vehicular channel model) for both DL and UL communications.

4. Conclusion

In this article, we have investigated the performance of multi-cell MIMO system with joint VBLAST/STBC processing for DL transmission and STBC processing for UL transmission aided by transmitter preprocessing. We have drawn comparisons between systems with and without TP and, also with other widely known precoding techniques. It is discerned from the analysis that the system with TP can significantly enhance the achievable SER performance thus allowing support for more users, and resulting in higher capacity than conventional system employing a linear ZF detector. Also, this study has confirmed that the presence of dominant interferers can degrade the system performance. Nevertheless, the performance gain in interference-limited environments is better than in the noise-limited scenario due to the presence of dominant noise in the latter case. Moreover, it is inferred that ICSI can considerably degrade the system performance due to eigenvalue perturbation. In the context of multi-cell MIMO systems, it is further observed that SVD-aided MUTP outperforms other precoding techniques by mitigating MSI and CCI. Throughout this article, we have made an idealistic assumption of perfect synchronization among the BSs. Our future study will focus on the assessment of the system performance under imperfect synchronization between BSs and network latency.

Competing interests

The authors declare that they have no competing interests.

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