Abstract
This article proposes the use of system valuebased optimization with a symbollevel minimum mean square error equalizer and a successive interference cancellation which achieves a system value upper bound (UB) close to the Gaussian UB for the highspeed downlink packet access system without affecting any significant computational cost. It is shown that by removing multicode channels with low gains, the available energy is more efficiently used, and a higher system throughput is observed close to the system value UB. The performance of this developed method will be comparable to the orthogonal frequency division multiplexingbased longterm evolution scheme, without the need to build any additional infrastructure. Hence, reduce the cost of the system to both operators and consumers without sacrificing quality.
Keywords:
HSDPA MIMO; Successive interference cancellation; Minimum mean square error equalization; Resource allocation1 Introduction
Wireless communication systems known as multipleinput multipleoutput (MIMO) systems, which have multiple transmit and receive antennas, can be used to exploit the diversity and the multiplexing gains of wireless channels to increase their spectral efficiency. As an extension to Shannon’s capacity [1], the MIMO channel capacity bound was obtained by Foschini and Gans [2] and Telatar [3] independently. Assuming that perfect channel state information (CSI) is available at the transmitter, the MIMO system capacity upper bound (UB) can be obtained using the eigen modes of the MIMO channel matrix by performing waterfilling (WF) over the spatial subchannels. An important MIMO system design consideration is to operate the system close to its capacity UB. The objective of this article is to show how the highspeed downlink packet access (HSDPA) MIMO system can operate close to its capacity UB.
The third generation partnership project (3GPP) has developed the HSDPA system, given in the Release 5 specification [4] of the Universal Mobile Telecommunications System, as a multicode wideband code division multiple access (CDMA) system. To further increase the data rate, the HSDPA system introduced new features [5] such as adaptive modulation and coding and fast scheduling. The standardization of the Dual Stream Transmit Diversity (DTxAA) HSDPA MIMO system for a singleuser in 3GPP Release 7 [6] further improved the downlink throughput without requiring a new spectrum or any additional bandwidth.
In [7], measurements are carried out to evaluate the performance of the standardized 3G HSDPA MIMO system with a CDMA transmission. It is shown that the current systems are utilizing only about 40% of the available downlink capacity. The capacity curve is approximately 10 dB away from the capacity UB [8] at high signal to noise ratios. There is an opportunity to improve the HSDPA system capacity, when operating over frequency selective channels, by enhancing the HSDPA MIMO standard of the equal energy allocation scheme as is specified in [6].
The frequency selectivity problem, which causes a large drop in throughput for the HSDPA due the intersymbol interference (ISI) problem, is not a major problem for the orthogonal frequency division multiplexing (OFDM)based systems [longterm evolution (LTE) advanced and WiMAX] as they use a guard period to deal with the ISI problem. If the throughput reduction problem is not solved in the HSDPA system, the OFDMbased systems will have the upper hand over the HSDPA system in urban environments. The HSDPA singleinput singleoutput (SISO) system has been the main focus of the study in [9], which provides tools to combat frequency selectivity, when bringing the HSDPA SISO performance close to the OFDMbased systems. Should the ISI problem be solved for the HSDPA MIMObased systems, the current HSDPA MIMO system would achieve throughputs close to the LTE advanced without the need to change the whole infrastructure by using throughput optimization methods. This is the focus of the current investigation.
2 Current investigation and related work
The downlink throughput optimization for the HSDPA multicode CDMA system [10] considers the signature sequence and the power allocation for downlink users. 3GPP standardized an approach to spread the transmission symbols by using a given fixed set size of orthogonal variable spreading factor (OVSF) signature sequences. A MIMO system requires a signature sequence set size higher than the given single set of OVSF signature sequences available for a SISO system. 3GPP standardized a method to increase the OVSF set size by multiplying the given set with precoding weights and then concatenating the weighted sets of the spreading sequences. Each concatenated spreading sequence is used to transmit one symbol and is orthogonal to the remaining set of spreading sequences available at the transmitter for the transmission of other symbols. However, the spreading sequences’ orthogonality is lost at the receiving end after transmission over frequency selective multipath channels. In [11,12], it is proposed that a linear minimum mean square error (MMSE) equalizer followed by a despreader could be used to restore partial orthogonality between the receiver despreading and the matched filter sequences in the detection process after receiving signals transmitted over a multipath channel. Recent developments have shown that linear MMSE equalizers suffer from a selfinterference (SI) problem caused by ISI and multiple access interference, when operating over multipath channels.
