Minimum Mean Square Error Receiver Research Articles

Spectral decomposition-based optimization for MMSE receiver design in an uplink MU-MIMO cooperative communication system with imperfect CSI

The receiver’s architecture is always a critical issue in multiple-input multiple-output (MIMO) systems, as it has a great impact on the system’s performance and complexity. Accordingly, in this paper, a spectral decomposition-based minimum mean squared error (MMSE) receiver is proposed in an uplink multi-user MIMO (MU-MIMO) system with a full-duplex decode and forward relay. Imperfect channel state information is assumed at the relay and base station where, least-squares channel estimation technique is applied due to its simplicity and low complexity. An equivalent relay is applied for self-interference cancellation. While, multi-user interference is mitigated by using the block diagonalization concept. A closed-form expression for the mean squared error (MSE) of the estimated data symbol is derived in the presence of channel estimation error. Moreover, an optimization problem is solved to derive an expression for the proposed MMSE receiver’s matrix. Finally, the performance of the proposed receiver is compared to that of the conventional receiver and Zero-forcing (ZF) receiver. Results show the superiority of the proposed receiver over both receivers.

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

Deep Learning OFDM Receivers for Improved Power Efficiency and Coverage

In this article, we propose multiple machine learning (ML) based physical-layer receiver solutions for demodulating orthogonal frequency-division multiplexing (OFDM) signals that are subject to high level of nonlinear distortion. Specifically, three novel deep learning based convolutional neural network receivers are devised, containing layers in time- and/or frequency-domains, allowing to demodulate and decode the transmitted bits reliably despite the high error vector magnitude (EVM) in the transmit signal. Applicable training procedures are also described, such that the learned layers in the receiver processing properly generalize over different nonlinear distortion and multipath channel characteristics. Extensive set of numerical results is provided, in the context of 5G NR uplink (UL) incorporating also measured terminal power amplifier (PA) characteristics. The obtained results show that the proposed receiver systems are able to clearly outperform the classical linear minimum mean-squared error (LMMSE) receiver as well as the existing ML receiver approaches, especially when the EVM is high compared to modulation order. This is particularly so when the devised ML receiver is of hybrid nature with layers both in time and frequency. The proposed ML receivers can thus facilitate pushing the terminal PA systems deeper into saturation, and thereon improve the terminal power-efficiency, radiated power and network coverage. Through combining the obtained radio link performance results with link budget calculations, all carried out at the 28 GHz mmWave band, it is shown that the proposed ML receivers can enhance the network coverage in terms of maximum UL link distances by close to 100%, when compared to classical LMMSE receiver based networks.

On the Performance of LDPC-Coded Large Intelligent Antenna System

This article studies Large Intelligent Systems (LIS) along with Single Carrier with Frequency Domain Equalization (SC-FDE), utilizing Low-Density Parity-Check (LDPC). Four different receivers are studied in the scenarios described above, namely Equal Gain Combining (EGC), Maximum Ratio Combining (MRC), Zero Forcing (ZF), and Minimum Mean Squared Error (MMSE). The results of this article show that the use of LDPC codes leads to an improvement of performance by about 2 dB for a 4X25 LIS system and by 3 dB for a 4X225 LIS system, as compared to similar systems without LDPC codes. Moreover, for all simulations, the MMSE receiver achieves the best overall performance, while EGC performs the worst.

Исследование детектирования ZF и MMSE в системах MIMO

The proliferation of obstacles in urban environments, such as buildings, wires, and trees, can cause signal re-reflection, resulting in difficulties in detecting the original one. Multipath propagation occurs when electromagnetic waves hit natural and man-made obstacles, leading to the reflection, scattering, and diffraction of waves. This can result in multiple waves arriving at the receiving antenna with different delays, attenuations, and phases. To address this problem, the widely used in modern wireless communication systems MIMO technology (Multiple Input Multiple Output) can be utilized. It uses multiple transmitting and receiving antennas to increase communication channel throughput and reduce errors that occur during data transmission. This paper examines a receiver with decorrelation (ZF receiver) and a receiver that minimizes the minimum mean square error (MMSE). Additionally, an algorithm for a MIMO transmission system model using ZF and MMSE receivers is presented. In the final section of the article, the results of Bit Error Rate (BER) modeling are presented for different numbers of transmitting and receiving antennas. The presented algorithm can significantly reduce errors that occur during data transmission in urban environments, where multipath propagation is common because of signal re-reflection. The use of MIMO technology with decorrelation and MMSE receivers can increase the efficiency of communication channels and make wireless communication more reliable in urban environments.

