MIMO-CDMA Systems Research Articles

Linear to multi-linear algebra and systems using tensors

In the past few decades, multi-linear algebra also known as tensor algebra has been adapted and employed as a tool for various engineering applications. Recent developments in tensor algebra have indicated that several well-known concepts from linear algebra can be extended to a multi-linear setting with the help of a special form of tensor contracted product, known as the Einstein product. Thus, the tensor contracted product and its properties can be harnessed to define the notions of multi-linear system theory where the input, output signals, and the system are inherently multi-domain or multi-modal. This study provides an overview of tensor algebra tools which can be seen as an extension of linear algebra, at the same time highlighting the differences and advantages that the multi-linear setting brings forth. In particular, the notions of tensor inversion, tensor singular value, and tensor eigenvalue decomposition using the Einstein product are explained. In addition, this study also introduces the notion of contracted convolution for both discrete and continuous multi-linear system tensors. Tensor network representation of various tensor operations is also presented. In addition, application of tensor tools in developing transceiver schemes for multi-domain communication systems, with an example of MIMO CDMA system, is presented. This study provides a foundation for professionals whose research involves multi-domain or multi-modal signals and systems.

A Novel Design of Pilot Aided Channel Estimation for MIMO-CDMA System

In order to estimate a fading channel characteristics, a pilot signal is propogated with traffic channel. Fading channel parameter estimation is of paramount importance as it may be utilized to design different equalization techniques. It may also be utilized to allocate weights of rake receiver to sturdiest multipaths as well as coherent reception and weighted combination of multipath constituents of wireless communication systems. In this paper, a pilot aided channel estimating technique for MIMO-CDMA systems is presented. This technique utilizes minimum mean squared error estimation of corrupted information in a flat fading channel along with noise. Simulation results predicts theoretical predictions are strongly validated for different values of SNR and users.

Performance Evaluation of CDMA - MIMO (STBC) System over Rayleigh Fading Channel for Image Transmission

Data transmission via wireless communication system is not only in text form but it also can be in image form. In the process of sending data or information, it often experiences interference in transmission media, which is fading. The method used in this research is by simulation using MATLAB. The simulation of CDMA-MIMO (STBC) system with Walsh spreading code is expected to reduce the disturbance of fading. Fading channels can be modeled using Rayleigh distribution. The number of users and spreading factors affect the performance of CDMA-MIMO (STBC) systems. The parameters used in this simulation were SNR, BER, and PSNR. The results showed that image reconstruction passing CDMAMIMO system with spreading factor 4 has better image quality. Its PSNR 33.9589dB when SNR -10dB. SNR was increased 10 dB then PSNR 60.00 dB. The increasing of spreading factor to 8 and 16 was obtained by increasing PSNR, PSNR 35.0685 dB and PSNR 37.5665 dB, respectively. For 4 users with Spreading Factor 4 and SNR 0 to 5 dB, it was changed the BER. This is influenced by changes in SNR. The higher SNR value, the average value of BER will be smaller. A growing number of users from 1 to 4 users were decreased the performance of the MIMO CDMA system when observed from the BER and PSNR.

Multiple access interference in MIMO-CDMA systems under Rayleigh fading: statistical characterization and applications

