MMSE Receiver Research Articles

New Insights Into Widely Linear MMSE Receivers for Communication Networks Using Data-Like Rectilinear or Quasi-Rectilinear Signals

New Insights Into Widely Linear MMSE Receivers for Communication Networks Using Data-Like Rectilinear or Quasi-Rectilinear Signals

Neural-Network-Based Equalization and Detection for Underwater Acoustic Orthogonal Frequency Division Multiplexing Communications: A Low-Complexity Approach

The performance of the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) system is often restrained by time-varying channels with large delays. The existing frequency domain equalizers do not work well because of the high complexity and difficulty of finding the real-time signal-to-noise ratio. To solve these problems, we propose a low-complexity neural network (NN)-based scheme for joint equalization and detection. A simple NN structure is built to yield the detected symbols with the joint input of the segmented channel response and received symbol. The coherence bandwidth is investigated to find the optimal hyperparameters. By being completely trained offline with real channels, the proposed detector is applied independently in both simulations and sea trials. The results show that the proposed detector outperforms the ZF and MMSE equalizers and extreme learning machine (ELM)-based detectors in both the strongly reflected channels of the pool and time-variant channels of the shallow sea. The complexity of the proposed network is lower than the MMSE and ELM-based receiver.

5G NOMA Defense Application Environment and Stacked LSTM Network Architectures

In 5G and beyond 5G wireless communication networks, the NOMA scheme is widely considered a major non-orthogonal access technique for improving system capacity and data rates. The main challenges in current NOMA systems are limited channel feedback and the difficulty of integrating it with advanced adaptive coding and modulation algorithms. This study analyses S-LSTM-based DL NOMA receivers in i.i.d. Nakagami-m fading channel circumstances as opposed to previously presented solutions. The LSTM has the advantage of responding dynamically to changing channel conditions. When compared to a typical NOMA system, a typical NOMA system has a 12% lower outage probability, a 39% increase in net throughput, and a maximum SER reduction of 48%. Complex modulated M-ary PSK and M-ary QAM data symbols are employed in D/L NOMA transmission. Classic receivers such as LS and MMSE are outperformed by the S-LSTM-based DL-NOMA receiver. The CP and non-linear clipping noise simulation curves compare the performance of the MMSE and LS receivers with that of the DL NOMA receiver in real-time propagation circumstances. The DL-based detector outperforms the MMSE for SNRs greater than 15 dB because the S-LSTM method is more robust than the clipping noise.

Performance of mMIMO FD Relay Networks With Limited Relay State Knowledge

Massive MIMO (mMIMO) is a key technology for improving propagation conditions and extending geographical coverage of wireless communications. We here address a mMIMO full-duplex relay network for machine-type-communications where channel state information availability at the transmitter is impractical. In this scenario, we argue that high end-to-end data rates can be achieved even if no precoding is performed at the transmitting nodes. We first formulate an optimization problem aiming at maximizing the achievable rate, considering the source transmit power to depend on the transmit power distribution at the relay node. We then solve this problem by letting the number of antennas grow large, and derive closed-form expressions for the transmit power at the source and relay, as well as for the system data rate. Our results, show that the rate obtained when no precoding is implemented at the relay, or at any of the transmitters, closely matches that of SVD precoding under the optimum receiver, and still achieves very high values in the case of the ZF and the MMSE receiver.

