Performance Of Minimum Mean Square Error Research Articles

Analysis of an LSTM-based NOMA Detector Over Time Selective Nakagami-m Fading Channel Conditions

This work examines the efficacy of deep learning (DL) based non-orthogonal multiple access (NOMA) receivers in vehicular communications (VC). Analytical formulations for the outage probability (OP), symbol error rate (SER), and ergodic sum rate for the researched vehicle networks are established Rusing i.i.d. Nakagami-m fading links. Standard receivers, such as least square (LS) and minimum mean square error (MMSE), are outperformed by the stacked long-short term memory (S-LSTM) based DL-NOMA receiver. Under real time propagation circumstances, including the cyclic prefix (CP) and clipping distortion, the simulation curves compare the performance of MMSE and LS receivers with that of the DL-NOMA receiver. According to numerical statistics, NOMA outperforms conventional orthogonal multiple access (OMA) by roughly 20% and has a high sum rate when considering i.i.d. fading links.

Efficient iterative massive MIMO detection using Chebyshev acceleration

Massive multiple-input multiple-output (MIMO) detection is one of the most important, yet complex parts of the fifth generation (5G) baseband receiver. The linear minimum mean square error (MMSE) signal detection achieves almost optimum efficiency when the number of antennas at the base station is asymptotically large. However, the matrix inversion required for MMSE can also be very complex when the number of users increases. In this paper, a low complexity signal detection algorithm based on modified accelerated overrelaxation (MAOR) method is proposed to iteratively approach the MMSE performance. We calculate optimal values of two key parameters of MAOR and also provide a suitable and less complex initial solution to accelerate the convergence. Furthermore, we adopt the Chebyshev polynomial acceleration technique to present the MAOR method with a new vector combinations, which enhances the performance of the detection algorithm. The spectral radius of MAOR is also calculated to demonstrate its suitability for Chebyshev acceleration. This complete solution is referred to as Chebyshev-MAOR. The results have revealed that the proposed method can achieve faster convergence and better performance than other state-of-the-art detection algorithms. It is also shown that Chebyshev-MAOR reduces computational complexity by an order of magnitude from O(K3) to O(K2), with K denoting the number of transmit antennas. Our performance results show that these complexity gains are achieved with negligible impact on the bit error rate (BER) performance.

Low-Complexity Detectors for Uplink Massive MIMO Systems Leveraging Truncated Polynomial Expansion

In this work, we propose low-complexity detectors for massive multiple-input multiple-output (MIMO) systems. Particularly, we leverage variants of truncated polynomial expansion (TPE) in order to reduce the computational complexity of the signal detection in the uplink direction. Linear detectors such as zero-forcing (ZF) and minimum mean square error (MMSE) involve expensive matrix-matrix multiplication and matrix inversion operations. TPE-based detectors are appropriate candidates for approximating these linear detectors. However, tuning the normalization factor of TPE-based detectors may require calculating the minimum and the maximum eigenvalues of the channel Gram matrix. These calculations become computationally expensive for some massive MIMO systems, especially for systems with a large ratio of single-antenna user terminals to the number of antennas at the base station, i.e., loading factor. We propose to tune the normalization factor using appropriate approximations for the extreme eigenvalues. The proposed TPE-based detectors exhibit a bit error performance similar to that of the TPE-based detector with the optimal normalization factor. Moreover, our proposed detectors achieve the error performance of ZF and MMSE for different loading factors of spatially correlated and uncorrelated massive MIMO channels. The computational complexity of the proposed detector is proportional to the number of base station antennas and the number of users.

Joint Transmit and Reflective Beamformer Design for Secure Estimation in IRS-Aided WSNs

Wireless sensor networks (WSNs) are vulnerable to eavesdropping as the sensor nodes (SNs) communicate over an open radio channel. Intelligent reflecting surface (IRS) technology can be leveraged for physical layer security in WSNs. In this letter, we propose a joint transmit and reflective beamformer (JTRB) design for secure parameter estimation at the fusion center (FC) in the presence of an eavesdropper (ED) in a WSN. We develop a semidefinite relaxation (SDR)-based iterative algorithm, which alternately yields the transmit beamformer at each SN and the corresponding reflection phases at the IRS, to achieve the minimum mean-squared error (MSE) parameter estimate at the FC, subject to transmit power and ED signal-to-noise ratio constraints. Our simulation results demonstrate robust MSE and security performance of the proposed IRS-based JTRB technique.

