Low-Complexity Signal Detection by Multi-Dimensional Search for Correlated MIMO Channels

We first develop a reduced-rank minimum mean square error (MMSE) detector for direct-sequence (DS) code division multiple access (CDMA) by forcing the linear MMSE detector to lie in a signal subspace of a reduced dimension. While a reduced-rank MMSE detector has lower complexity, it cannot outperform the full-rank MMSE detector. We then concentrate on the blind reduced-rank MMSE detector which is obtained from an estimated covariance matrix. Our analysis and simulation results show that when the desired user's signal is in a low-dimensional subspace, there exists an optimal subspace so that the blind reduced-rank MMSE detector lying in this subspace has the best performance. By properly choosing a subspace, we guarantee that the optimal blind reduced-rank MMSE detector is obtained. An adaptive blind reduced-rank MMSE detector, based on a subspace tracking algorithm, is developed. The adaptive blind reduced-rank MMSE detector exhibits superior steady-state performance and fast convergence speed.

This paper investigates low complexity detection for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with co-channel interference (CCI). We firstly derive minimum mean square error (MMSE) detection based on sorted QR decomposition (SQRD) and modified MMSE SQRD detection for MIMO-OFDM systems with CCI. Although better performance can be achieved by the new detectors than liner MMSE (LMMSE) detection, the computational complexity is still high due to the required matrix inversion operation. In order to overcome such an issue and design low complexity detection method for MIMO-OFDM systems with CCI, then, we propose an improved MMSE SQRD detector by utilizing a regularization method. The simplification of the regularization parameter calculation in the proposed method is then discussed. Simulation results show that the error performance of the proposed method approaches modified MMSE SQRD detection in presence of CCI, while keeping a much lower complexity.

A combined minimum mean square error (MMSE) and maximum likelihood (ML) multiuser detector with reduced-complexity is proposed for uplink space-time block coded (STBC) orthogonal frequency division multiplexing (OFDM) systems. In this combined detector, received signals from co-channels are first detected by an MMSE multiuser detector. Then an ML-based post-detection processor (PDP) is designed to detect estimated outputs from the MMSE detector with the highest probability of errors and correct them to reduce the system bit error rate (BER). An efficient algorithm is proposed for the PDP which requires only a small additional complexity but can improve the system BER performance significantly compared with the conventional MMSE multiuser detector.

An analytical study is presented on the performance of the variable spreading factor orthogonal frequency and code division multiplexing (VSF-OFCDM) system with hybrid multi-code interference (MCI) cancellation and minimum mean square error (MMSE) detection. The weights of MMSE are derived, and should be updated stage by stage of MCI cancellation. Various values of time and frequency domain spreading factors are dealt with in a QPSK-modulated VSF-OFCDM system. It is shown that the hybrid detection scheme performs much better than the conventional MMSE. For the hybrid detection, a larger value of the frequency domain spreading factor is expected.

The receiver in a wireless communication system has the task of computing good estimates for the data symbols that have been transmitted. The best (optimum) detector is the Maximum Likelihood (ML) detector. However, it requires a high computational complexity. This work aims to efficiently detect the transmitted symbols with a reduced complexity. In order to produce a near optimum receiver, two methods are presented. These methods are obtained by convex optimization relaxations which yield global optimum solutions. The relaxations are combined with the idea of using the structure of the channel matrix to reduce the computational complexity. The channel matrix exhibits a banded Toeplitz structure. In each case, the dual problem of the convex optimization relaxation is solved to estimate the noise power. Gradient descent algorithm is used to solve the dual problem in the first relaxation while the bisection method is applied for the second relaxation. In both cases, the result is a Generalized Minimum Mean Squared Error (GMMSE) detector which has a form similar to the Minimum Mean Square Error (MMSE) detector and a performance almost the same as the MMSE detector, but it is not require the knowledge of the noise power. The GMMSE detectors can be used in scenarios where adapted or blind adaptive detection is not suitable, for instance when the channel is rapidly changing. Using a circular approximation of banded Toeplitz matrix the Fast Fourier Transform (FFT) can be applied to reduce the computational complexity of the detectors. Finally, the local search method is applied to enhance the performance of the proposed GMMSE detector. The proposed detector is a near optimum detector with low computational complexity.