A major limiting factor in the performance of multiple-input-multiple-output (MIMO) code division multiple access (CDMA) systems is multiple access interference (MAI) which can reduce the system’s capacity and increase its bit error rate (BER). Thus, a statistical characterization of the MAI is vital in analyzing the performance of such systems. Since the statistical analysis of MAI in MIMO-CDMA systems is quite involved, especially when these systems are fading, existing works in the literature, such as successive interference cancellation (SIC) or parallel interference cancellation (PIC), employ suboptimal approaches to detect the subscriber without involving the need for MAI statistics. The knowledge of both MAI and noise statistics plays a vital role in various applications such as the design of an optimum receiver based on maximum likelihood (ML) detection, evaluation of the probability of bit error, calculation of the system’s capacity, evaluation of the outage probability, estimation of the channel’s impulse response using methods including the minimum mean-square-error (MMSE), the maximum likelihood(ML), and the maximum a posteriori probability (MAP) criterion. To the best of our knowledge, there is no existing work that explicitly evaluates the statistics of the MAI-plus-noise in MIMO fading channels. This constitutes the prime objective of our proposed study here. In this work, we derive the expressions for the probability density function (PDF) of MAI and MAI-plus-noise in MIMO-CDMA systems in the presence of both Rayleigh fading channels and additive white Gaussian noise. Moreover, we evaluate the probability of the bit error rate in the presence of optimum reception using a ML receiver. Our theoretical findings can provide a reliable basis for both system design and various performance analyses of such systems. Our simulation results show that the theoretical findings are very well substantiated.

MAI and Noise Constrained LMS Algorithm for MIMO CDMA Linear Equalizer

This paper presents a constrained least mean squared (LMS) algorithm for MIMO CDMA linear equalizer is presented, which is constrained on spreading sequence length, number of subscribers, variances of the Gaussian noise and the multiple access interference (MAI) plus the additive noise (introduced as a new constraint). The novelty of the proposed algorithm is that MAI and MAI plus noise variance has never been used as a constraint in MIMO CDMA systems. Convergence analysis is performed for the proposed algorithm in case when statistics of MAI and MAI plus noise are available. Simulation results are presented to compare the performance of the proposed constrained algorithm with other constrained algorithms and it is proved that the new algorithm has outperformed the existing constrained algorithms.

A Complete Complementary Coded MIMO System and Its Performance in Multipath Channels

In this paper, we propose a new system architecture using complete complementary (CC) codes for a multicarrier MIMO CDMA system to combat multipath fading in wireless channels. Unlike traditional MIMO systems, complementary codes were designed at chip-level to achieve time and frequency-spreading for each antenna. We analyze the system performance in multipath fading channels. A closed form expression of bit error rate (BER) performance is obtained. Extensive simulations were conducted to verify the analytical results. Our results indicate that a CC coded MIMO system can effectively decrease BER and take advantage of diversity gain.

BER Analysis of Various Channel Equalization Schemes of a QO-STBC Encoded OFDM based MIMO CDMA System

BER Analysis of Various Channel Equalization Schemes of a QO-STBC Encoded OFDM based MIMO CDMA System

Turbo receiver for MIMO-CDMA systems employing parity bit selected and permutation spreading

In this paper, a turbo receiver for MIMO-CDMA systems employing parity bit selected and permutation spreading is proposed. In such systems, spreading codes used by transmit antennas are dependent on the transmitted data. In the proposed system, convolutional coding is used as an outer code, while the parity bit selected scheme is used as the inner code. Detection and decoding are performed iteratively for each detected bit. When parity bit selected spreading is used, the parity bits generated by a linear block encoder are used to select a spreading code from a set of orthogonal spreading sequences. The selected spreading code is then used to spread the signals in all transmit antennas. In contrast, in permutation spreading, a permutation of orthogonal spreading sequences is used in each transmit antenna. In the proposed receiver, soft information passes between the detector and the decoder on multiple iterations. Detection is performed using the received signal from all receive antennas in combination with the extrinsic likelihood provided by a SISO decoder. The turbo receiver is further extended to a multiple user system, where the MAI is estimated in each iteration and subtracted out from the received signal. Simulations show a significant improvement in BER when a turbo receiver is used in these systems.