Jamming-Assisted Proactive Eavesdropping Over Two Suspicious Communication Links

This paper studies a new and challenging wireless surveillance problem where a legitimate monitor attempts to eavesdrop two suspicious communication links simultaneously. To facilitate concurrent eavesdropping, our multi-antenna legitimate monitor employs a proactive eavesdropping via jamming approach, by selectively jamming suspicious receivers to lower the transmission rates of the target links. In particular, we are interested in characterizing the achievable eavesdropping rate region for the minimum-mean-squared-error (MMSE) receiver case, by optimizing the legitimate monitor's jamming transmit covariance matrix subject to its power budget. As the monitor cannot hear more than what suspicious links transmit, the achievable eavesdropping rate region is essentially the intersection of the achievable rate region for the two suspicious links and that for the two eavesdropping links. The former region can be purposely altered by the monitor's jamming transmit covariance matrix, whereas the latter region is fixed when the MMSE receiver is employed. Therefore, we first analytically characterize the achievable rate region for the two suspicious links via optimizing the jamming transmit covariance matrix and then obtain the achievable eavesdropping rate region for the MMSE receiver case. In addition, we also consider the MMSE with successive interference cancellation (MMSE-SIC) receiver case and characterize the corresponding achievable eavesdropping rate region by jointly optimizing the time-sharing factor between different decoding orders. Furthermore, extensions to the imperfect channel state information case and the more than two suspicious links scenario are also examined. Finally, numerical results are provided to corroborate our analysis and evaluate the eavesdropping performance.

Subset MMSE Receivers for Cell-Free Networks

This paper formulates linear MMSE receivers that are both network- and user-centric for the uplink of cell-free wireless networks with centralized processing. Precisely, every user’s reception involves a distinct subset of access points (APs) while every AP participates in the reception of a distinct subset of users, hence the moniker subset MMSE receivers . These subsets, defined on the basis of the large-scale channel gains between users and APs, capture the most relevant signal and interference contributions while disregarding those whose processing is cost-ineffective and whose associated channel estimations would incur unnecessary overheads. With that, subset reception approaches the performance of network-wide MMSE reception, offering a multiple-fold improvement over cellular and matched-filtering counterparts, while being scalable in terms of cost and channel estimation. Moreover, because the subsets overlap considerably, they can sometimes be advantageously combined and the computation of the corresponding receivers can share a hefty amount of processing.

Optimal Power Allocation and Training Duration for Uplink Multiuser Massive MIMO Systems With MMSE Receivers

This paper investigates the optimal training duration and the optimal power allocation for the training and the data transmission that maximize the ergodic sum rate in single-cell uplink massive MIMO with MMSE receivers. Our channel model assumes that each user experiences the same spatial channel correlation. The expression for the ergodic sum rate is obtained in the large system regime where the number of antennas ( $N$ ) at the base station and the number of users ( $K$ ) tend to infinity with a fixed ratio. Interestingly, we show that the optimal training duration is equal to $K$ and independent of the spatial correlation. We also derive the optimal power allocation that in facts depends on the spatial correlation, the channel coherence interval, and the uplink SNR. We show that more energy should be allocated for the training if the data transmission duration ( $t_{d}$ ) is less than $K$ , and vice versa. Moreover, equal power allocation is optimal when $t_{d}=K$ . We also obtain an approximation for the optimal power allocation that depends on the mean of the correlation matrix eigenvalues. Numerical simulations show that our results based on the large system approximation are accurate and applicable for finite-size systems. The simulations also show that (1) the resulting ergodic sum rates obtained by employing the optimal power allocation and its approximation are indistinguishable, and (2) the optimal power allocation obtained from the uncorrelated channel model can be applied to the cases involving the correlated channels with indiscernible penalties on the ergodic sum rates.

Design of QAM-FBMC Waveforms Considering MMSE Receiver

Due to its high spectral confinement characteristics and spectral efficiency, QAM-FBMC is considered a candidate waveform to replace CP-OFDM. QAM-FBMC has inevitable non-orthogonality both in time and frequency, and the system and filter must be well-designed to minimize the interferences. However, existing QAM-FBMC studies utilize a matched filter as the receiver filter, which is not suitable for a non-orthogonal system. Therefore, in this paper, we design the prototype filters considering the MMSE criterion, and propose a system providing the highest SINR in QAM-FBMC which cannot avoid non-orthogonality. In addition, we confirm that the proposed filters show best performance at target SNR than the reference filters.