SI reduces the system throughput performance, but good receiver design will minimize the degradation caused by the SI. When encountering SI various versions of interference cancellers could be used in conjunction with nonoptimal receivers to improve the system throughput for the HSDPA system over frequency selective parallel channels. In [13], it is shown that a successive interference cancellation (SIC) scheme performs better than a parallel interference cancellation scheme, when the signaltonoise ratio (SNR) differs over each frequency selective parallel channel. The works reported in [1416] focus on the use of linear MMSE equalizers and SIC in reduction of the overall SI.
A twostage SIC detection scheme with transmitter power optimization is examined in [16,17] to improve the throughput performance for multicode downlink transmission. In [18], the power at the transmitter and a twostage SIC receiver are jointly and iteratively optimized for a multicode MIMO system. However, at each iteration of the SIC, the equalizer coefficient and the power allocation calculations require an inversion of a covariance matrix for the received signal. The dimension of the covariance matrix is usually large and, as such, the iterative power allocation, the linear MMSE equalizer and the SIC implementations at the receiver become computationally expensive.
The focus of the article is on an HSDPA MIMObased radio downlink system, which has a number of parallel SISO or MIMO frequency selective channels over which data are transmitted. The data are represented by a number of data symbols, which are spread by a group of spreading sequences when using the HSDPA system either with or without a SIC scheme. A set of signature sequences generated from the OVSF codes with precoding, as specified in the 3GPP Release 7, will be considered. A receiver with a symbollevel linear MMSE equalizer will be examined to jointly optimize the transmission energy allocation and the receiver for a single user system either with or without a SIC.
At the receiver each spreading sequence
Figure 1. System block diagram for the nonSIC based MIMO HSDPA system.
Figure 2. Receiver system block diagram for SIC based detection. The block diagram for the SIC based HSDPA MIMO system is given.
The objective of the total transmission rate maximization for a given total number of spreading sequences will be to bring the downlink throughput close to the system value UB. This will be achieved by retaining the spreading sequences with the highest system values for a given total received SNR corresponding to a given total transmission energy E_{T}. A given number of sequences will be ordered so that the corresponding system values are used at the transmitter in ascending order. The optimum number K^{∗} of signature sequences will be determined to select the first K^{∗}ordered signature sequences, which maximize the transmission throughput. The receivers will operate in a sequence, where the detection is ordered in the descending order of the corresponding system values for the SICbased systems.
As shown in [19], the WF optimization is generally used for parallel channels with different subchannel gains to provide optimum subchannel selection, energy distribution, and also channel ordering. The iterative WF sumcapacity optimization is extensively examined in [2023] and is proven to converge to the sum capacity UB of the multipleaccess channel [20] to provide an UB for nondiscrete rates. Other subchannel removal methods have been studied in [2426] to determine the number of active data streams. In [24], the eigen decomposition of the covariance matrix is used to isolate the “bad” data streams so that the sum MSE is minimized. In [25], it is suggested that low signaltointerference and noise ratio (SINR) streams will be switched off to focus the available power on the remaining streams during the iterative power allocation process. In [26], the removal of subchannels is proposed to improve the capacity when the rounding of the discrete rate does not improve the system throughput. The WF and channel removal schemes do not use the system value concept for signature sequence selection nor use rate adjustment to maximize the total throughput.
In this article, three bit rate adjustment methods will be considered with the appropriate energy allocation schemes. These methods will be applicable to both SIC and nonSICbased receivers, when using discrete and nondiscrete rates. Initially, an iterative WF algorithm will be proposed with a subchannel removal for the selection of signature sequences. The system values will be used to maximize the throughput for nondiscrete rate allocation by accounting for the channel SINRs corresponding to the received signature sequences instead of using only the channel gains to find the water levels. When using discrete rates the signature sequence selection scheme will be further extended to optimize the total rate for the HSDPA system downlink. The system values will be used to select an optimum number of spreading signature sequences from a given total number of sequences without any prior energy allocation. The chosen optimum number of sequences will be loaded with discrete rates using both the equal SINR allocation methods proposed in this article and the equal energy allocation schemes as specified in the current HSDPA standard. The equal SINR and energy loading schemes will use the mean and the minimum of system values for a given total energy to transmit the symbols at the required discrete rates. These three methods will be named as the iterative WFbased continuous bit loading method, the mean system valuebased discrete bit loading method, and the minimum system valuebased discrete bit loading method.