On the Asymptotic Spectral Efficiency of Uplink MIMO-CDMA Systems Over Rayleigh Fading Channels With Arbitrary Spatial Correlation

In this paper, we study the asymptotic spectral efficiency (ASE) of the uplink multiple-input-multiple-output direct-sequence code-division multiple-access (MIMO-CDMA) systems supporting multiple users, when assuming communications over flat-fading channels with arbitrary correlation in the spatial domain. In the MIMO-CDMA systems considered, the system-channel-related matrix expressed by H is a block random matrix, whose entries may be correlated due to the spatial correlation. In this paper, the theory of operator-valued free probability is employed to derive the approximate asymptotic eigenvalue distribution (AED) of the correlation matrix RH = HH H, where the size of the block matrix H tends to infinity. Based on the approximate AED, the spectral efficiency (SE) performance of multiuser MIMO-CDMA systems is studied by both analysis and simulations. Our simulation and numerical results show that the corresponding ASE is, in general, capable of providing very good prediction of the SE achieved by the practical MIMO-CDMA systems.

Improvement of BER performance in MIMO–CDMA systems by using initial–phase optimized gold codes

This paper describes a new approach to improve the bit error rate (BER) performance of a multiple-input multiple-output code-division multiple-access (MIMO-CDMA) system over quasi-static Rayleigh fading channels. The system considered employs robust space-time successive interference cancellation detectors and initial-phase optimized Gold codes for the improvement. The results clearly indicate that the use of initial-phase optimized Gold codes can significantly improve the BER performance of the system compared to the performance of a multiuser MIMO-CDMA system with conventional nonoptimized Gold codes. Furthermore, this performance improvement is achieved without any increase in system complexity.

Efficient Scheduling Algorithms for Multiantenna CDMA Systems

In multiple-input-multiple-output (MIMO) multiuser systems, simultaneously serving multiple users achieves high data rates. However, high-performance transmit beamforming requires an adequately designed user-selection scheme. Optimal scheduling can be only obtained through a high computationally complex exhaustive search, and hence, low-complexity heuristic algorithms are required. In addition, employing a multiple-access scheme such as code division (CDMA) largely increases the complexity of optimal scheduling, and it becomes unemployable even for a moderate number of users and antennas. In this context, this paper proposes three heuristic scheduling algorithms for MIMO CDMA systems using zero-forcing beamforming (ZFBF). We use a graph-theoretical approach to model the system as a weighted undirected graph. The problem of user selection is then formulated as a graph coloring problem, namely, the maximum weight N-colorable subgraph problem. Then, we design two heuristics to solve this graph problem. The first algorithm is a low-complexity greedy algorithm. The second algorithm is based on a tabu search approach to resolve efficiently the complexity/performance tradeoff. Numerical and simulation results show the sub-optimal performances and robustness of the proposed low-complexity algorithms.

A Blind Two-Stage Receiver for MIMO-CDMA Systems

A blind two-stage multiple-input multiple-output (MIMO) receiver is proposed for code-division multiple access (CDMA) systems utilizing space-time block coding (STBC) over a multipath fading channel. Specifically, in the first stage, a signal-blocked (SB) interference-blocked (IB) detector is first constructed for collection of the desired signals and suppression of multiple access interference (MAI). In the second-stage, a decision-directed scheme is developed to alleviate desired signal cancellation. Computer simulations demonstrate that the proposed blind receiver can achieve a reliable output signal-to-interference-plus-noise ratio (SINR) performance approximating that of the optimal minimum mean squared error (MMSE) receiver and can exhibit the robustness against the finite data sample effect.

A Channel-Estimation and Data-Detection Scheme for Multiuser MIMO-CDMA Systems in Fading Channels

In this paper, we examine the effect of channel estimation errors on the performance of multiple-input-multiple-output (MIMO) systems that employ code-division multiple-access (CDMA) transmission. Channel estimation based on training techniques has widely been considered throughout the literature. However, employing these training techniques in MIMO-CDMA systems degrades system performance due to multiuser interference. This degradation is clear as the diversity advantage of the MIMO system diminishes with the increased level of interference. As a remedy to this problem, we propose a channel-estimation and data-detection scheme based on the superimposed training technique for space-time spreading systems. The proposed scheme enhances the performance of the space-time system by eliminating the interference effect from both the channel and data estimates using two decorrelators: channel and data decorrelators. We investigate the performance of the proposed estimation technique considering an asynchronous CDMA uplink transmission over frequency-selective slow-fading channels. In particular, we analyze the bit-error-rate (BER) performance of the multiuser system with two-transmit-antenna and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> -receive-antenna configuration over Rayleigh fading channels. Compared with other conventional estimation techniques, our results show that the proposed estimation technique is more robust to channel-estimation errors. Furthermore, both simulations and analytical results indicate that full system diversity is achieved.

