Minimum Mean Square Error Detector Research Articles

On Multiple-Input Multiple-Output OFDM with Index Modulation for Next Generation Wireless Networks

Multiple-input multiple-output orthogonal frequency division multiplexing with index modulation (MIMO-OFDM-IM) is a novel multicarrier transmission technique which has been proposed recently as an alternative to classical MIMO-OFDM. In this scheme, OFDM with index modulation (OFDM-IM) concept is combined with MIMO transmission to take advantage of the benefits of these two techniques. In this paper, we shed light on the implementation and error performance analysis of the MIMO-OFDM-IM scheme for next generation 5G wireless networks. Maximum likelihood (ML), near-ML, simple minimum mean square error (MMSE) and ordered successive interference cancellation (OSIC) based MMSE detectors of MIMO-OFDM-IM are proposed and their theoretical performance is investigated. It has been shown via extensive computer simulations that MIMO-OFDM-IM scheme provides an interesting trade-off between error performance and spectral efficiency as well as it achieves considerably better error performance than classical MIMO-OFDM using different type detectors and under realistic conditions.

MIMO 채널 대각화 : 선형 검출 ZF, MMSE

Compared to the MIMO system using the spatial multiplexing methods and the MIMO system using the diversity scheme achieved a high rate, but the lower the diversity gain to improve the data transmission reliability should separate the spatial stream at the MIMO receiver. In this paper, we compared Channel capacity detection methods with the Lattice code, the 3-user interference channel and linear channel interference detection methods ZF (Zero Forcing) and MMSE (Minimum Mean Square Error) detection methods. The channel is a Diagonal channel. In other words, Diagonal channel is confirmed by the inverse matrix satisfies the properties of Jacket are element-wise inverse to _N^{-1}

Low Complexity Polynomial Expansion Detector With Deterministic Equivalents of the Moments of Channel Gram Matrix for Massive MIMO Uplink

We consider a low complexity polynomial expansion (PE) detector in a massive multiple-input multiple-output (MIMO) uplink channel. In contrast to most massive MIMO systems in the literature, where single antenna user equipments (UEs) are assumed, multiple antenna UEs are employed in this paper. Moreover, the channel between a base station (BS) and a UE is a jointly correlated Rician fading channel. The PE detector reduces the computational complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. The coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel Gram matrix. We use operator-valued free probability, which is a more general version of free probability, to derive the deterministic equivalents. In particular, we use the operator-valued moment-cumulant formula. The proposed low complexity PE detector is easy to compute. Simulation results show that the proposed detector can achieve performance close to the MMSE detector.

Low-complexity soft-output detection for massive MIMO using SCBiCG and Lanczos methods

Massive MIMO is a promising technology to improve spectral efficiency, cell coverage, and system capacity for 5G. However, these benefits take place at great cost of computational complexity, especially in systems with hundreds of antennas at the base station. This paper aims to address the minimum mean square error (MMSE) detection in uplink massive MIMO systems utilizing the symmetric complex bi-conjugate gradients (SCBiCG) and the Lanczos method. Both the proposed methods can avoid the large scale matrix inversion which is necessary for MMSE, thus, reducing the computational complexity by an order of magnitude with respect to the number of user equipment. To enable the proposed methods for soft-output detection, we also derive an approximating calculation scheme for the log-likelihood ratios (LLRs), which further reduces the complexity. We compare the proposed methods with existing exact and approximate detection methods. Simulation results demonstrate that the proposed methods can achieve near-optimal performance of MMSE detection with relatively low computational complexity.

Design and Implementation of Flexible Dual-Mode Soft-Output MIMO Detector With Channel Preprocessing

This paper proposes a flexible dual-mode soft-output multiple-input multiple-output (MIMO) detector to support open-loop and closed-loop in Chinese enhanced ultra high throughput (EUHT) wireless local area network (LAN) standard. The proposed detector uses minimum mean square error (MMSE) sorted QR decomposition (MMSE-SQRD) to produce channel preprocessing result, which is realized by a modified systolic array architecture with concurrent sorting. Moreover, the adopted square-root MMSE algorithm for closed-loop reuses MMSE-SQRD preprocessing to largely save hardware overhead. In addition, an optimized K-Best detection algorithm is proposed for open-loop, which increases throughput by odd-even parallel sorting and produces high quality soft-output with discarded paths (DPs). A flexible VLSI architecture is designed for the proposed dual-mode detector, which supports $1\times 1\sim 4\times 4$ antennas and BPSK $\sim$ 64-QAM modulation configuration. Implemented in SMIC 65 nm CMOS technology, the detector is capable of running at 550 MHz, which has a maximum throughput of 2.64 Gb/s for K-Best detection and 3.3 Gb/s for linear MMSE detection. The proposed detector is competitive to recent published works and meets the data-rate requirement of the EUHT standard.