The mean and minimum system valuebased methods will require different and equal transmission energy allocations, respectively. The iterative energy allocation methods will be described for the mean system valuebased discrete bit loading systems.
The link throughput improvements for these three methods will be described, when considering the receiver design, power control, and signature sequence selection algorithms. A complexity reduction method will be presented for covariance matrix inversions. The results show that the HSDPA MIMO system, using the optimization methods proposed in this article, achieve a system throughput close to the system value capacity UB for the frequency selective channels. The results are then comparable with the LTE system, without incurring the cost of building new infrastructures.
In Section 3, two HSDPA MIMO system models will be described for receivers with the nonSIC and the SICbased MMSE despreading units. In Section 4, the system value formulation will be presented and the MMSE filter coefficient calculations will be given. The system value UB concept for both the nonSIC and the SICbased receivers will be presented in Section 5. The formulation of a simplified iterative covariance matrix for use in the design of the SICbased receivers with MMSE equalizers will be described in Appendix Appendix 2 to support the material presented in Section 5. The system valuebased sum capacity/throughput maximization methods for optimum signature sequence selection, energy allocation, and rate maximization methods will be described in Section 6. These schemes will be based on the iterative WF and the mean and the minimum system value optimization methods. Finally, the results will be described in Section 7 before the conclusions are given in Section 8.
3 System model
3.1 Notation
a is a scalar,
3.2 Transmitter and a nonSICBased receiver model
The HSDPA MIMO system model used in the following sections will be briefly described
in this section for both the nonSIC and the SICbased receivers. Initially, a nonSICbased
multicode CDMA MIMO downlink transmission system will be considered with N_{T} transmit antennas and N_{R} receive antennas with their respective indices represented by N_{T} and N_{R}. Given the spreading factor N of the system, the maximum number K of spreading sequences satisfies the relationship K≤ min(N_{T},N_{R})N where each spreading sequence index is represented by k. When selecting the optimum number K^{∗} of spreading sequences, weak channels corresponding to a specific set of signature
sequences will be excluded to maximize the total rate. The system under consideration
will operate with the selected optimum number K^{∗} of spreading sequences. Each spreading sequence will transmit a symbol operating
at a discrete rate chosen from a set of rates according to the CSI updated at regular
transmission time intervals (TTIs). In the system model, each parallel binary bit
packet
A nonSICbased system model is shown in Figure 1. In the CDMA system, the number of symbols transmitted per packet is given by
Each spreading sequence will have an energy allocated, where the assigned energies
are stored in a K^{∗}×K^{∗} dimensional amplitude matrix
where
Assuming the clocks at the transmitter and the receiver are fully synchronized, the signals arriving at the receive antennas will be firstly down converted to the baseband before sampling at every T_{c} at the output of the receiver chip match filter.
The receiver matched filtered signal vector
The vector
At the output of each receiver, the mean square error (MSE) between the transmitted
symbol y_{k}(ρ) and the estimated symbol
3.3 The SICbased receiver model
Figure 2 illustrates the system model for a SICbased receiver, which collects the received
signals
At each kth channel, the estimated symbol vector
4 System value and MMSE despreading filter coefficient formulations
In this section, the system values and the corresponding MMSE despreading filter
coefficients are expressed in terms of the received signal vector
4.1 System values for a nonSICbased receiver
The received signal vector
and the received signal matrix is given by
The channel convolution matrix between the pair of antennas
The spatiotemporal MIMO channel matrix for the previous symbol block and the next symbol block are given as
where J is a vector shifting matrix. The notation J_{N+L−1} is the shift matrix of dimension (N+L−1)×(N+L−1) defined as
The N_{R}(N+L−1)×K^{∗}dimensional receiver matched filter signature sequence matrix Q is calculated as follows:
The system value for the spread spectrum system based on a receiver without the SIC scheme is given by
where
The normalized MMSE despreading coefficients
These coefficients are then stored in a matrix
4.2 System values and MMSE despreading filter coefficients for a SICbased receiver
Similar to the received signal vector
where
where
After all iterations k=1,…,K^{∗} have been completed the covariance matrix given in (30) is set to be
When calculating the system values for the SIC scheme, each system value λ_{k} in (11) for k=1,…,K^{∗} involves one matrix inversion
The inverse matrices
using the steps in (35) to (38) given in Appendix Appendix 2. Therefore, γ_{k} can be calculated when
The MMSE linear equalizer despreading filter coefficients
for k=1,…,K^{∗}.