Spreading Code Assignment Strategies for MIMO-CDMA Systems Operating in Frequency-Selective Channels

Code Division Multiple Access (CDMA) and multiple input multiple output- (MIMO-) CDMA systems suffer from multiple access interference (MAI) which limits the spectral efficiency of these systems. By making these systems more power efficient, we can increase the overall spectral efficiency. This can be achieved through the use of improved modulation and coding techniques. Conventional MIMO-CDMA systems use fixed spreading code assignments. By strategically selecting the spreading codes as a function of the data to be transmitted, we can achieve coding gain and introduce additional degrees of freedom in the decision variables at the output of the matched filters. In this paper, we examine the bit error rate performance of parity bit-selected spreading and permutation spreading under different wireless channel conditions. A suboptimal detection technique based on maximum likelihood detection is proposed for these systems operating in frequency selective channels. Simulation results demonstrate that these code assignment techniques provide an improvement in performance in terms of bit error rate (BER) while providing increased spectral efficiency compared to the conventional system. Moreover, the proposed strategies are more robust to channel estimation errors as well as spatial correlation.

Design of spreading permutations for MIMO-CDMA based on space-time block codes

In this paper we propose a new method for designing the spreading permutations based on space time block code matrices for MIMO-CDMA systems. The new designs improve the bit error rate (BER) compared to MIMO-CDMA systems that use spreading permutations based on T-designs. This BER improvement comes without any increase in system complexity.

Sequential detection for multiuser MIMO CDMA systems with single spreading code per user

We consider multiuser MIMO CDMA systems where each user has multiple transmit antennas and different transmit antennas of the same user use the same spreading code. Because transmit antennas of the same user use the same spreading code, inter antenna interference would degrade the system performance. We propose a novel decision-window-based data detection (sequential detection) method to mitigate the inter antenna interference. We also modify the existing single-user single-antenna channel estimation algorithm for multiuser multiantenna systems. The simulation results show that, under the same channel estimation algorithm, the proposed sequential detection scheme with decision window of two symbols significantly outperforms the non-sequential one which is a special case of the proposed one when the decision window is of one symbol. It also outperforms the existing SIC-VBLAST, decorrelator-VBLAST, and MMSE-VBLAST schemes.

On the Performance of Code Acquisition in MIMO CDMA Systems

This letter investigates the effects of using multiple transmit antennas on code acquisition for preamble search in the CDMA uplink when MIMO is used for signal transmission and reception. The performance of a ML code acquisition technique in the presence of MIMO channel is analyzed by considering the detection and miss probabilities. The acquisition performance is numerically evaluated on a frequency selective fading channel. It is found that the performance of code acquisition scheme for a SIMO system is better than that for the case of MIMO on the low thresholds in terms of detection performance and MAT.