An Efficient Massive MIMO Detector Based on Second-Order Richardson Iteration: From Algorithm to Flexible Architecture

Aiming at reducing the complexity of minimum mean square error (MMSE) detection in massive multiple-input multiple-output (MIMO) systems, this paper proposes a detection algorithm with high convergence rate and an efficient hardware architecture based on second-order Richardson iteration (SORI). In the proposed algorithm, a pre-iteration-based initialization method is presented to accelerate the convergence without extra complexity. In addition, the approximation of relaxation factor and the log-likelihood ratio (LLR) is introduced to further reduce computing load. Theoretical analysis demonstrates the advantages of the proposed algorithm in fast convergence and low complexity, and simulation results show that the proposed algorithm can efficiently approach MMSE performance. Based on this algorithm, a flexible hardware architecture is designed, which is deeply pipelined to support 128 × U (8 ≤ U ≤ 32 ) massive MIMO detection with the configurable number of iterations, and a folded dual-mode systolic array (DMSA) is fully utilized to achieve the flexibility with low hardware consumption. Implemented on Xilinx Virtex-7 FPGA and SMIC 40nm CMOS technology, the proposed detector is competitive in terms of energy and area efficiency compared to state-of-the-art iterative detectors, and it can adapt to the varied channel condition and the number of users in massive MIMO systems.

Performance improvement of space diversity technique using space time block coding for time varying channels in wireless environment

Performance improvement of space diversity technique using space time block coding for time varying channels in wireless environment

Efficient Successive Over Relaxation Detectors for Massive MIMO

Massive multiple-input and multiple-output (MIMO) is considered as an advanced technique in wireless communication due to its high spectral efficiency, data rates, and transmission reliability. However, the large number of antennas makes it challenging to design efficient detectors since computational complexity is much higher. Thus, conventional linear methods like minimum mean square error (MMSE) detection suffer from prohibitive complexity. To balance complexity and performance, a class of iterative linear methods are considered to approach MMSE performance with $\mathcal {O}({N_{T}}^{2})$ complexity, where $N_{T}$ is the number of transmit antennas. Among them, successive over relaxation (SOR) detector is promising since it achieves near MMSE performance with affordable complexity and fast convergence. However, error performance of previously proposed SOR detectors is sensitive to a relaxation factor $\omega $ , especially when the channel varies. To address this issue, two detectors are proposed in this paper: non-adaptive SOR (NA-SOR) detector (with fixed $\omega $ ) and adaptive SOR (A-SOR) detector (with iteratively changed $\omega $ ). Compared to prior SOR detectors, the performance of the NA-SOR detector is more robust to $\omega $ , and the A-SOR detector achieves better performance, especially in highly correlated channels. An efficient pipelined hardware architecture of the A-SOR detector is proposed. Implementation results show advantages when compared to the state-of-the-art (SOA).

Low‐complexity signal detection for large‐scale MIMO systems with second‐order Richardson method

Linear minimum mean-square error (MMSE) detection achieves near-optimal performance in large-scale multiple-input multiple-output (LS-MIMO) systems but entails high computational complexity due to large matrix inversion operations. In this Letter, a novel computationally efficient algorithm based on second-order Richardson method is proposed to solve the LS-MIMO detection problem. While no a priori information for the first iteration of the second-order Richardson method is available, the conjugate gradient scheme is exploited that greatly reduces the number of iterations to achieve the desired performance. Moreover, the eigenvalue-based acceleration parameters are proposed to further accelerate the convergence rate. Numerical results demonstrate that the proposed detector outperforms the existing methods and approaches the performance of MMSE with a small number of iterations.

A Pragmatic Approach to Massive MIMO for Broadband Communication Satellites

In this paper, we analyze the performance of Massive Multiple Input Multiple Output (M-MIMO) techniques aiming at increasing the throughput of broadband satellites. In particular, we investigate a “pragmatic” approach to the design of the M-MIMO to ease its implementation both at system and satellite payload level. We compare the performance of optimized classical Minimum Mean Square Error (MMSE), Zero Forcing (ZF), Matched Filter (MF) schemes with the proposed “pragmatic” M-MIMO one dubbed fixed Multi-Beam (MB). To further boost the M-MIMO performance, a novel radio resource management approach based on Mixed Integer Quadratic Programming (MIQDP-RRM) is proposed. The adoption of MIQDP-RRM is shown to greatly enhance the M-MIMO throughput performance. It is shown that the MB scheme closely approximate the MF, ZF and MMSE performance with a much simpler active antenna-based payload architecture and without requiring any user channel estimation. The MB MIQDP-RRM M-MIMO pragmatic solution allows to achieve higher satellite broadband throughput compared to a conventional four colors frequency reuse scheme (CFR) with affordable complexity for both space and ground segments. At the same time we show that by non-conventional CFR multi-beam array design, the performance gap compared to MB MIQDP-RRM M-MIMO can be significantly reduced.