5 Sum capacity optimization using system values
The main focus of this article is to find the optimum number K^{∗} of spreading sequences, which maximizes the total rate, where K^{∗} is a subset of the total number K of spreading sequences used for transmission. The total rate
where λ is the Lagrangian multiplier. The minimization of the total MSE using the
above equation provides solutions for E_{k} and the Lagrangian multiplier λ, subject to the energy constraint
The mean system value λ_{mean} is calculated by allocating energies equally such that
The total system capacities for the MMSE receivers for both the SIC and the nonSICbased receivers are then given as
where Γ is the gap value. To relate the system values to discrete bit rate optimization,
one can use the discrete bit rate and its SINR relationship
and the corresponding target system value
The next section will provide a detailed description of the system value based throughput optimization methods for both the nonSIC and the SICbased spread spectrum MIMO systems.
6 System valuebased discrete and WF algorithmbased nondiscrete bit loading
In this section, an iterative WF algorithm and two discrete bit loading algorithms will be presented using the system value approach. These methods operate with a given total energy E_{T} when implemented with or without the proposed SIC receiver. First, the iterative WF algorithms will be presented for continuous bit loading. Two iterative discrete bit loading methods will then be proposed to maximize the total rate without the need for any prior energy allocation. These discrete bit loading methods maximize the total rate by jointly allocating the discrete rate and then selecting the optimum number K^{∗} of ordered spreading sequences. The first discrete bit loading algorithm will use the mean system value λ_{mean} to determine the optimum number K^{∗} of spreading sequences and to select the sequences prior to allocating the energy for each sequence. The second discrete bit loading method will use the minimum system value λ_{min} to select the optimum number of sequences.
The system values will be ordered in an ascending order for all combinations of K_{opt}=K,…,1 for both discrete bit loading methods prior to selecting the optimum number of signature sequences. The temporary number K_{opt} of optimum spreading sequences is used as an initial value for each loop in an iterative sequence number optimization process.
For the discrete bit loading methods with λ_{mean} and λ_{min}, margin adaptive (MA) loading (equal rate) algorithms will be considered initially
so that all spreading sequences have the same rate
6.1 Iterative WFbased continuous bit loading
The iterative WF was originally developed to remove subchannels, which contain negative
energies, and to maximize the total rate. This section describes the iterative WF
optimization, which finds the optimum subchannels
The iterative WF algorithm initializes K_{opt}=K and the procedure is summarized as follows:
1. Initialize the loop counter as I=1. The number of energies E_{k} is K_{opt} and vectors
2. Perform energy allocation:
(a) Calculate the channel SINR per energy unit vector
(b) Determine the WF constant
3. Perform signature sequence reordering procedure:
(a) Find the term c_{k}, the indices of the kth smallest element of
(b) Reorder vectors
4. Carry out the channel removal process:If E_{1}< 0, remove this channel by setting K_{opt}=K_{opt}−1. Set
6.2 System valuebased signature sequence ordering for discrete loading
This section will describe the use of system values for ordering the signature sequences to maximize the system capacity by determining and selecting the optimum number of signature sequences for receivers with and without the SIC scheme. The signature sequence ordering process starts with by setting K_{opt}=K and continues by iteratively adjusting K_{opt}=K_{opt}−1 until K_{opt}=1 is reached. In each iteration, the system values are calculated, then the signature sequences (or coded channels) are ordered, and the signature sequence containing the smallest system value is removed. This generates a new set of selected and ordered signature sequences for each K_{opt}th iteration.
By allocating energies equally to all selected spreading sequences k=1,…,K_{opt} for that iteration, the system values are obtained from (9) or (11) for the nonSIC
and SIC cases, respectively. These system values are stored in a K_{opt} length vector
The system values given in
The next step is to find the K_{opt}length vector
Defining Q_{orig},Q_{orig1}, and Q_{orig2} as the original unmodified receiver signature sequence matrices of Q,Q_{1}, and Q_{2} with its order is equivalent to S, reordering procedure is carried out by setting
The procedure can be summarized as below.
