Minimum Mean Square Error Detector Research Articles

Extrinsic Information Analysis of a New Iterative Method Using the Stair Matrix for Massive MIMO Uplink Signal Detection

In this letter, we have proposed a new convergence model to account for both symbol detection and soft-output derivation. In the new convergence model, the extrinsic information analysis is conducted. Through extrinsic information analysis, we have validated the performance superiority of a new iterative method using the stair matrix in the development over the existing near linear minimum mean-square error detection proposals. The extrinsic information analysis also reveals a significant performance loss of the existing proposals. We have evaluated the system bit error rate performance and the results are consistent with the extrinsic information analysis.

Closed-formed distribution for the SINR of MMSE-detected MIMO systems and performance analysis

In this paper, we investigate the error performance of multiple-input multiple-output (MIMO) wireless communications systems using minimum mean-square error (MMSE) detection. Particularly, a new closed-form statistical distribution for the output signal-to-interference-plus-noise ratio (SINR) of MMSE receiver is derived, for independent Rayleigh fading channels. The expression for the distribution of SINR is shown to be a linear combination of gamma distributions and polynomial of 11+x, where x is the SINR. Base on the derived distribution for the SINR, closed-form and approximated expressions for the symbol error probability (SEP) of quadrature amplitude modulation (QAM) and phase shift keying (PSK) signaling are obtained, respectively. The derived SINR density and SEP are valid for arbitrary number of transmit and receive antennas. Furthermore, a reduced complexity approximation is introduced to obtain the SINR distribution and SEP performance of MMSE-Detected MIMO Systems with a large number of antennas. The provided simulation results confirm the validity of our theoretical analysis for both the SINR and SEP.

Low Complexity Signal Detector for MIMO MCCDMA System for Longer Delay Channel

In recent years Multiple-input multiple-output (MIMO) Multi carrier code division multiple access (MCCDMA), which combines the advantage of diversities with high spectral efficiency has drawn great attention. In this paper we introduce a novel low-complexity multiple-input multiple-output (MIMO) MMSE detector tailored for MCDCDMA systems, suitable for frequency selective channel. The proposed detector begins with estimation of the minimum mean square error (MMSE) on less reliable symbols followed by iterative de-correlation as post-detection processing for mitigating multiple access interferences. Efficient high-throughput VLSI architecture is used to achieve superior performance compared to the conventional MMSE detectors. The performance of the proposed MMSE detector is close to the efficient maximum likelihood, with significant complexity reduction over higher order constellations. The efficiency of MIMO MCCDMA over high order constellations and its quality retentions are verified through MATLAB BER simulation.

Stair Matrix and Its Applications to Massive MIMO Uplink Data Detection

In this paper, we investigate low-complexity data detection scheme for massive multiple-input multiple-output (MIMO) uplink transmission. We propose to utilize the stair matrix, instead of diagonal matrix in existing proposals, for the development, and achieve near linear minimum mean-square error detection performance. We first demonstrate the applicability of the proposed method by showing that the probability (that the convergence conditions are met) approaches one as long as sufficiently large number of antennas are equipped at the base station. We then propose an iterative method to perform data detection and show that much improved performance can be achieved with the computational complexity remaining at the same level of existing iterative methods, where the diagonal matrix is adopted. Furthermore, we conduct numerical simulations, and the results validate the significant performance enhancement of using the stair matrix over the diagonal matrix in all performance aspects. Moreover, we apply the proposed scheme to a massive MIMO system, where the extended vehicular A channel data are generated. The performance improvement of the proposed scheme over existing proposals is also validated.

Fast Symbol Detection for Massive G-STBC MIMO Systems

In this paper, a group-based fast symbol detection scheme is proposed for massive Group-wise Space–Time Block Code Multiple-Input Multiple-Output systems. The proposed scheme first chooses a number G, (e.g. $$G=4,6,8$$ ) as the size of each group and then conducts the Minimum Mean Square Error (MMSE) detectors to facilitate symbol detection group by group. In particular, instead of directly using huge computational complexity to compute the MMSE detectors, the proposed scheme recursively finds the corresponding assistant matrices to determine the groups and calculate the MMSE detectors. As a result, the transmitted symbols can be recursively estimated group by group. Finally, simulation results and complexity analysis show the proposed scheme performs very close to the existing methods, while using lower computational complexity.