Spectrum Efficient Resource Allocation of NOMA Downlink System With MMSE Receiver

Non-orthogonal multiple access (NOMA) with the effective successive interference cancellation (SIC) is proved as a promising solution to improve the spectrum efficiency (SE). However, since the effective SIC usually requires complex algorithm and leads to higher processing delay, it may not be accepted by the B5G wireless communication due to the limited hardware resource of the mobile terminal and strict real-time request of service. Therefore, whether the NOMA with simple receiver could keep performance advantage directly relate to the promotion and application of NOMA in future. In this paper, we mainly investigate the SE performance of the NOMA downlink system with Minimum Mean Squared Error (MMSE) receiver (MMSE-NOMA) under the imperfect SIC (ipSIC) and CSI (ipCSI) assumption. Based on the analysis of residual interference caused by the ipSIC and ipCSI, the alterative first-order approximation iteration (A-FOAI) algorithm is proposed to optimal the SE performance of MMSE-NOMA. To make the research more objective and comprehensive, we evaluate the SE performance of NOMA with perfect SIC (pSIC) and CSI (pCSI) by adopting the first-order approximation iteration (FOAI) algorithm firstly. Numerical results show that the performance advantage of NOMA heavily depends on the differential degree among various channel gains. Especially, under the ipSIC and ipCSI conditions, the SE of MMSE-NOMA may even be lower than that of the traditional orthogonal multiple access (OMA) system with MMSE receiver when the differential degree among various channel gains is relatively insignificant. This conclusion can help us correctly adopt MMSE receiver to avoid high hardware resource consumption and processing delay in the future NOMA system.

Deep Learning-Based Signal Detection for Rate-Splitting Multiple Access Under Generalized Gaussian Noise

In this paper, we propose a long short-term memory-based deep learning (DL) architecture for signal detection in uplink and downlink rate-splitting multiple access systems with multi-carrier modulation, over Nakagami-m fading and generalized Gaussian noise (GGN). The proposed DL detector completely eliminates the need for the use of successive interference cancellation (SIC), which suffers from disadvantages such as error propagation. In an orthogonal frequency division multiplexing setting, we show that the proposed DL detector outperforms the standard SIC receivers such as the least squares detector and the minimum mean-squared error receiver, and attains the performance of the optimal maximum likelihood detector, in terms of the symbol error rate (SER). Furthermore, we study the effects of the shaping parameter of GGN, hyperparameters of the DL network such as batch size and learning rate on the SER performance.

Low-Complexity MMSE Receiver Design for Massive MIMO OTFS Systems

We design a low-complexity minimum mean square error (MMSE) receiver for a practical rectangular pulse-shaped orthogonal time frequency space (OTFS) massive multiple-input multiple-output (mMIMO) system. The proposed receiver is designed by exploiting the OTFS channel sparsity, and the structure of matrices involved in the MMSE receiver. We show that the sparse OTFS channel matrix is multi-banded, and has a high bandwidth. This is because its non-zero elements, which occur in multiple bands, are scattered throughout the matrix. We reduce its bandwidth by using the Reverse Cuthill-Mckee algorithm. The proposed MMSE receiver does not use any approximation, and thus has the same bit error rate (BER) as that of its conventional counterpart. We show that the proposed receiver, without any BER loss, achieves significantly lower complexity than the existing state-of-the-art receivers.

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.