1. Find all system values corresponding to each K_{opt} from K_{opt}=K to K_{opt}= 1 by using the following steps.
(a) Allocate energy equally for each signature sequence such that
(b) Find λ_{k} for k=1,…,K_{opt} using (9) and C from (30) for nonSIC, or λ_{k} from (11) and C_{k} from (12) for SIC. Store
(c) Store the minimum system value
2. Reorder the signature sequences and remove the signature sequence with the minimum λ_{k} for each K_{opt} iteration:
(a) Find the indices of the kth smallest elements for k=1,…,K_{opt} of
(b) Store the system values in
(c) Find the vector
(d) Use a_{k} to reorder
(e) If K_{opt}>1, set K_{opt}=K_{opt}−1. Set
6.3 Mean system valuebased discrete bit loading algorithm
To achieve the same SINR distribution at the output of each despreading unit so that
a higher b_{p} is selected for equal rate loading, transmission energies need to be adjusted to
achieve a target (fixed) SINR at each receiver. The discrete transmission rate will
be identified using the mean of the system value λ_{mean}. This method will operate with an energy constraint
With the relationship of the target system value λ^{∗} and the bit rates b_{p} in (19), a set of target system values stored in the Plength vector
1. For the set of bit rates
2. Find
3. Store the total rate
4. Select the optimum signature sequences satisfying
5. Construct the signature sequence matrix
The TG optimization can be used to further maximize the total rate by loading m channels with b_{p+1} so that the total rate becomes
6.3.1 Energy allocation for nonSIC
This section describes the energy allocation schemes for the mean system valuebased
discrete bit loading allocation for both the nonSIC receiver and the SIC receiver
with equal rate or TG allocation. When allocating equal rate, the bit rates of each
channel are equal, i.e.,
With K^{∗},
where i is the iteration number. The term
6.3.2 Energy allocation for SIC
As the iterative calculation of energy E_{k,i} depends on
The energies for the SICbased receiver can be iteratively calculated from E_{1} to
By using (33), the energy calculation given in (23) can be simplified to
where the weighting factors ξ, ξ_{1}, ξ_{2}, ξ_{3}, ξ_{4,}ξ_{5}, and ξ_{6} are constructed from
6.4 Minimum system valuebased discrete bit loading algorithm
An equal energy loading method is adopted for the current HSDPA standards to load
a discrete rate to each spreading sequence. Equal energy allocation produces varying
SINRs at the receivers, but makes it simpler to allocate energies than the equal SINR
loading scheme. As the channel with the minimum SINR is chosen as the target SINR
to guarantee the quality of the service, this will also be referred to as the minimum
system valuebased discrete bit loading method. This section will describe how to
select the optimum number and the corresponding signature sequences to maximize the
total rate for the HSDPA downlink. For the minimum system valuebased discrete bit
loading, the transmission energies are allocated equally
1. For the set of bit rates
2. Find
3. Store the total rate
4. Select the optimum number of signature sequences by using
5. Construct the signature sequence matrix
Again, a TG allocation can be performed to further increase the total rate. For the
equal energy allocation, the channels that have system values
The next section will provide the results obtained from the simulations and the discussions about the performance of the different loading algorithms.
7 Results
Two separate experimental setup systems were developed using the Matlab and the National
Instruments (NI) LabVIEW platforms with the parameters as listed in Table 1. The proposed system value optimization methods both with and without the SIC implementation
were tested using the Matlab and LabVIEW simulation packages with the parameters:
a spreading factor of N=16, the full number of spreading sequences K_{f}=2N, an additive white noise variance of σ^{2}=0.02, and a gap value of Γ=0 dB. A set of discrete rates
Table 1. System parameters used for experimental set up
The objective of using the two experimental platforms is to cross check the system performance obtained from the Matlab simulation environment and the LabVIEW environment. A realtime channel emulator was implemented by modifying the National Instruments FPGA channel emulation software. This emulator is fed with the vectors containing the channel impulse response samples which are externally generated from power delay profiles (PDP) as specified by the standardization organizations such as ITU and 3GPP. Two industry standard profiles, known as the pedestrians A and B PDP, shown in Tables 2 and 3, were adopted in this article as specified [29] by the ITU organization.
