Maximal Ratio Combining Receiver Research Articles

Developing Laboratory Experiments to teach Undergraduate Engineering Students Multi-User Massive MIMO Technology for 5G Cellular Networks

An effective method of facilitating student learning in a laboratory environment is “practice by doing”. The study of modules related to signal-processing for digital communications requires deep mathematical and theoretical foundations but the practice goal is not really emphasized in the undergraduate curriculum at the University of Mauritius. This causes the students to lose interest in the corresponding modules resulting in high rate of failures. In this work, we propose to develop laboratory experiments with a view to bridge the gap between theoretical and practical aspects in the field of Massive Multiple-Input Multiple-Output (MIMO) systems for 5G cellular networks. Various laboratory scenarios are set up that consider a Maximum Ratio Combining (MRC) receiver in the uplink with an uncorrelated Rayleigh fading channel. Moreover, from a signal processing perspective to enhance the student’s understanding, we analyze the efficiency and error performance of Massive MIMO systems with MPSK and MQAM modulation schemes as well as perfect and imperfect channel estimates. The leading industry software package MATLAB R2022 is used to develop all laboratory experiments and the codes are elaborated in this analysis. Data collected from the experiments are used to generate spectral efficiency and error performance curves which can be used for future research. The findings underscore the significance of accounting for both scenarios and illuminate promising avenues for future research in the realm of massive MIMO education and learning. The assimilation of MATLAB® flowcharts for each MRC receiver, MPSK, and MQAM with perfect and imperfect Channel State Information (CSI) adds further depth to the study, ensuring a comprehensive understanding of the intricacies of massive MIMO systems. Ultimately, this contribution helps in the nurturing of expertise such that future generations of wireless communication pioneers can be inspired.

Deep Reinforcement Learning-Based Sum Rate Fairness Trade-Off for Cell-Free mMIMO

The uplink of a cell-free massive multiple-input multiple-output with maximum-ratio combining (MRC) and zero-forcing (ZF) schemes are investigated. A power allocation optimization problem is considered, where two conflicting metrics, namely the sum rate and fairness, are jointly optimized. As there is no closed-form expression for the achievable rate in terms of the large scale-fading (LSF) components, the sum rate fairness trade-off optimization problem cannot be solved by using known convex optimization methods. To alleviate this problem, we propose two new approaches. For the first approach, a use-and-then-forget scheme is utilized to derive a closed-form expression for the achievable rate. Then, the fairness optimization problem is iteratively solved through the proposed sequential convex approximation (SCA) scheme. For the second approach, we exploit LSF coefficients as inputs of a twin delayed deep deterministic policy gradient (TD3), which efficiently solves the non-convex sum rate fairness trade-off optimization problem. Next, the complexity and convergence properties of the proposed schemes are analyzed. Numerical results demonstrate the superiority of the proposed approaches over conventional power control algorithms in terms of the sum rate and minimum user rate for both the ZF and MRC receivers. Moreover, the proposed TD3-based power control achieves better performance than the proposed SCA-based approach as well as the fractional power scheme.

Performance analysis of coherent DPSK SIMO laser-based satellite-to-ground communication link over weak-to-strong turbulence channels considering Kolmogorov and non-Kolmogorov spectrum models

The performance of satellite-to-ground laser-based communication links is highly affected by atmospheric turbulence. Coherent detection with spatial diversity at the ground station receiver can mitigate the scintillation effects caused by atmospheric turbulence. Traditionally, the scintillation effects are modeled based on the Kolmogorov spectrum model. However, the experiments have indicated that scintillation effects on the laser beam propagation have non-Kolmogorov properties. Our goal in the present work is to analyze the average bit error rate (BER), outage probability (OP), and ergodic capacity of the satellite-to-ground heterodyne optical communication system with receiver spatial diversity. A differential phase-shift keying modulation technique is considered in this work. The propagated laser signal from the satellite to the ground station is assumed to be subjected to Málaga-distributed atmospheric turbulence. The atmospheric turbulence statistics are carried out based on the conventional Kolmogorov spectrum model and the three-layer altitude (TLA) non-Kolmogorov spectrum model. The performance of popular diversity combining techniques, namely, maximum ratio combining (MRC) and equal gain combining (EGC) techniques are analyzed. The statistical models of the MRC technique under the Málaga-distributed atmospheric channel model are obtained in analytical form expressions. The statistical models of the EGC technique under the Málaga-distributed atmospheric channel model are obtained via the fast Fourier transform representation of the characteristic function method. Based on these statistical models, average BER, OP, and ergodic capacity expressions for each type of diversity combining technique are derived. For the communication system under investigation, the performance of MRC and EGC multiple aperture receiver systems are compared to a single aperture receiver with the same total aperture area. These comparisons are carried out under the same conditions in terms of zenith angle and signal-to-noise ratio. The obtained results show that the performance of the optical communication system under investigation with MRC and EGC receivers can be improved by increasing the order of diversity. In addition, it is found that the difference in the performance between Kolmogorov and TLA non-Kolmogorov spectrum models is not significant at low zenith angles, while this difference increases as the zenith angle increases. All numerical results are verified by Monte-Carlo simulations.