A Comprehensive Review on Channel Estimation in OFDM System

In wireless communication, orthogonal frequency division multiplexing (OFDM) plays a major role because of its high transmission rate. Channel estimation and tracking have many different techniques available in OFDM systems. Among them, the most important techniques are least square (LS) and minimum mean square error (MMSE). In least square channel estimation method, the process is simple but the major drawback is it has very high mean square error. Whereas, the performance of MMSE is superior to LS in low SNR, its main problem is it has high computational complexity. If the error is reduced to a very low value, then an exact signal will be received. In this paper an extensive review on different channel estimation methods used in MIMO-OFDM like pilot based, least square (LS) and minimum mean square error method (MMSE) and least minimum mean square error (LMMSE) methods and also other channel estimation methods used in MIMO-OFDM are discussed.

DE/PSO‐aided hybrid linear detectors for MIMO‐OFDM systems under correlated arrays

In this paper, we analyze the performance of evolutionary heuristic-aided linear detectors deployed in Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency-Division Multiplexing (OFDM) systems, considering realistic operating scenarios. Hybrid linear-heuristic detectors under different initial solutions provided by linear detectors are considered, namely differential evolution (DE) and particle swarm optimization (PSO). Numerical results demonstrated the applicability of hybrid detection approach, which can improve considerably the performance of minimum mean-square error (MMSE) and matched filter (MF) detectors. Furthermore, we discuss how the complexity of the presented algorithms scales with the number of antennas, besides of verifying the spatial correlation effects on MIMO-OFDM performance assisted by linear, heuristic and hybrid detection schemes. The influence of the initial point in the performance improvement and complexity reduction is evaluated numerically.

Genetic Grey Wolf Optimizer Based Channel Estimation in Wireless Communication System

Various methods are available for channel estimation in the orthogonal frequency division multiplexing and orthogonal frequency and code division multiplexing (OFCDM) based wireless communication schemes. Along with this, the most utilized techniques are namely the minimum mean square error (MMSE) and least square (LS). The process of LS channel estimation method is simple but it occupies a very high mean square error. On the other hand, the performance of MMSE is better than LS in terms of SNR, though it shows high computational complexity. Compared to MMSE and LS based techniques, the combination of MMSE and LS techniques using evolutionary programming reduces the error significantly to receive exact signal. In this study, we propose a hybrid method namely GGWO that includes grey wolf optimization (GWO) and genetic algorithms (GA) for estimate the channel in MIMO–OFCDM schemes. At first, the best channel is estimated using GWO and afterwards, the MMSE and LS are hybridized through GA for calculating the best channel to decrease error. Overall, the GWO and GA contribute in fine tuning the obtained channel scheme so that the channel model is derived further to correlate with the ideal scheme. Our results demonstrate that the proposed scheme is superior to conventional MMSE and LS in terms of BER and SNR.

A survey on OFDM channel estimation techniques based on denoising strategies

Channel estimation forms the heart of any orthogonal frequency division multiplexing (OFDM) based wireless communication receiver. Frequency domain pilot aided channel estimation techniques are either least squares (LS) based or minimum mean square error (MMSE) based. LS based techniques are computationally less complex. Unlike MMSE ones, they do not require a priori knowledge of channel statistics (KCS). However, the mean square error (MSE) performance of the channel estimator incorporating MMSE based techniques is better compared to that obtained with the incorporation of LS based techniques. To enhance the MSE performance using LS based techniques, a variety of denoising strategies have been developed in the literature, which are applied on the LS estimated channel impulse response (CIR). The advantage of denoising threshold based LS techniques is that, they do not require KCS but still render near optimal MMSE performance similar to MMSE based techniques. In this paper, a detailed survey on various existing denoising strategies, with a comparative discussion of these strategies is presented.