The pedestrians A and B PDP correspond to the channel impulse responses taken at nonregular intervals with a resolution of 10 ns. The PDP given in the ITU specification as shown in Tables 2 and 3 can be written as
where P_{i} is the linear power (not the logarithmic scale) at delay τ_{i}. This PDP is sampled with a sampling rate of
where
The pedestrians A and B channels shown in Tables 2 and 3 are resampled at the chip period intervals as shown in Table 4. After sampling, power is normalized so that the PDP has a unity power gain. This
produces the normalized square root PDP given in a vector form as
Table 4. Pedestrians A and B square root PDP sampled at chip period intervals of T_{c }= 260 ns
Two PDP sampled at chip period intervals for the pedestrians A and B channels were
produced as:
Each entry in columns 2 and 3 of Table 4 corresponds to the nonzero squareroot PDP coefficient for the pedestrian channel
impulse response vectors
and then the response is normalized using
Table 5. Six MIMO channel impulse responses for pedestrian A for PDP
Table 6. Three MIMO channel impulse responses produced using pedestrian B PDP
Results were produced for the throughput UBs and different optimization strategies
for discrete rates in terms of system throughput in bits per symbol against the total
SNR per symbol period per receiver antenna for 2×2 MIMO. The total received SNR is
expressed in dB by using
For the UB throughput examination, the system value and the iterative WF UBs were simulated using the methods described in Sections 5 and 6.1, respectively. The corresponding curves for the water filling and the system value UBs both with and without the SIC schemes were labeled using the labels SIC WF UB, SIC SV UB, WF UB, and SV UB. Figure 3 shows the results for the WF UBs and system value UBs for both the nonSIC and the SIC schemes for the pedestrian A channel. The proposed system value UB achieves the same system capacity as the iterative WF for the systems with and without SIC. However, the system value UB is a good alternative to the WF UB due to its simplicity and its shorter processing time for calculating the system capacity. In the same figure, it is shown that the SIC UB achieves a much higher sum capacity especially at a high input SNR, where the total available energy is greater, and the energy per channel is higher. Thus, a higher interference is introduced to other parallel channels above a given total SNR and the system capacity saturates at an asymptotic value. To improve the sum capacity the SICbased receiver cancels the interference corresponding to the detected symbols, starting from those which have the highest system value. As the SIC UB achieves a much higher sum capacity than the nonSIC system, it will be used as the ultimate UB, when comparing the performance and improvements obtained through different optimization strategies for the rest of this section.
Figure 3. The system value UBs for the Pedestrian A channels. The figure shows the results for the system value UB and WF UBs for both non SIC and SIC schemes when operating the Pedestrian A channel.
Discrete bit rate allocation methods based on the use of the mean and the minimum system values for the equal energy and SNR cases were simulated as described in Section 6. The corresponding curves in various figures have been labeled using SIC TG ES, SIC TG EE, TG ES, and TG EE for the systems with and without SIC. The term ES refers to the equal SNR loading case and the term EE refers to the equal energy loading case. These labels were appended with either FULL or OPT for the configurations corresponding to the systems with the full and optimum number of spreading sequences. The signature sequence ordering for a given set of total receiver SNRs was implemented using the algorithm described in Section 6.2. The optimum number of spreading sequences and also the data rates to be transmitted for the mean and minimum system valuebased algorithms were calculated using the methods described in Sections 6.3 and 6.4, respectively.
The mean system valuebased rate allocation requires iterative energy calculations,
which were produced using the methods described for the nonSIC and the SICbased
systems, respectively, in Sections 6.3.1 and 6.3.2. Iterative energy allocation methods
were used to achieve equal SINR levels at the output of the despreading units. For
the nonSIC receiver with the equal SNR (ES)based transmission energy allocation,
the iterative power allocation stops, either when the sum difference between the current
energy and the previous energy in the energy iteration loop is less than 1% of the
total energy, i.e.,
The processes described above were repeated for various total signal to noise ratios at the output of the despreading units for channels with pedestrians A and B channel PDP.