MMSE Turbo Equalization and Detection for Multicarrier Faster-Than-Nyquist Signaling

In this paper, two minimum mean-squared error (MMSE) turbo equalization and detection schemes for spectral efficient multicarrier faster-than-Nyquist (MFTN) signaling system are presented. First, the two-dimensional (2-D) soft input and soft output (SISO) MMSE equalization intended for magnetic recording channels, i.e., 2-D intersymbol interference (ISI), is extended to the detection of MFTN signals. Although the 2-D MMSE turbo equalization exhibits an attractive bit-error-rate (BER) performance under certain time-frequency spacing packing between adjacent symbols/subcarriers, the BER performance will be degraded when introducing serious intercarrier interference. Second, a 1-D SISO MMSE equalization combined with soft successive interference cancellation (SIC) is further proposed for the detection of MFTN signals, and it shows that the MMSE equalization combined with SIC could asymptotically approach the maximum a posterior equalization combined with SIC with negligible BER performance loss. Our computational complexity analysis and numerous simulation results demonstrate that the proposed MMSE turbo equalization schemes may be more preferred choice in the practical detection of MFTN signals.

Iterative Intercell Interference Cancellation in MIMO Multicell Networks

An iterative intercell interference cancellation algorithm is introduced to improve the receiver performance of uplink transmission in multicell networks. At first, the uplink signal detection is performed independently in each cell according to minimum mean squared error (MMSE) criterion. Subsequently, the detection results are applied to reconstruct the transmit signals of different users and cancel their interference to neighboring cells. With the help of reconstruction results, the MMSE detection matrix of each cell is updated. The channel responses of both efficient and interference links are estimated with the help of pilots. The pilot allocation parameter is introduced to indicate the quality of channel estimation. The simulation results indicate that intercell interference can be greatly mitigated by the proposed algorithm with a moderate number of receiver antennas at the base station.

Precoding Aided Generalized Spatial Modulation With an Iterative Greedy Algorithm

This paper divides antennas at the transmitter into several transmit antenna groups (TAGs) and extends the generalized spatial modulation (GSM) idea to a new precoding-aided multiple-input multiple-output system, which is referred to as precoding-aided GSM (PGSM) system. To mitigate the influence caused by correlated channels, we consider the interleaved grouping scheme which leads to a minimum antenna correlation within the same TAG. To select the receive antenna subset with low complexity, we propose an iterative greedy (IG) algorithm that contributes to a maximum equivalent channel gain with low-computational complexity. To reduce the complexity of maximum likelihood (ML) detector, a low complexity IG algorithm-based ML (IG-ML) detector is also derived. Simulation results show that the bit error rate (BER) performance gain up to 3.5 dB is obtained by the proposed PGSM with IG-ML detector over the PGSM with an ordered block minimum mean-squared error detector at a given BER of 10−4. It is also shown that the proposed PGSM with the IG-ML detector achieves a similar BER performance in a high signal-to-noise power ratio region compared with that of an ideal precoding for the GSM with an optimal ML detector.

Low-complexity MMSE detector based on refinement Jacobi method for massive MIMO uplink

Minimum mean square error (MMSE) linear detector can achieve the near-optimal bit error rate (BER) performance for uplink multi-user massive multiple input multiple output (MIMO) systems, but it involves matrix inversion with high complexity, especially when the number of users is high. In order to reduce the complexity, Jacobi iterative method has been applied for low-complexity MMSE detector without employing the computationally intensive matrix inversion. However, its convergence rate is low. In this paper, we propose a novel low-complexity MMSE detector based on the refinement of Jacobi iterative method. This refinement is given by the use of band matrix in order to accelerate the convergence rate, as well as guaranteeing the near-optimal BER performance. Analytical and simulation results show the efficiency of the proposed detector in comparison to the recently Jacobi-based detector.

Design, Simulation & Concept Verification of 4 × 4, 8 × 8 MIMO With ZF, MMSE and BF Detection Schemes

AbstractA conventional MIMO system is designed consisting of 4 antenna elements at both the receiver and transmitter ends. Different kinds of signal detection techniques, namely, zero forcing (ZF), minimum mean square error (MMSE) and beamforming (BF), are used at the receiver end for signal detection. The performance of the system is analyzed by calculating BER vs SNR for each of the above techniques separately. The present work has been thoroughly analyzed and implemented using MATLAB. On the basis of the results obtained, it is summarized that as the values of SNR increase, BER decreases for ZF and MMSE and it almost vanishes to zero even for low SNR values if BF is used. Although ZF and MMSE are suitable for designing a conventional MIMO system with 4 antenna elements, it becomes too difficult for a large number of antenna elements due to its complexity of calculating the inverse of a (N×N) matrix. Based on the results analyzed so far, it is concluded that beamforming (BF) is a suitable technique for designing a system that has a large number of antenna elements at the base station. A further improved system with enhanced performance regarding lower BER for even smaller values of SNR is designed in the present study, consisting of 8 antennas at the base station. The results obtained are enthusiasm-provoking and encouraging for further studies to develop a concept for next-generation wireless communication systems with an optimum design.