This paper considers a two-user downlink multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) system using minimum mean-squared error (MMSE) detection under imperfect channel estimation. By taking account of both errors in channel estimation and MMSE detection, we derive approximated users' capacities and design a closed-form power allocation scheme to maximize the minimum (max-min) of them. The design problem is equivalent to max-min optimization of users' signal-to-interference-plus-noise ratios (SINRs), and the solution can be obtained by SINR balancing. The proposed power allocation scheme involves solving two quadratic equations, and is easy to implement in practical applications. As compared with an existing robust MIMO-NOMA power allocation method based on generalized singular value decomposition and SINR balancing, the proposed one offers slightly worse bit-error-rate performance with much lower complexity.

Enhanced genetic algorithms (GA) applied in space-time block coded (STBC) multiuser detection (MUD) systems in Rayleigh flat-fading channels are reported in this paper. Firstly, an improved objective function, which is designed to help speed up the search for the optimal solution, is introduced. Secondly, a decorrelating detector (DD) and a minimum mean square error (MMSE) detector have been added to the GA STBC MUD receiver to create the seed chromosome in the initial population. This operation has improved the receiver performance further because some signal information has been intentionally embedded in the initial population. Simulation results show that the receiver employing the improved objective function and the DD or MMSE detector can converge faster with the same bit error rate (BER) performance than the receiver with the initial population chosen randomly. The total signal-to-noise ratio (SNR) improvement contributed by these two modifications can reach 4 dB. Hence the proposed GA receiver is a promising solution of the STBC MUD problem.

The algorithm and the results of a blind multiuser detector using a machine learning technique called support vector machine (SVM) on a chaos-based code division multiple access system is presented in this paper. Simulation results showed that the performance achieved by using SVM is comparable to existing minimum mean square error (MMSE) detector under both additive white Gaussian noise (AWGN) and Rayleigh fading conditions. However, unlike the MMSE detector, the SVM detector does not require the knowledge of spreading codes of other users in the system or the estimate of the channel noise variance. The optimization of this algorithm is considered in this paper and its complexity is compared with the MMSE detector. This detector is much more suitable to work in the forward link than MMSE. In addition, original theoretical bit-error rate expressions for the SVM detector under both AWGN and Rayleigh fading are derived to verify the simulation results.

As the promising novel multiple access scheme for the 5th generation (5G) wireless communication system, pattern division multiple access (PDMA) technology can improve the spectral efficiency and support the massive connection based on the reasonable unequal diversity between users. Compared with traditional multiple access technologies, PDMA brings more serious multiple address interference to hinder the multiuser detection. The universal detection algorithm with low complexity and high performance is one of the main challenges of PDMA technology. In this paper, we proposed a new iterative detection and decoding algorithm, which is a successive interference cancellation (SIC) iterative processing based on the minimum mean square error (MMSE) detection and channel decoding algorithm. It is essentially a SIC iterative processing based on some users' information has been correctly decoded by the MMSE detection and the channel decoder. The proposed multiuser detection algorithm can prevent the error propagation by the cyclic redundancy check (CRC). The simulation results show that the proposed algorithm can get significant performance gains over traditional multiuser detection algorithms.

Extreme learning machine detector for millimeter-wave massive MIMO systems

This paper proposes a Group Detection (GD) algorithm with Max-Log-MAP Sphere Decoder (MLM-SD) in order to reduce the complexity of signal detection in a Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system. The proposed algorithm divides spatial streams into multiple partial spatial streams by using Minimum Mean Square Error (MMSE) detector, followed by multiple MLM-SDs with reduced number of spatial streams. Although the spatial diversity gain in the MLM-SD degrades because of the lack of the degrees of freedom exploited by the MMSE detector, its diversity gain is recovered by combining the metrics obtained by the multiple MLM-SDs. In a MIMO wireless LAN multipath fading environment, the complexity of the proposed algorithm is 10% of that of the original MLM-SD and the performance degradation in terms of SNR is slightly less than that of the original MLM-SD in 4-by-4 MIMO architecture with 64QAM achieving 216 Mbps. It is also found that the proposed algorithm is robust against the limitation of the number of searches in sphere decoder.