In Figure 4, the results are shown for the twogroup equal SINR allocation using an optimum subchannel selection and SIC optimization strategies, when transmitting spread signals over pedestrian A channel. The improved system for the equal SINR allocation with SIC achieves system throughputs corresponding to the curves SIC TG ES OPT, SIC TG ES FULL, and these achieved throughputs are very close to the SIC UB. It is not necessary for the SICbased receiver to determine the optimum number of spreading sequences, when allocating equal SINR as the SIC scheme reduces these interferences. The SIC TG ES OPT scheme provides a 3dB improvement over the transmission system with the TG ES FULL strategy. The TG ES OPT scheme, on the other hand, provides a 1.5dB enhancement over the TG ES FULL scheme, when the total SNR is 35 dB.
Figure 4. The two group equal SINR throughput results for SIC and optimum signature sequence selection for the Pedestrian A channels. Results for twogroup equal SINR allocation with the use of optimum subchannels selection and SIC optimization strategies transmitted over the pedestrian A channel are shown.
Figure 5 shows the pedestrian A results for a system with the optimum number of ordered spreading sequences, the SIC receiver and the discrete bit loading method based on minimum system value. It is shown that the SIC TG EE OPT scheme has a 4.5dB improvement over the TG EE FULLbased system before the system throughput saturates at the total SNR value of 35 dB. The use of an optimum number of ordered signature sequences at the total SNR of 35 dB results in the TG EE OPT scheme having a 2.5dB improvement over the TG EE FULL scheme. The performance of the receiver with the SIC TG EE FULL scheme is enhanced by 3 dB over the TG EE FULL scheme using the full number of spreading sequences. It is observed that the system with the TG equal energy (EE) allocation, SIC and the optimum number of spreading sequences approaches the nonSIC system value UB. It is further noted that at the total SNR value of 35dB a 3dB difference is observed compared with the SIC UB before the system throughput diverges.
Figure 5. The minimum system value based discrete bit loading system throughput versus total SNR for the Pedestrian A channels. The optimization strategies using optimum subchannels selection and SIC for the TG with minimum system value loading are shown.
Figure 6 shows the simulation results corresponding to data transmitted over the pedestrian B channel. The system throughput saturates for the TG ES FULL scheme at a lower total SNR (at 30 dB) compared to the pedestrian A channel. At the total discrete data rate of 100 bps, the SIC TG ES OPT provides 7 and 4 dB improvements, respectively, over the systems with TG ES FULL and TG ES OPT schemes. At the total discrete rate of 120 bps, more than 10dB improvement is observed when using the SIC TG EE OPT scheme with the optimum number of spreading sequences over the TG EE FULL scheme. An 8dB improvement is achieved by using the optimum number of ordered spreading sequences. Around the total SNR value of 30 dB the SIC TG EE OPT receiver with the optimum number of channels produces a 3dB improvement over the TG EE OPT scheme without the SIC receiver. For the pedestrian B channel, the SIC TG EE OPT scheme for the TG discrete bit loading method produces a throughput, which exceeds the throughput of the TG method TG ES OPT with the optimum number of spreading sequences. The collaborative use of the SIC scheme with the optimum number of signature sequence selection scheme achieves a system throughput close to the system value UB.
Figure 6. Total throughput versus total received SNR results for the pedestrian B channels when using SIC based receivers and optimum signature selection scheme. Results showing greater improvements when using SIC based receivers and optimum subchannels selection and when operating over the pedestrian B channel.
The results extracted from Figures 3, 4, 5, and 6 are tabulated for the pedestrians A and B channels as shown in Tables 7 and 8, respectively. The entries in Tables 7 and 8 express the SNRs for specific data rates together with the total discrete rates at specific signal to noise ratios. The SIC scheme provides higher throughputs for both pedestrians A and B channels at an SNR of 35 dB. Specific entries as shown in Table 9 are extracted from Tables 7 and 8 for achievable data rates at the SNR of 35 dB for pedestrians A and B channels. The performances for all three SIC TG ES OPT, SIC TG EE OPT, and SIC TG EE FULL schemes for the pedestrian A channel are very close to each other. The TG EE FULL scheme achieves 29.7% of the SIC TG ES OPT performance and 37.4% of the SIC TG EE OPT performance for pedestrian B channel. On the other hand, the corresponding figures for the TG EE FULL scheme is 82% of the SIC TG ES performance and 85.8% of the SIC TG EE OPT performance for pedestrian A channel (Table 9).