Decision‐aided Jacobi iteration for signal detection in massive MIMO systems

Massive MIMO with high spectral efficiency is one of the key technologies for future 5G wireless communications. For signal detection in such systems, a decision-aided Jacobi (DA-Jacobi) iteration is proposed, which can improve the convergence speed as compared with the conventional Jacobi iteration for calculating the result of the linear minimum mean-squared error (MMSE) detection, and, at the same time, can come with lower computational complexity. Simulation results confirm these advantages and demonstrate that the error-rate performance of the proposed DA-Jacobi iteration can be even better than that of the exact linear MMSE detection.

Time-Domain Turbo Equalization for Single-Carrier Generalized Spatial Modulation

In this paper, low-complexity time-domain turbo equalization (TDTE) detectors based upon soft-interference-cancellation (SIC)-aided minimum mean-square error (MMSE) criterion are proposed for single carrier generalized spatial modulation (SC-GSM) systems. First, a symbol-by-symbol-aided TDTE detector for application to the small-scale GSM systems is proposed, where the zero symbols are considered as constellation points when performing SIC. Then, vector-by-vector-aided TDTE (VV-TDTE) detectors for application to larger-scale antenna systems are introduced, where the GSM symbol is treated as an entire vector when performing SIC. As for the proposed VV-TDTE detectors, in addition, different time-varying filter coefficients are designed, in order to strike a flexible tradeoff between complexity and performance. By relying upon extrinsic information transfer chart analysis, we show that the proposed TDTE detectors are capable of providing considerable bit error rate performance gains over existing TDTE detectors and over the classic frequency-domain equalization-based MMSE detector, especially for the unbalanced antenna configurations.

Iterative MMSE‐based soft MIMO detection with parallel interference cancellation

Minimum mean square error (MMSE)-based techniques are often used for the joint iterative detection and decoding that is for coded multi-input-multi-output (MIMO) system due to a sound complexity and the performance trade-off. This study proposes an enhanced MMSE-based soft MIMO-detection scheme by using three main ideas. The first idea is an efficient complexity-reduced soft-bit estimation technique, the second one is a performance improvement method utilised inside the MMSE detection process, and the third one is a complexity-reduced soft-symbol estimation method for quadrature amplitude modulation. The proposed ideas enable the interference-cancellation processes to be activated in parallel on each symbol layer, thereby reducing the processing time. The simulation results show that the proposed method efficiently contributes to the improvement of the performance in addition to its reduction of the linear-order complexity.

Low Complexity ZF and MMSE Detectors for the Uplink MU-MIMO Systems With a Time-Varying Number of Active Users

The classical multiuser detection algorithms such as zero forcing (ZF) and minimum mean square error (MMSE) receivers are designed with the assumption that the number of active users is constant and known. When the number of the active users changes, the receiver may exhibit a serious performance loss if it does not react quickly to such variations. In this paper, we address the problem of reducing the complexity of the reevaluation of the popular ZF and MMSE detectors for multiuser multiple-input multiple-output (MU-MIMO) systems with a time-varying number of users in the channel. For each technique, we propose a detection approach with low complexity and without performance loss. The proposed algorithms avoid the direct computation of matrix inverses required by the ZF and MMSE detectors. Moreover, the performance losses, due to the use of the ZF and MMSE detectors intended for the scenario with a fixed number of active users, are evaluated with Monte Carlo simulation results.

Simultaneous Spectrum Sensing and Data Reception for Cognitive Spatial Multiplexing Distributed Systems

A multi-user cognitive (secondary) radio system is considered, where the spatial multiplexing mode of operation is implemented amongst the nodes, under the presence of multiple primary transmissions. The secondary receiver carries out minimum mean-squared error detection to effectively decode the secondary data streams, while it performs spectrum sensing at the remaining signal to capture the presence of primary activity or not. New analytical closed-form expressions regarding some important system measures are obtained, namely, the outage and detection probabilities, the transmission power of the secondary nodes, the probability of unexpected interference at the primary nodes, and the detection efficiency with the aid of the area under the receive operating characteristics curve. The realistic scenarios of channel fading time variation and channel estimation errors are encountered for the derived results. Finally, the enclosed numerical results verify the accuracy of the proposed framework, while some useful engineering insights are also revealed, such as the key role of the detection accuracy to the overall performance and the impact of transmission power from the secondary nodes to the primary system.