Remarks on the Performance of the Linear Detectors in MIMO Spatial Multiplexing Systems

Linear minimum mean square error (MMSE) detector has been shown to alleviate the noise amplification problem associated with the conventional zero-forcing (ZF) detector. In this paper, we analyze the performance improvement by the MMSE detector in terms of the condition number of its filtering matrix, the post-processing signal to noise ratio (SNR) improvement, and the variance of the postprocessing SNRs. To this end, we derive explicit formulas for the condition numbers of the filtering matrices and the post-processing SNRs. Analytical and simulation results demonstrate that the improvement achieved by the MMSE detector over the ZF detector does not only depend on the noise variance and the condition number of the channel matrix, but also on how close the smallest singular values are to the noise variance. This conjecture is also proven correct via analyzing the post-processing SNR of both detectors.

Effect of Different Modulation Techniques Comparison of Linear MIMO Receivers

In wireless communication, Multiple-Input Multiple-Output (MIMO) is the most propitious technology that enhances the system capacity and data rate by using multiple antennas at the receiver and at the transmitter. Efficient signal detection at the receiver is complex task in MIMO systems. The computational complexity of equalization based linear detection algorithms such as Minimum Mean Square Error (MMSE) and Zero Forcing (ZF) is less than that of algorithmic schemes. The simulated results presented in this paper are using various MIMO system configurations from 2x2 to 8x8. The results are compared and analyzed on the basis of Bit Error Rate (BER) for M-QAM modulation techniques using MMSE, ZF reduced complexity algorithms under Rayleigh fading channel. Simulations results reveal that the MMSE detection offers better performance over ZF detection however for 64-QAM modulation both linear detection shows same performance.

Performance of Multi-User Transmitter Pre-Processing Assisted Multi-Cell IDMA System for Downlink Transmission

In this paper, we present the performance of multi-user transmitter pre-processing (MUTP) assisted coded-interleave division multiple access (IDMA) system over correlated frequency-selective channels for downlink communication. We realize MUTP using singular value decomposition (SVD) technique, which exploits the channel state information (CSI) of all the active users that is acquired via feedback channels. We consider the MUTP technique to alleviate the effects of co-channel interference (CCI) and multiple access interference (MAI). To be specific, we estimate the CSI using least square error (LSE) algorithm at each of the mobile stations (MSs) and perform vector quantization using Lloyd's algorithm, and feedback the bits that represents the quantized magnitudes and phases to the base station (BS) through the dedicated low rate noisy channel. Finally we recover the quantized bits at the BS to formulate the pre-processing matrix. The performance of MUTP aided IDMA systems are evaluated for five types of delay spread distributions pertaining to long-term evolution (LTE) and Stanford University Interim (SUI) channel models. We also compare the performance of MUTP with minimum mean square error (MMSE) detector for the coded IDMA system. The considered TP scheme alleviates the effects of CCI with less complex signal detection at the MSs when compared to MMSE detector. Further, our simulation results reveal that SVD-based MUTP assisted coded IDMA system outperforms the MMSE detector in terms of achievable bit error rate (BER) with low signal-to-noise ratio (SNR) requirement by mitigating the effects of CCI and MAI.

기회적 간섭 정렬의 실현 가능성 연구: 전력 제어를 통한 에너지 효율성 개선

In this paper, we introduce an energy-efficient opportunistic interference alignment (OIA) scheme that greatly improves the sum-rates in multi-cell uplink networks. Each user employs optimal transmit vector design and power control in the sense of minimizing the amount of generated interference to other-cell base stations while satisfying a required signal quality. As our main result, it is shown that owing to the reduced interference level, the proposed OIA schemes attains larger sum-rates than those of OIA with no power control for almost all signal-to-noise ratio regions. In addition, when both zero-forcing and minimum mean square error (MMSE) detectors are employed at the receiver along with the OIA scheme, it is shown that the OIA scheme with MMSE detection shows superior performance.