Unitary Precoding and Basis Dependency of MMSE Performance for Gaussian Erasure Channels

We consider the transmission of a Gaussian vector source over a multidimensional Gaussian channel where a random or a fixed subset of the channel outputs are erased. Within the setup where the only encoding operation allowed is a linear unitary transformation on the source, we investigate the minimum mean-square error (MMSE) performance, both in average, and also in terms of guarantees that hold with high probability as a function of the system parameters. Under the performance criterion of average MMSE, necessary conditions that should be satisfied by the optimal unitary encoders are established and explicit solutions for a class of settings are presented. For random sampling of signals that have a low number of degrees of freedom, we present MMSE bounds that hold with high probability. Our results illustrate how the spread of the eigenvalue distribution and the unitary transformation contribute to these performance guarantees. The performance of the discrete Fourier transform (DFT) is also investigated. As a benchmark, we investigate the equidistant sampling of circularly wide-sense stationary signals, and present the explicit error expression that quantifies the effects of the sampling rate and the eigenvalue distribution of the covariance matrix of the signal. These findings may be useful in understanding the geometric dependence of signal uncertainty in a stochastic process. In particular, unlike information theoretic measures such as entropy, we highlight the basis dependence of uncertainty in a signal with another perspective. The unitary encoding space restriction exhibits the most and least favorable signal bases for estimation.

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).

Channel Estimation of MIMO–OFDM System Using PSO and GA

In wireless communication, multiple input multiple output-orthogonal frequency division multiplexing (MIMO–OFDM) plays a major role because of its high transmission rate. Channel estimation and tracking have many different techniques available in OFDM systems. Among them, the most important techniques are least square (LS) and minimum mean square error (MMSE). In least square channel estimation method, the process is simple but the major drawback is it has very high mean square error. Whereas, the performance of MMSE is superior to LS in low SNR, its main problem is it has high computational complexity. While comparing with LS and MMSE method individually, the combined LS and MMSE method using evolutionary programming can greatly reduce the error. If the error is reduced to a very low value, then an exact signal will be received. Thus, we propose a hybrid technique that includes particle swarm optimization (PSO) and genetic algorithm (GA) for channel estimation in MIMO–OFDM systems. The technique performs the conventional LS and MMSE channel estimation followed by enabling a fine tuning on the obtained channel model. The PSO and GA contribute in fine tuning the obtained channel model so that the channel model is derived further to correlate with the ideal model. The result shows the performance of the proposed method is better than LS and MMSE method in all the mutation and crossover values and also in all the iterations computed. The performance of OFDM systems using proposed technique can be observed from the imitation and relative results.

Low-Complexity Near-Optimal Decoding for Analog Joint Source Channel Coding Using Space-Filling Curves

Analog Joint Source-Channel Coding (JSCC) is a communication strategy that does not follow the separation principle of conventional digital systems but approaches the optimal distortion-cost tradeoff over AWGN channels. Conventional Maximum Likelihood (ML) analog JSCC decoding schemes suffer performance degradation at low Channel Signal to Noise Ratio (CSNR) values, while Minimum Mean Square Error (MMSE) decoding presents high complexity. In this letter we propose an alternative two step decoding approach which achieves the near-optimal performance of MMSE decoding at all CSNR values while maintaining a low complexity comparable to that of ML decoding. An additional advantage of the proposed analog JSCC decoding approach is that it can also be used in Multiple Input Multiple Output (MIMO) fading channels.

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the link between the discrete gradient and Haar-wavelet shrinkage with cycle spinning. The redundancy of the representation implies that some wavelet-domain estimates are inconsistent with the underlying signal model. However, by imposing additional constraints, our method finds wavelet-domain solutions that are mutually consistent. We confirm the MMSE performance of our method through statistical estimation of Levy processes that have sparse derivatives.

Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?

We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.

MMSE Performance Analysis of Generalized Multibeam Satellite Channels

Aggressive frequency reuse in the return link (RL) of multibeam satellite communications (SatComs) is crucial towards the implementation of next generation, interactive satellite services. In this direction, multiuser detection has shown great potential in mitigating the increased intrasystem interferences, induced by a tight spectrum reuse. Herein we present an analytic framework to describe the linear Minimum Mean Square Error (MMSE) performance of multiuser channels that exhibit full receive correlation: an inherent attribute of the RL of multibeam SatComs. Analytic, tight approximations on the MMSE performance are proposed for cases where closed form solutions are not available in the existing literature. The proposed framework is generic, thus providing a generalized solution straightforwardly extendable to various fading models over channels that exhibit full receive correlation. Simulation results are provided to show the tightness of the proposed approximation with respect to the available transmit power.