Performance Analysis of STBC/SFBC System in Time-varying and Multi-path Channels

This study analyzed STBC and SFBC-OFDM systems having two or four transmission antennas in the time-varying and multi path fading channels environment. According to the performance analysis result, performance degradation was confirmed in this study, as channel variation period becomes shorter, when orthogonal or quasi-orthogonal STBC/SFBC technique was applied to the system having two or four transmission antennas in the time-varying and multi path fading channels. Also, the detection method using synchronization was applied for performance improvement. As a result of performance analysis on the STBC system in a time-varying channel and on the SFBC-OFDM system in the multi path channel, performance fell, as maximum time delay increased due to coherence time decline arising from the decrease of channel correlation coefficient, respectively, and the increase of the number of taps. However, BER (bit error rate) performance at SNR 25dB or higher was ascertained to improve up to 10 -3 ~10 -4 . Compared to the detection technique using ZF (zero forcing), the MMSE (minimum mean square error) detection technique showed good performance by acquiring 1~5dB or higher SNR gain. But, the ZF detection technique had a merit of being simpler from the hardware complexity aspect, compared to the MMSE detection technique. This study showed a possibility of high speed data transmission without additional bandwidth expansion by increasing the number of transmission antennas as a result of a performance analysis in the time-varying and multi path fading generated according to user mobility in the mobile communications environment.

Resource allocation for pilot-assisted massive MIMO transmission

This paper is on the resource allocation problem for pilot-assisted multi-user massive multiple-input-multiple-output (MIMO) uplink with linear minimum mean-squared error (MMSE) channel estimation and detection. We utilize the angular domain channel representation for uniform linear antenna arrays, and adopt its equivalent independent and nonidentical distributed channel model. For a given coherence interval and total energy budget, we study the joint optimization of the training length and the training power to maximize the achievable sum-rate. For tractable analysis and low-complexity solution, a tight approximation on the achievable sum-rate is derived first. Then the training length optimization for fixed training power and the training power optimization for fixed training length with respect to the approximate sum-rate maximization are both shown to be concave. An alternative optimization that solves the training length and power iteratively is proposed for the joint resource allocation. In addition, for the special case that the training and data transmission powers are equal, we derive the optimal training lengths for both high and low signal-to-noise- ratio (SNR) regions. Numerical results show the tightness of the derived sum-rate approximation and also the significant performance advantage of the proposed resource allocation.

Convergence Analysis and Assurance for Gaussian Message Passing Iterative Detector in Massive MU-MIMO Systems

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for massive Multiuser Multiple-Input Multiple-Output (MU-MIMO) system, in which a base station with $M$ antennas serves $K$ Gaussian sources simultaneously. Both $K$ and $M$ are very large numbers, and we consider the cases that $K<M$. The GMPID is a low-complexity message passing algorithm based on a fully connected loopy graph, which is well understood to be not convergent in some cases. As it is hard to analyse the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. Firstly, we prove that the variances of the GMPID definitely converge to the mean square error of Minimum Mean Square Error (MMSE) detection. Secondly, we propose two sufficient conditions that the means of the GMPID converge to those of the MMSE detection. However, the means of GMPID may not converge when $ K/M\geq (\sqrt{2}-1)^2$. Therefore, a new convergent GMPID called SA-GMPID (scale-and-add GMPID) , which converges to the MMSE detection in mean and variance for any $K<M$ and has a faster convergence speed than the GMPID, but has no higher complexity than the GMPID, is proposed. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results.

FPGA design of box‐constrained DCD‐based detector for large‐scale MIMO systems

AbstractThis paper proposes an improved architecture of a low‐complexity box‐constrained multiple‐input multiple‐output (MIMO) detector which is based on the dichotomous coordinate descent (DCD) algorithm. This architecture allows a simple field‐programmable gate‐array implementation of the detector and explores the parallel implementation to reduce the number of clock cycles required in the design. We investigate the proposed design and compare its detection performance, hardware resources, and convergence speed with that of known designs. It is shown that the proposed design provides improvement in the detection performance compared to the minimum mean square error (MMSE) detector. The numerical results also show that the proposed architecture requires as few as 184, 210, and 223 slices for 16 × 16, 64 × 64, and 128 × 128 MIMO systems, respectively, which is significantly less than that required by known designs of the MMSE detector. By comparing the serial and parallel implementations of the box‐constrained detector, we show that the parallel implementation requires 15% fewer clock cycles.

Thỏa hiệp phẩm chất BER-độ phức tạp trong các hệ thống chuyển tiếp vô tuyến MIMO-SDM-AF sử dụng tách tín hiệu kết hợp rút gọn dàn

Relay communication systems have attracted great attention recently due to their advantages in coverage extension, improved signal quality as well as increased end-to-end throughput. In the multiple-input multiple-output (MIMO) spatial-division multiplexing (SDM) amplify-and-forward (AF) relay communication systems, the bit error rate (BER) performance of the system depends significantly on the signal detector at the destination. However, optimal detectors which provide the minimum BER often require probitive complexity. In order to make it possible for practical implementation, we propose to apply the lattice reduction (LR) to the linear detectors at the destination receiver in order to balance the trade-off between their detection performance and computational complexity. Our analysis shows that the LR-aided (LRA) linear detectors using zero forcing (ZF) and minimum mean square error (MMSE) can achieve signifcant improvement in BER performance over the linear ZF and MMSE detectors while requiring the same complexity order.