A High-Throughput VLSI Architecture for Hard and Soft SC-FDMA MIMO Detectors

This paper introduces a novel low-complexity multiple-input multiple-output (MIMO) detector tailored for single-carrier frequency division-multiple access (SC-FDMA) systems, suitable for efficient hardware implementations. The proposed detector starts with an initial estimate of the transmitted signal based on a minimum mean square error (MMSE) detector. Subsequently, it recognizes less reliable symbols for which more candidates in the constellation are browsed to improve the initial estimate. An efficient high-throughput VLSI architecture is also introduced achieving a superior performance compared to the conventional MMSE detectors with less than 28% added complexity. The performance of the proposed design is close to the existing maximum likelihood post-detection processing (ML-PDP) scheme, while resulting in a significantly lower complexity, i.e., 4.5×10 2 and 7×10 4 times fewer Euclidean distance (ED) calculations in the 16-QAM and 64-QAM schemes, respectively. The proposed design for the 16-QAM scheme is fabricated in a 0.13 μm CMOS technology and fully tested, achieving a 1.332 Gbps throughput, reporting the first fabricated design for SC-FDMA MIMO detectors to-date. A soft version of the proposed architecture is also introduced, which is customized for coded systems.

Minimizing the Symbol-Error-Rate for Amplify-and-Forward Relaying Systems Using Evolutionary Algorithms

In this paper, a new detector is proposed for an amplify-and-forward (AF) relaying system. The detector is designed to minimize the symbol-error-rate (SER) of the system. The SER surface is non-linear and may have multiple minimas, therefore, designing an SER detector for cooperative communications becomes an optimization problem. Evolutionary based algorithms have the capability to find the global minima, therefore, evolutionary algorithms such as particle swarm optimization (PSO) and differential evolution (DE) are exploited to solve this optimization problem. The performance of proposed detectors is compared with the conventional detectors such as maximum likelihood (ML) and minimum mean square error (MMSE) detector. In the simulation results, it can be observed that the SER performance of the proposed detectors is less than 2 dB away from the ML detector. Significant improvement in SER performance is also observed when comparing with the MMSE detector. The computational complexity of the proposed detector is much less than the ML and MMSE algorithms. Moreover, in contrast to ML and MMSE detectors, the computational complexity of the proposed detectors increases linearly with respect to the number of relays.

Achievable Ergodic Capacity of a MIMO System with a MMSE Receiver

This paper considers the multiple-input multiple-output (MIMO) system with linear minimum mean square error (MMSE) detection under ideal fast fading. For <TEX>$N_t$</TEX> transmit and <TEX>$N_r({\geq}N_t)$</TEX> receive antennas, we derive the achievable ergodic capacity of MMSE detection exactly. When MMSE detection is considered in a receiver, we introduce a different approach that gives the approximation of a MIMO channel capacity at high signal-to-noise ratio (SNR). The difference between the channel capacity and the achievable capacity of MMSE detection converges to some constant that depends only on the number of antennas. We validate the analytical results by comparing them with Monte Carlo simulated results.

Low-Complexity Detector for Spatial Modulation Multiple Access Channels With a Large Number of Receive Antennas

In this letter, a low-complexity detector, called ordered nearest neighbor search (NNS) minimum mean square error (MMSE) detector, is proposed for the spatial modulation multiple-access channel with a large number of receive antennas. In the proposed detector, the antenna index is first determined based on the channel direction information, and then, the modulation signal is recovered by the MMSE detector. Furthermore, to improve the separable detection performance, an ordered candidate list of the antenna index is acquired through NNS. Simulation results show that the proposed detector approaches the interference-free performance with very low complexity.

Achievable Rates of MIMO Systems With Linear Precoding and Iterative LMMSE Detection

We establish area theorems for iterative detection over coded linear systems (including multiple-input multipleoutput (MIMO) channels, inter-symbol-interference (ISI) channels, and orthogonal frequency-division multiplexing (OFDM) systems). We propose a linear precoding technique that asymptotically ensures the Gaussianness of the messages passed in iterative detection, as the transmission block length tends to infinity. We show that the proposed linear precoding scheme with iterative linear minimum mean-square error (LMMSE) detection is potentially information lossless, under various assumptions on the availability of channel state information at the transmitter (CSIT). Numerical results are provided to verify our analysis.

Vector orthogonal frequency division multiplexing system over fast fading channels

The performance of the vector orthogonal frequency division multiplexing (V-OFDM) system over fast fading channels is investigated. The channel is time varying within one V-OFDM data-block period, which causes the inter-carrier interference (ICI). With the help of an equivalent V-OFDM system model and an auxiliary transform matrix, a novel mathematical expression for the received signal with the ICI signal is derived, which clearly expresses how the signal of a target vector block (VB) is interfered by other VBs. The ICI signal is analysed and two theorems about its property are proposed. The first theorem presents the expression of the power of the ICI signal, showing that the ICI signal power increases with the VB number. The other one indicates that ICI signals at different subcarriers are not correlated. With the two theorems, a novel detection method utilising the correlation of the ICI signal is therefore proposed. Numerical results verify the validity of the derived theorems and simulation results demonstrate that the proposed minimum mean square error (MMSE) detection can suppress the ICI effect and it is superior to the conventional MMSE detection in terms of both detection mean square error and bit error rate performance.