Performance Analysis of Hardware Impairment Aware MMSE Receiver With Channel and CFO Estimation Error Statistics for a Large MIMO-OFDM System

In this treatise, we conceive a hardware impairment aware receiver design of a large multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, taking into account the error statistics of parameter estimations. The hardware impairment includes the quantization noise, phase noise etc. There are two key contributions in this work. Firstly, consideration of error statistics of residual parameters in the receiver design improves receiver performance. In this work, we propose a linear equalizer based data detector at the receiver for a large MIMO-OFDM system and the parameters of interest are the channel impulse response (CIR) and carrier frequency offset (CFO) along with the hardware impairments awareness both at transmitter and receiver. The design criterion chosen for designing the detector equalizer is based on the linear minimum mean square error (LMMSE) one and it will consider the statistics of estimation error and hardware impairments. However, in any practical communication system, the availability of statistics for these parameter errors is inconceivable. Hence, we propose further to consider the Bayesian Crammer Rao lower bound (BCRLB) as the variance of the error with the key assumption of zero mean. Numerical simulation demonstrates that, consideration of such statistics attains an SNR gain of $2$ dB with respect to a fixed symbol error ratio (SER). It also shows that the SER performance with BCRLB matches very closely with the case, when exact error variance is used. For the second contribution, an extensive theoretical analysis has been performed to evaluate the MSE improvement of data detection with the LMMSE criterion with parameter estimation error statistics consideration in the large MIMO-OFDM system. This theoretical analysis of improved MSE has been conceived with the usage of large dimension random matrix theory and a closed-form expression has been obtained. Numerical simulation demonstrates that the theoretical analysis for MSE improvement matches closely with the simulated one.

Fast Beamforming Design via Deep Learning

Beamforming is considered as one of the most important techniques for designing advanced multiple-input and multiple-output (MIMO) systems. Among existing design criterions, sum rate maximization (SRM) under a total power constraint is a challenge due to its nonconvexity. Existing techniques for the SRM problem only obtain local optimal solutions but require huge amount of computation due to their complex matrix operations and iterations. Unlike these conventional methods, we propose a deep learning based fast beamforming design method without complex operations and iterations. Specifically, we first derive a heuristic solution structure of the downlink beamforming through the virtual equivalent uplink channel based on optimum MMSE receiver which separates the problem into power allocation and virtual uplink beamforming (VUB) design. Next, beamforming prediction network (BPNet) is designed to perform the joint optimization of power allocation and VUB design. Moreover, the BPNet is trained offline using two-step training strategy. Simulation results demonstrate that our proposed method is fast while obtains the comparable performance to the state-of-the-art method.

Accurate Performance Analysis of Coded Large-Scale Multiuser MIMO Systems with MMSE Receivers

In this paper, we estimate the uplink performance of large-scale multi-user multiple-input multiple-output (MIMO) networks. By applying minimum-mean-square-error (MMSE) detection, a novel statistical distribution of the signal-to-interference-plus-noise ratio (SINR) for any user is derived, for path loss, shadowing and Rayleigh fading. Suppose that the channel state information is perfectly known at the base station. Then, we derive the analytical expressions for the pairwise error probability (PEP) of the massive multiuser MMSE–MIMO systems, based on which we further obtain the upper bound of the bit error rate (BER). The analytical results are validated successfully through simulations for all cases.

Coverage and Cell-Edge Sum-Rate Analysis of mmWave Massive MIMO Systems With ORP Schemes and MMSE Receivers

In this study, we consider the downlink of millimeter-wave massive multiple-input multiple-output systems that employ orthogonal random precoding (ORP) and minimum-mean-square-error (MMSE) receivers. In the ORP scheme, a precoding matrix consisting of orthogonal vectors is utilized at the transmitter, which provides beamforming gains to enhance the maximum signal-to-interference-plus-noise ratio (SINR) at the receivers. In this study, the ability of the ORP scheme with MMSE receivers to extend the cell coverage and its sum-rate performance for cell-edge users are investigated. In particular, we first derive the approximate distribution of the maximum SINR at the output of the MMSE receiver. Then, to analyze and optimize the ORP scheme with MMSE receivers in terms of coverage and sum-rate performance, the analytical expressions for the downlink coverage probability and sum rate are derived. It is shown that there is a tradeoff between coverage and sum-rate performance in the ORP scheme. In particular, a smaller number of precoding vectors provides larger coverage; however, it leads to a lower sum rate. To achieve optimal tradeoff between coverage and sum rate for the ORP scheme, we propose using multiple random precoder groups over multiple time slots. It is shown that the proposed scheme is capable of significantly enhancing coverage performance while preserving an acceptable sum rate for cell-edge users. The simulation results validate the analytical findings.