Performance Evaluation of VBLAST and Linear Receivers for mmWave MIMO Systems with Ray-Tracing Channel Models

In this paper, the performance of a millimeter wave (mmWave) Multi-Input Multi-Output (MIMO) system is investigated using low complexity receivers. The receivers include linear Maximum Ratio Combiner (MRC), linear Zero Forcing (ZF) receiver, or linear Minimum Mean-Square Error (MMSE) receiver, in addition to ZF Vertical Bell Laboratories Layered Space-Time (ZF-VBLAST). A MIMO channel model based on a ray-tracing approach and the uniform theory of diffraction has been used. The effect of increasing the number of rays used in the channel model is investigated on the performance of all receivers. For all the scenarios, it has been found out that the ZF-VBLAST structure provides the best symbol-error-rate performance followed by the linear MMSE, then the ZF receiver, and finally the MRC receiver. The trade-off paid for achieving better performance is the increased receiver complexity. The system’s performance is compared under a conventional statistical channel model and a ray-based channel model for a fifth-generation (5G) mobile radio system. It is noted that these models do not accurately characterize the specific environment, hence resulting in an optimistic estimate of the system performance. Finally, the ray-tracing channel model is modified to account for the impact of the presence of trees within the environment. The results show that the performance degradation due to the presence of trees is between 2 to 5 dB for ZF and MMSE receivers, respectively.

HF Skywave Massive MIMO Communication

In this paper, we investigate massive multi-input multi-output (MIMO) high frequency (HF) skywave communications. We first introduce a model for HF skywave massive MIMO channels within the orthogonal frequency division multiplexing transmission framework by using the matrix of sampled steering vectors. Considering the large antenna array aperture and increased signal bandwidth, the effect of the propagation delay across the large-scale antenna array cannot be ignored, and thus the steering vectors vary across different subcarriers. Specifically, we derive a wideband beam based channel model and show that the beam domain statistical channel state information (CSI) is frequency-independent. Then, we consider minimum mean-squared error (MMSE) based uplink receiver and downlink precoder with perfect CSI at the base station (BS). With a large number of antennas at the BS, the sum-rate can be asymptotically increased proportionally to the number of user terminals (UTs) while the transmit power per UT is scaled down inverse-proportionally to the number of antennas. In order to reduce the design complexities of the MMSE receiver and precoder, we derive a polynomial expansion based design using a deterministic equivalent. Simulation results demonstrate very significant performance advantages of the proposed HF skywave massive MIMO system.

MU-MIMO Receiver Design and Performance Analysis in Time-Varying Rayleigh Fading

Minimizing the symbol error in the uplink of multi-user multiple input multiple output systems is important, because the symbol error affects the achieved signal-to-interference-plus-noise ratio (SINR) and thereby the spectral efficiency of the system. Despite the vast literature available on minimum mean squared error (MMSE) receivers, previously proposed receivers for block fading channels do not minimize the symbol error in time-varying Rayleigh fading channels. Specifically, we show that the true MMSE receiver structure does not only depend on the statistics of the CSI error, but also on the autocorrelation coefficient of the time-variant channel. It turns out that calculating the average SINR when using the proposed receiver is highly non-trivial. In this paper, we employ a random matrix theoretical approach, which allows us to derive a quasi-closed form for the average SINR, which allows to obtain analytical exact results that give valuable insights into how the SINR depends on the number of antennas, employed pilot and data power and the covariance of the time-varying channel. We benchmark the performance of the proposed receiver against recently proposed receivers and find that the proposed MMSE receiver achieves higher SINR than the previously proposed ones, and this benefit increases with increasing autoregressive coefficient.

GFDM-Based Asynchronous Grant-Free Multiple-Access

For next-generation Internet-of-Things (IoT) networks, asynchronous instant transmission has attracted increasing research interest with the expectation of achieving near-zero latency without excessive initiation procedure. However, in an asynchronous multiple-access scenario, there exist significant inter-carrier interference between sub-carriers allocated to different users. To suppress out-of-band emission (OOBE) of each sub-carrier, a new generalized frequency division multiplexing (GFDM) has been proposed, which has lower OOBE than the conventional orthogonal frequency division multiplexing (OFDM). In this paper, by using GFDM, two types of receivers are proposed with the aim of reducing latency and improving throughput: a GFDM-based minimum mean square error (MMSE) receiver and a GFDM-based MMSE-successive interference cancellation (SIC) receiver. Then, we develop a lightweight scheme using an <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-conservative rate control with GFDM-based MMSE receivers and also invent a performance-focused scheme using an advanced rate control with GFDM-based MMSE-SIC receivers. In particular, the latter scheme provides higher throughput with limited increase in computational load of user equipments. Numerical results show that with a high successful transmission probability higher than 99 &#x0025;, the performance-focused scheme and the lightweight scheme achieve up to 85 &#x0025; and up to 70 &#x0025; higher throughput compared to the conventional OFDM-based asynchronous multiple-access scheme, respectively. Furthermore, since our proposal does not require any centralized user scheduling or initiation procedure, it presents a significant reduction in latency compared to the existing low-latency technologies.