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for Multiple-Input Multiple-Output systems with Non-Orthogonal Multiple Access (MIMO-NOMA), in which a base station with $N_r$ antennas serves $N_u$ sources simultaneously. Both $N_u$ and $N_r$ are very large numbers and we consider the cases that $N_u>N_r$. The GMPID is based on a fully connected loopy graph, which is well understood to be not convergent in some cases. The large-scale property of the MIMO-NOMA is used to simplify the convergence analysis. Firstly, we prove that the variances of the GMPID definitely converge to that of Minimum Mean Square Error (MMSE) detection. Secondly, two sufficient conditions that the means of the GMPID converge to a higher MSE than that of the MMSE detection are proposed. However, the means of the GMPID may still not converge when $ N_u/N_r< (\sqrt{2}-1)^{-2}$. Therefore, a new convergent SA- GMPID is proposed, which converges to the MMSE detection for any $N_u> N_r$ with a faster convergence speed. Finally, numerical results are provided to verify the validity of the proposed theoretical results.

3GPP (3rd Generation Partnership Project) LTE (Long Term Evolution) Advanced standards are currently under way, where 4×4 MIMO (Multiple Input Multiple Output) scheme is the minimum structure. One of the best solutions to support the maximum data rate transmission is to adopt a MIMO scheme, especially spatial multiplexing mode, which means that each antenna port can transmit separate data. To realize this algorithm, the main issue is to cancel interferences added to each antenna port, and therefore, the algorithm at the receiver should have good performances. In the aspect of implementation, MMSE (Minimum Mean Square Error) detection algorithm is a reasonable method considering both complexity and performance. Furthermore, an iterative receiver (IR) algorithm can also be applied to this system. An IR algorithm has a tradeoff between complexity and performance. In this paper, we designed a reasonable and implementable MIMO receiver structure and showed performance for 3GPP LTE Advanced system, and verified that hard decoded bits, PIC-MMSE (Parallel Interference Cancellation - MMSE) and 1-iteration PIC are enough to meet the required SNR using the implemented test-bed system.

Linear precoding is a well known effective technique to boost the performance of orthogonal frequency-division multiplexing (OFDM) systems. A drawback of linearly precoded OFDM (LP-OFDM) systems is the high computational complexity required by maximum-likelihood (ML) detection, which is mandatory to capture all the channel diversity. Conversely, low-complexity techniques, such as the linear minimum mean-squared error (MMSE) detection, suffer from nonnegligible performance loss with respect to the ML performance. This paper proposes a detection technique that performs a local ML (LML) search in the neighborhood of the output provided by the MMSE detector. The trade-off between performance and complexity of the proposed LML-MMSE detector, which fall between the ones of the MMSE and ML detectors, can be nicely adjusted by appropriately setting the neighborhood size. Simulation results show that the LML-MMSE detector with minimum neighborhood size outperforms a block decision-feedback equalization (DFE) approach, while preserving a similar complexity.

The Bell Labs layered space-time (BLAST) architecture is a simple and efficient multiantenna coding structure that can achieve high spectral efficiency. Many BLAST detectors require more receiver antennas than transmitter antennas. We propose two novel turbo-processing BLAST detectors that can operate in systems with fewer receiver antennas than transmitter antennas. Both detectors are based on the group-detection strategy. The first proposed detector, the reduced-dimension maximum a posteriori (RDMAP) detector uses a dynamically formed group for each bit decision, while the second proposed detector, the group maximum a posteriori (GMAP) uses a static grouping. For both detectors, a maximum a posteriori (MAP) decision is made using a group of transmitted symbols, and the remaining signal contribution is treated as interference. The interference is characterized as nonzero mean colored-noise source that is whitened before a decision is made. Both proposed detectors are generalizations of the MAP detector and the turbo-processing minimum mean-squared error (MMSE) detector in Sellathurai and Haykin, and Abe and Matsumoto. An uncoded bit-error rate analysis for an independent Rayleigh fading environment is also presented. Simulated results are presented which show that both the RDMAP and GMAP detectors have a performance improvement over the MMSE detector, especially in systems having an excess number of transmitter antennas.