Asymptotic analysis for low-resolution massive MIMO systems with MMSE receiver

The uplink achievable rate of massive multiple- input-multiple-output (MIMO) systems, where the low-resolution analog-to-digital converters (ADCs) are assumed to equip at the base station (BS), is investigated in this paper. We assume that only imperfect channel station information is known at the BS. Then a new MMSE receiver is designed by taking not only the Gaussian noise, but also the channel estimation error and quantizer noise into account. By using the Stieltjes transform of random matrix, we further derive a tight asymptotic equivalent for the uplink achievable rate with proposed MMSE receiver. We present a detailed analysis for the number of BS antennas through the expression of the achievable rates and validate the results using numerical simulations. It is also shown that we can compensate the performance loss due to the low-resolution quantization by increasing the number of antennas at the BS.

Bit Error Probability for MMSE Receiver in GFDM Systems

In this letter, we consider the minimum mean-square error receiver for the generalized frequency division multiplexing system (GFDM) over frequency selective fading channels. We derive an approximate probability density function for the signal-to-interference-plus-noise ratio. This expression allows us to obtain a new approximate, but rather accurate formulation for the bit error probability for a $\mathcal {M}$ -quadrature amplitude modulation scheme. Our results resort on the pivotal properties exhibited by eigenvalues of a circulant matrix. Since the entries of the channel matrix $\text {H}_{\text {ch}}$ are complex Gaussian distributed, and the eigenvalues are given as a weighted sum of its entries, the joint eigenvalue distribution is also Gaussian. Comparisons of the simulated and analytical results validate our formulation and allow a quick and efficient tool to compute the bit error rate for the GFDM system.

Optimum low complexity filter bank for generalized orthogonal frequency division multiplexing

Generalized frequency division multiplexing (GFDM) is one of the multicarrier modulation candidates proposed for the 5th generation of wireless networks. Among GFDM linear receivers, GFDM MMSE receiver achieves the best error performance for multipath fading channels at the cost of high numerical complexity. Hence, the combination of GFDM match filter (MF) receiver and double-side successive interference cancellation (DSIC) method is used instead. However, there is a significant gap between the error performance of GFDM MMSE and DSIC/MF receivers for the case of employing modern channel coding. Recently, we have proposed a new multicarrier scheme based on GFDM architecture called generalized orthogonal frequency division multiplexing (GOFDM). This study derives an optimized cyclic tree-structured perfect reconstruction-quadrature mirror filter (PR-QMF) bank for GOFDM transceiver and then introduces a novel method for implementation of the optimum filter bank in the frequency domain. Employing such a fast and optimum filter bank provides several advantages for GOFDM transceiver. GOFDM transmitter mitigates out-of-band spectrum leak to the level of that of GFDM. In addition, choosing an appropriate configuration of filter bank yields lower peak to average power ratio in transmit signal of GOFDM compared to that of OFDM. On the other hand, while GOFDM MMSE receiver has lower numerical complexity compared with GFDM DSIC/MF receiver, its coded bit error rate curve is close to that of GFDM MMSE receiver. The aforementioned advantages envision GOFDM as a competitive candidate to be employed in the physical layer of new wireless applications.