Achieving the performance of the MMSE receiver with the maximum ratio combiner

In this article, we propose a new pilot mapping method to jointly estimate the channel state information of the user while reducing the interference effects of multiuser multicell mobile scenarios. The problem of achieving the wireless performance of the minimum mean square error (MMSE) receiver with the maximum ratio (MR) combiner for massive multiple-input multiple-output (MIMO) systems in the frequency bands of 2.5 GHz and 28 GHz is addressed. By transmitting fewer pilots in the uplink communications and arranging those pilots to reduce interuser interference, we can achieve higher spectral efficiency (SE) with the MR and MMSE receivers. Numerical results show significantly fewer floating-point operations for MIMO processing when the proposed pilot mapping strategy is combined with Kalman filtering estimation and MR processing, achieving an SE comparable to the MMSE receiver.

Outage Performance Analysis of Widely Linear Receivers in Uplink Multi-User MIMO Systems

This paper considers the application of widely linear (WL) receivers in an uplink multi-user system using real-valued modulation schemes, where the cellular base station (BS) with multiple antennas provides connectivity for randomly deployed single-antenna users. The targeted use case is massive machine type communication (mMTC) with grant-free access in the uplink, where the network is required to host a large number of low data rate devices transmitting in an uncoordinated fashion. Four types of WL receivers are investigated, namely the WL zero-forcing (ZF) and the WL minimum mean-squared error (MMSE) receivers, along with their enhanced versions employing successive interference cancellation (SIC) with channel-dependent ordering, i.e., the WL-ZF-SIC and WL-MMSE-SIC receivers. The outage performances of these receivers are analytically characterized in the high signal-to-noise ratio (SNR) regime and compared to those of conventional linear (CL) receivers using complex-valued modulation schemes. For the non-SIC receivers, we show that, when compared to the CL counterparts, the WL receivers yield a higher diversity gain when decoding the same number of users and have the same diversity gain but a decreased coding gain when the number of users is nearly doubled. The outage performance analysis of WL-SIC receivers is facilitated by the marginal distribution of ordered eigenvalues of a real-valued Wishart matrix. It is shown that the SIC operation with channel-dependent ordering brings no additional diversity gain to the WL receivers but instead increases the coding gain. Moreover, the coding gain of WL-SIC receivers grows as the number of users increases and even exceeds that of CL-SIC receivers under suitable conditions. For the mMTC scenario with grant-free transmission, it is demonstrated that the WL receivers outperform their CL counterparts in terms of offering a lower outage (and packet drop) probability and a higher system throughput for a given packet drop probability.

Third-order Volterra MMSE receivers for enhanced single and multiple antenna interference cancellation

Data-like interference mitigation in wireless communications systems, and in mobile cellular networks in particular, has always been a challenging problem which is becoming even more so for 5G networks and beyond including the Internet of things (IoT), to support a massive number of low data rate devices for given spectral resources. A promising solution to this problem consists in using one dimensional signaling (i.e., real-valued modulations) jointly with widely linear (WL) processing at the receiver, which has the capability to process up to 2N−1 data-like interference from N antenna receivers, and to fulfill, for N=1, single antenna interference cancellation (SAIC) of a one-dimensional interference in particular. However, when the signal of interest (SOI) and observations are jointly non-Gaussian, which is the case for most of digital radiocommunications systems, WL receivers become sub-optimal and optimal receivers become non-linear. It is then of interest to propose new non-linear receivers to improve performance of WL receivers. In this context, the paper aims at introducing, for small-scale systems, third-order complex Volterra (CV) minimum mean square error (MMSE) receivers, for the reception of a digital linearly modulated SOI whose waveform is known, corrupted by potentially non-Gaussian and non-circular interference, omnipresent in practical situations. Properties, performance and adaptive implementation of these receivers in the presence of non-Gaussian and potentially non-circular interference up to the 6th-order are analyzed in this paper. In particular, some of these receivers are shown to enhance WL receiver performance for SAIC of one rectilinear interference such as binary phase-shift keying (BPSK) interference. Whereas some other receivers allow us to fulfill SAIC of 4th-order non-circular interference such as quadrature phase-shift keying (QPSK) interference, which is not possible using WL receivers. These new receivers open new perspectives for cancellation of non-Gaussian and potentially non-circular interference up to 6th-order in radiocommunication networks.