Multiuser Antenna Partitioning for Cellular MIMO–CDMA Systems

Improving the capacity of code-division-multiple-access (CDMA) systems through advanced signal processing has been an area of intensive research for many years, with limited success. Multiantenna technologies called multiple-input multiple-output (MIMO) are an obvious candidate to increase, particularly, downlink capacity. Nearly all research on MIMO-CDMA, however, has focused on increasing the throughput achieved per user, rather than increasing the number of supportable users, which is still the most important design goal in QoS-constrained voice systems. In this paper, we consider the downlink of a heavily loaded multicell CDMA system with multiple transmit and receive antennas. Straightforward application of the known MIMO techniques to such a system does not substantially increase the number of supportable users. To overcome this, a novel MIMO-CDMA system design based on user partitioning is developed, in which each user is assigned to a single transmit antenna either without regard to channel knowledge (static) or based on antenna-selection feedback bits (dynamic). These proposed multiuser-antenna-partitioning techniques have a minimal increase in complexity and would require only small changes to existing CDMA standards. The outage probability and capacity of the proposed systems are derived, and it is shown that, particularly, the dynamic partitioning scheme has a large gain over both the conventional CDMA and the static MIMO-CDMA scheme. This gain can be credited to multiuser antenna selection diversity. Unlike prior research, the multiuser antenna selection diversity gain is achieved without the typical expense of a loss in spatial multiplexing gain.Improving the capacity of code-division-multiple-access (CDMA) systems through advanced signal processing has been an area of intensive research for many years, with limited success. Multiantenna technologies called multiple-input multiple-output (MIMO) are an obvious candidate to increase, particularly, downlink capacity. Nearly all research on MIMO-CDMA, however, has focused on increasing the throughput achieved per user, rather than increasing the number of supportable users, which is still the most important design goal in QoS-constrained voice systems. In this paper, we consider the downlink of a heavily loaded multicell CDMA system with multiple transmit and receive antennas. Straightforward application of the known MIMO techniques to such a system does not substantially increase the number of supportable users. To overcome this, a novel MIMO-CDMA system design based on user partitioning is developed, in which each user is assigned to a single transmit antenna either without regard to channel knowledge (static) or based on antenna-selection feedback bits (dynamic). These proposed multiuser-antenna-partitioning techniques have a minimal increase in complexity and would require only small changes to existing CDMA standards. The outage probability and capacity of the proposed systems are derived, and it is shown that, particularly, the dynamic partitioning scheme has a large gain over both the conventional CDMA and the static MIMO-CDMA scheme. This gain can be credited to multiuser antenna selection diversity. Unlike prior research, the multiuser antenna selection diversity gain is achieved without the typical expense of a loss in spatial multiplexing gain.

Spatial Multiplexing in Cellular MIMO-CDMA Systems with Linear Receivers: Outage Probability and Capacity

Even though spatial multiplexing provides a significant spectral efficiency advantage in a single point-to-point noise- limited link, recent studies have shown that this advantage can be lost in cellular MIMO systems unless extra diversity is provided. Spread spectrum is a likely candidate for the extra diversity because spread spectrum can simultaneously provide frequency diversity and robustness to interference. This paper investigates the effectiveness of spatial multiplexing in the forward link of cellular MIMO-CDMA systems with linear receivers. Through the development of new closed-form results on outage probability and capacity for MIMO-CDMA, we show that even MIMO-CDMA loses the spatial multiplexing gain in a cellular context. These results indicate that a practical cellular MIMO system, which will be interference-limited and have a low-complexity receiver, requires new study on techniques to efficiently reduce the impact of the other-cell interference. The developed analytical framework can be used for evaluating other techniques.

Turbo Interference Mitigation in Layered Space-Time MIMO DS-CDMA Uplink with TTCM(Turbo Trellis Coded Modulation)

In this paper we propose the use of a turbo receiver for the uplink of a MIMO CDMA system employing layered space-time transmission. The proposed receiver consists of a low complexity layered space-time multi-user detector using minimum mean squared error (MMSE) filtering with a-priori information and a bank of MAP SISO decoders. Using the soft estimates from a bank of MAP decoders we obtain soft values of the interfering symbols. The SISO multiuser detector subtracts the vector of the interfering symbols from the incoming signal. The resulting vector is then filtered by an adaptive MMSE filter to reduce the residual MAI. This process iterates by exchanging extrinsic informations between the bank of MAP decoders and the SISO multiuser detector. Turbo Trellis Coded Modulation (TTCM) is used as Forward Error Correcting (FEC) code due to its high bandwidth efficiency. Our computer simulations show that the proposed structure outperforms a classical iterative receiver based on parallel interference cancellation (PIC) as well as a non-iterative MMSE receiver. Furthermore, in a multiuser context, the proposed receiver offers an error performance similar to that of single-user case at high SNR.