Performance of image transmission over MC-CDMA based on super resolution technique

Multi-carrier code-division-multiple-access (MC-CDMA) is a promising technique to obtain high data rate in wireless communication. Contemplation of medical image transmission for various patient’s information using MC-CDMA system through wireless media is discussed. Arnold cat map encryption algorithm is ensured to enhance the image transmission securely. At each mobile station, transmitted bit stream of encrypted images is estimated using minimum-mean-square error (MMSE) algorithm. The picture quality is ensured at the receiver by adopting super resolution through sparse technique. The performance of considered system through stanford channel model specification is illustrated. PSNR metric is also considered for image transmission. From the analysis, it is observed that considered MC-CDMA system with encryption algorithm and sparse based super resolution technique mitigates multi-user interference effects while retaining the quality of individual medical images. Further, it is witnessed that the channel encoded proposed system’s performance achieves the promising bit-error-rate for MMSE receiver. Furthermore, from the simulation it is discerned that the computational time for super resolution is minimized using considered sparse technique.

Spectral Efficiency of Massive MIMO Systems With Low-Resolution ADCs and MMSE Receiver

This letter considers an uplink multi-user massive multi-input multi-output (MIMO) system with non-uniform low-resolution analog-to-digital converters (ADCs) and minimum mean-square error receivers at the base station side. Additive quantization noise model is utilized to measure the effect of finite ADC resolution. Non-uniform quantization brings difficulty in obtaining the asymptotic equivalent expression of the spectral efficiency. Based on the random matrix theory, a closed-form asymptotic equivalent expression is derived. Numerical results show the tightness of the asymptotic equivalent. It also shows that massive antennas are able to compensate for the loss of low-resolution quantization, implying the capability of low-resolution ADCs in massive MIMO systems.

Error performance analysis for generalized orthogonal frequency division multiplexing

Generalized Frequency Division Multiplexing (GFDM) is a cyclic filtered multicarrier modulation that may be employed for many new wireless applications. However, due to its non-orthogonal structure, a trade-off between the complexity and error performance should be considered in the design of GFDM receivers. This study proposes an orthogonal cyclic filtered multicarrier modulation called Generalized Orthogonal Frequency Division Multiplexing (GOFDM), which is based on the cyclic Perfect Reconstruction-Quadrature Mirror Filter (PR-QMF) bank. We first derive the frequency domain matrix descriptions for GOFDM linear receivers based on which, the impact of PR-QMF bank on the GOFDM error performance has been theoretically analyzed. Furthermore, the error performance of GOFDM and GFDM linear receivers are compared for AWGN and multipath fading channels. As shown through simulations, GOFDM MMSE receiver outperforms GFDM receiver where the performance gap is significant in case of low-order QAM constellations and multipath fading channels.

EM-Based Phase Noise Estimation in Vector OFDM Systems Using Linear MMSE Receivers

Vector orthogonal frequency-division multiplexing (V-OFDM) for single-transmit-antenna systems is a generalization of OFDM where single-carrier frequency-domain equalization and OFDM are just two special cases. Phase noise in a V-OFDM system leads to a common vector block phase error (CVBPE) and an intervector block carrier interference effect. Severe performance degradation may occur if these two effects are not estimated and compensated well. In this paper, blind and semiblind phase noise estimation and compensation in a V-OFDM system is investigated by using the expectation-maximization (EM) algorithm. This is motivated by the fact that the conventional frequency-domain phase noise suppression schemes based on pilot-aided common phase error (CPE) or CVBPE estimation and compensation are not spectrally efficient as the vector block size is increased. Two novel schemes are proposed: One estimates the CVBPE only, and the other estimates the entire phase noise sequence in the time domain. General closed-form formulas for the maximization step of the EM algorithm for the two schemes are derived, and their computational complexity values are analyzed. The performances of the two schemes are investigated by using linear-minimum-mean-square-error (LMMSE) receivers. Simulations show that the two proposed schemes are very effective in estimating and compensating for phase noise in V-OFDM systems. It turns out that the second proposed scheme not only outperforms the traditional CPE or CVBPE schemes but is computationally efficient as well when applied to V-OFDM systems.

Iterative Robust MMSE Receiver for STBC under Channel Information Errors

Iterative Robust MMSE Receiver for STBC under Channel Information Errors