Asymptotic Performance Analysis of MMSE Receivers in Multicell MU-MIMO Systems

For large-scale antenna array multiple-input multiple-output (MIMO) systems, a typical solution often put forward for uplink detection consists in applying low-complexity linear receivers such as zero-forcing (ZF) and minimum mean-square error (MMSE) combiners. In this paper, the performance of uplink MMSE detection has been analyzed in the context of a multi-cell multiuser MIMO system. An approximate expression for the signal-to-interference-plus-noise ratio (SINR) is proposed, which is in simple form and becomes exact in the low SNR regime. This approximate SINR applies to systems where the base station (BS) has the statistical information of the out-of-cell interfering signals, and systems where the BS ignores the presence of such interfering signals. This approximate SINR is tight for arbitrary user powers, arbitrary number of antennas at the base station, and arbitrary channel correlation matrix associated with any particular user. Approximate expressions for capacity and bit-error rate/symbol-error rate have also been derived. Particularly, it can be proven that, when the MMSE receiver ignores the presence of out-of-cell interfering signals, the performance gap between ZF and MMSE vanishes in the high SNR regime.

Limited-Fronthaul Cell-Free Massive MIMO With Local MMSE Receiver Under Rician Fading and Phase Shifts

A cell-free Massive multiple-input multiple-output (MIMO) system is considered, where the access points (APs) are linked to a central processing unit (CPU) via the limited-capacity fronthaul links. It is assumed that only the quantized version of the weighted signals are available at the CPU. The achievable rate of a limited fronthaul cell-free massive MIMO with local minimum mean square error (MMSE) detection is studied. We study the assumption of uncorrelated quantization distortion, which is commonly used in literature. We show that this assumption will not affect the validity of the insights obtained in our work. To investigate this, we compare the uplink per-user rate with different system parameters for two different scenarios; 1) the exact uplink per-user rate and 2) the uplink per-user rate while ignoring the correlation between the inputs of the quantizers. Finally, we present the conditions which imply that the quantization distortions across APs can be assumed to be uncorrelated.

Correlation-Aided Nonlinear Spectrum Detection

It is shown that a higher spectral efficiency (SE) can be achieved in a narrow-bandwidth b-modulated NFDM subsystem than a moderate-bandwidth one. Exploiting the statistical correlation between the noise in the sub-carriers-which is shown to be stronger in narrow-bandwidth b-modulated NFDM subsystems than in moderate or wide-bandwidth ones-a linear minimum mean-squared error receiver improves signal detection. The achievable SE is increased by 0.94 b/s/Hz compared to that achieved by the matched filter receiver in a 5 GHz b-modulated NFDM subsystem.

A New Power Control Algorithm in MMSE Receiver for D2D Underlying Massive MIMO System

Device to device (D2D) underlying massive MIMO cellular network is a robust deployment which enables network to enhance its throughput. It also improves services and applications for the proximity-based wireless communication. However, an important challenge in such deployment is mutual interference. Interference, in the uplink spectrum, reusing the same resource with cellular user, is caused by D2D users. In this paper, we study a distributed power control (DPC) algorithm, using minimum mean square error (MMSE) filter in receiver, to mitigate the produced interference in this deployment scenario. For the DPC algorithm, employing the coverage probability of D2D links, an optimal power control approach is proposed, which maximizes the spectral efficiency of D2D links. Using this modeling approach, it is possible to derive closed-form analytical expressions for the coverage probabilities and ergodic spectral efficiency, which give insight into how the various network parameters interact and affect the link.‎ Also, the DPC algorithm is modeled by stochastic geometry and receiver filter is designed by estimation theory that a new structure in this robust network is an approach to improve spectral efficiency. Simulation results illustrate enhancing coverage probability performance of D2D links in term of the target (signal to interference ratio) SIR with respect to different receiver filter and other parameters which are existing in D2D links.