English

This paper presents a Multiple-Input Multiple-Output (MIMO) transmission scheme that combines the spatial modulation (SM) with MIMO spatial multiplexing technique. The SM uses NA number of active antennas to transmit the same symbol, the proposed MIMO model uses the NA number of active antennas to transmit different symbols at the same time to increases the spectral efficiency of the system. A Zero-Forcing based equalizer is used at the receiver to jointly estimate the transmitted symbols as well as the index of active antennas combination. The zero-forcing based detection scheme suffers from a higher complexity and Inter channel Interference (ICI) with less probability of error (BER). For solving the problem in this paper a MMSE based detection scheme is used which improve the BER (bit error probability). The performance of MMSE based detection scheme is evaluated in an uncorrelated flat Rayleigh fading channel and compared with the Zero-forcing based spatial modulation and MMSE Detector. Keywords-,AWGN(Additive white Gaussian noise) ,Rayleigh fading channel, Antenna Combination Binary phase shift keying (BPSK), Bit error rate (BER), Inter-symbol interference (ISI), Minimum mean square error (MMSE), MIMO System, Spatial Modulation, Spatial Multiplexing, Zero Forcing (ZF).

MMSE SQRD based SISO detection for coded MIMO-OFDM systems

In this paper, we propose a minimum mean square error (MMSE) sorted QR decomposition (SQRD) based soft-input soft-output (SISO) detection algorithm for coded multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The proposed detection is derived from the SISO MMSE detection, which is a popular detection strategy for iterative receivers. For each transmitted symbol in the proposed detection, a soft successive interference cancellation (SIC) is performed based on a posteriori probabilities of past detected symbols. Simulation results show that the proposed detection, while needing less computational efforts, achieves significant performance gain compared with the SISO MMSE detection.

A hybrid multiuser detector based on MMSE and AFSA for TDRS system forward link.

This study mainly focuses on multiuser detection in tracking and data relay satellite (TDRS) system forward link. Minimum mean square error (MMSE) is a low complexity multiuser detection method, but MMSE detector cannot achieve satisfactory bit error ratio and near-far resistance, whereas artificial fish swarm algorithm (AFSA) is expert in optimization and it can realize the global convergence efficiently. Therefore, a hybrid multiuser detector based on MMSE and AFSA (MMSE-AFSA) is proposed in this paper. The result of MMSE and its modified formations are used as the initial values of artificial fishes to accelerate the speed of global convergence and reduce the iteration times for AFSA. The simulation results show that the bit error ratio and near-far resistance performances of the proposed detector are much better, compared with MF, DEC, and MMSE, and are quite close to OMD. Furthermore, the proposed MMSE-AFSA detector also has a large system capacity.

Frequency-Domain Equalization of Faster-than-Nyquist Signaling

In this letter, motivated by the recent rediscovery of faster-than-Nyquist (FTN) signaling transmissions, we conceive a frequency-domain equalization (FDE)-assisted FTN receiver architecture, which is capable of attaining a low demodulating complexity. The proposed scheme is especially beneficial for a long channel tap FTN scenario. More specifically, in our scheme the resultant inter-symbol interference imposed by FTN signaling is approximated by a finite-tap circulant matrix structure, which allows us to employ an efficient fast Fourier transform operation and a low-complexity channel-inverse-based minimum mean-square error detection algorithm. Our simulation results demonstrate that the proposed scheme is capable of attaining a near-optimal error-rate performance without imposing any substantial demodulating complexity as well as power penalty.

A maximum-likelihood bound approaching minimum bit error rate linear multiuser detector for frequency-selective DS-CDMA systems

In this letter, a minimum bit error rate (MBER) linear multiuser detector (MUD) is considered for direct-sequence code-division multiple-access (DS-CDMA) communication systems, distorted by time-varying and frequency-selective multipath fading channels. Based on the approach for finding filter coefficients of the proposed MBER MUD, an efficient Newton method with a barrier parameter is developed. The BER performance of the MBER MUD is compared to other conventional detectors. The study finds that the proposed MBER MUD has more than 2dB gain over the linear minimum mean-squared error (LMMSE) detector. Furthermore, in the high SNR region, the BER performance of the proposed MBER MUD approaches the performance of the maximum-likelihood (ML) detector.