Table 7. Pedestrian A experimental results
Table 8. Pedestrian B experimental results
Table 9. Comparing of HSDPA system performance over pedestrians A and B channels at 35dB SNR
The reason the TG EE FULL scheme achieves 29.7 and 82% of the SIC TG ES performances for pedestrians A and B channels, respectively, is that the PDP lengths or delay spreads for the pedestrians A and B channels are 3 and 15 chip periods, respectively. The HSDPA system, which uses the equal energy discrete bit loading method without the optimum number of spreading sequences suffers from a reduction in the total throughput compared with an HSDPA MIMO system with the optimum number of ordered spreading sequences, when encountering multipath channels with PDP lengths approaching the processing gain, N, of the system. The proposed method of finding the optimum number of ordered signature sequences improves the performance of equal energy loading systems.
8 Conclusion
This article has developed and proposed algorithms, which maximize the system throughput, while reducing the computational cost. Complexity reduced system value UBs are proposed, which achieve the same sum capacity as iterative WF. In terms of complexity reduction, the use of system values proposed in this article finds the rates and provides optimum subchannels selection before power allocation is performed. This eliminates the requirement to undertake iterative searches for the optimum bit rates combined with computationally intensive iterative power allocation for the equal SNR (ES) allocation. The optimum number of signature sequences can produce the maximum system throughput close the system value capacity UB. The proposed SIC increases the system throughput, but also simplifies the covariance matrix inversion process required for both the EE and the ES allocations. The computational reduction is especially significant for the ES allocation, where iterative energy allocation is required.
It is shown that a system throughput improvement is achieved close to the SIC UB for both the pedestrians A and B channels by using the SICbased receivers for the ES allocation. The SIC schemes with the full and optimum number of channels produce identical total rate results, when plotted against the total signal to noise ratio. It was observed that the signature sequence ordering was not essential for the equal SNR discrete bit loading algorithm. The identification of the optimum number of signature sequences for the equal energy allocation scheme significantly improves the total system throughput. The resultant scheme with the equal energy allocation, when using an SICbased receiver with the ordered optimum number of signature sequences achieves a system throughput close to the nonSIC UB.
The mobile radio channels with a longer channel impulse response length, which are measured in terms of the number of chip period intervals, have severe sum capacity throughput degradations compared with the system value UBs for equal energy loading HSDPA MIMO systems without the optimum number of ordered spreading sequences. The influence of the Doppler frequency on the performance of the proposed HSDPA system is currently under investigation and will be reported in future publications.
The results presented in this article confirm that the proposed optimum signature sequence selection scheme for the SIC receiver provides a significant performance improvement for the HSDPA system. As it is now possible to obtain system throughput near the UB. The proposed schemes with HSDPA will achieve results comparable to the LTE, without incurring significant additional cost to modify the existing HSDPA infrastructures.
Appendices
Appendix 1
The receiver matched filter sequences
where ⊗ is the Kronecker product, Q_{e}=[Q,Q_{1},Q_{2}] is the extended Q matrix of dimension N_{R}(N+L−1)×3K^{∗}, Q_{1} represents the previous symbol period components and Q_{2} represents ISI from the next symbol period formed as
where
Appendix 2
Using the matrix inversion lemma, the inverse matrices
where the distance vectors
the weighting functions ξ,ξ_{1},ξ_{2},ξ_{3},ξ_{4}, ξ_{5}, and ξ_{6} are produced using
Then, the weighted energy terms ζ,ζ_{1}, and ζ_{2} can be calculated as follows:
while the interim matrices Z_{1},Z_{2},Z_{3}, and Z_{4} are formed as shown below:
For a given energy allocation E_{k} for k=1,…,K, the parameters
1. Calculate
2. Form
3. Obtain the system value using
Repeat this process from steps 1 to 3 for all selected transmission channels from k=1 to k=K^{∗}.
Competing interests
The authors declare that they have no competing interests.
Acknowledgements
During the development of the experimental apparatus several divisions of the National Instruments (NI) USA, UK, and Europe groups have loaned a NI PXIebased 2×2 MIMO transceivers to enable Imperial College London to develop the MIMO channel emulator. National Instruments have also supplied a copy of their channel emulation software, which was modified by Imperial College London to operate with the experimental apparatus. We acknowledge the technical support given by the National Instruments team involving James Kimery, Robert Morton, Yiannis Pavlou, Ben Lavasani, David Baker, Trang Nguyen, Erik Luther, Jaeweon Kim, Ian Wong, and Ahsan Aziz.
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