Secrecy Rate of TAS in AF-Relay Systems With Multi-Antenna Relay and User Over Non-Identical Channel Estimation Error

This work evaluates the secrecy rate of transmit antenna selection (TAS) in the amplify and forward (AF)-relay system with multi-antenna relay and user. This paper considers that the receiver of relays, users, and an eavesdropper have non-identical channel estimation error. To assess the secrecy rate, this work derives new analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the received signal to noise ratio (SNR) using infinite series for maximal-ratio combining (MRC) and selection combining (SC) receivers. Using the CDF for the received SNR, we derive new exact analytical expressions for the secrecy rate with non-identical channel estimation error for four scenarios. Further, using the PDF for the received SNR, we derive the asymptotic analytical expressions for the secrecy rate and quantify the high SNR slope and the high SNR power offset for four scenarios. From the numerical results, we observe that the relay and user selection has the high SNR power offset gain compared to the non-selection. The secrecy rate of the proposed system can be improved according to legitimate receiver's parameters such as the number of receive antennas and channel correlation coefficient and can be degraded according to eavesdropper's parameters. The superiority of the secrecy rate of the MRC receiver and the SC receiver depends on the channel estimation accuracy of the MRC receiver.

Performance of NOMA‐assisted MRC receivers in presence of imperfect SIC and CSI errors

SummaryIn this paper, we analyze the performance of maximum‐ratio combining (MRC) receivers for single‐input multiple‐output (SIMO) non‐orthogonal multiple access (NOMA) system. We explore the aforesaid system performance in presence of impairments like imperfect channel state information (CSI) and successive interference cancellation (SIC) errors. In general, receive diversity provides diversity gain and helps to maintain quality of service (QoS), while the NOMA system achieves higher spectral efficiency compared to orthogonal multiple access (OMA). Power‐domain NOMA system transmits superimposed‐coded signal, which utilize SIC detection method at the receiving users. Here, we derive the closed‐form expression of the average bit error rate (BER) for the MRC‐based NOMA system. We also analyze the performance of the system in high signal‐to‐noise ratio (SNR) regime through derived asymptotic expression. Furthermore, the outage probability, diversity order, and sum rate comparison between NOMA and OMA system are also presented. Simulation results also validate the derived theoretical expressions and confirm the diversity gain achieved for the considered system.

Maximizing the spectral efficiency of finite dimensional multiuser massive MIMO

In this paper, we derive a closed-form approximation for the achievable uplink ergodic rate of the users in a single-cell multi-user multiple-input multiple-output (MIMO) system, where the angular domain in the physical channel model is divided into a finite number of separate directions and the base station (BS) is equipped with a large number of antenna elements. Then, we develop an approximation for the spectral efficiency of various detectors such as maximum-ratio combining (MRC), zero-forcing (ZF), and linear minimum mean square error (LMMSE). We also propose a resource allocation scheme in which the pilot power, data power, and training duration are optimally chosen in order to maximize the spectral efficiency in a given total power budget. By employing the proposed power allocation scheme, the simulation results illustrate a notable improvement in the achievable spectral efficiency. Moreover, the results show that the performance of the proposed method is much superior when the number of channel directions or the number of antennas at BS increases. Furthermore, while the advantage of the proposed method is more notable in the case of ZF and LMMSE receivers, it still outperforms the equal power allocation method for the MRC receiver in terms of spectral efficiency.

Secrecy Analysis of Relay-User Selection in AS-AF Systems Over Nakagami Fading Channels

This paper presents the secrecy outage probability of relay and user (RU) selection in the antenna selection (AS)-amplify and forward (AF) system over integer-valued $m$ Nakagami fading channels for the physical layer security. This work derives the lower bound (LB) and asymptotic cumulative density functions (CDFs) of the signal to noise ratio (SNR) for the RU selection in the AS-AF system. This study also considers the impact of the two types of receivers, i.e., maximal ratio combining (MRC), selection combining (SC) for the authorized system and eavesdropper. Using the lower bound CDFs, the LB expressions of the secrecy outage probability are derived for various scenarios. Applying the asymptotic CDFs, the diversity order of the secrecy performance is also quantified for each case. From analysis results, we show that the diversity order of the secrecy outage probability in the proposed system is only affected by authorized system's parameters, not by eavesdropper's parameters. Further, the relay and user nodes with the MRC receiver provide the SNR gain compared to the SC receiver regardless of eavesdropper's receiver type. Finally, the secrecy outage probability of the proposed RU system with the SC eavesdropper has the SNR gain compared to the MRC eavesdropper, while the diversity order is identical to each other.

Massive MIMO Channel Estimation With Low-Resolution Spatial Sigma-Delta ADCs

We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ( ΣΔ) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC), zero-forcing (ZF) and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the ΣΔ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.

Optimum Combiner for Spatially Correlated Nakagami-m Fading Channels

This paper proposes a novel optimum combiner that raises the time-averaged signal-to-interference-plus-noise ratio (SINR) for maximal-ratio combining (MRC) reception over spatially correlated Nakagami-m fading channels. By exploiting the principal component analysis (PCA) with eigenvalue decomposition (EVD) of the covariance matrix analytically evaluated offline, a complete set of orthonormal basis functions can be obtained. A decorrelation process analyzes and then projects the received signal into the space spanned by the basis functions. In accordance with the theorem of irrelevance, a principal component selection combining (PCSC) method is proposed to remove components in a few dimensions in which SINRs are considered low to raise the resulting time-averaged SINR on the subsequent MRC reception. The proposed technique also avoids noise enhancement occurring with MRC reception in the scenario where noises on different branches are correlated. The SINR distribution, level-crossing rate (LCR) and average fade duration (AFD) are derived. Based on a novel scattering model interpretation, a simulator consisting of spatially correlated Nakagami-m fading channels is developed according to the analytically evaluated covariance matrix. Computer simulations show that the proposed optimum combiner not only decreases interference and noise from the irrelevant subspace to achieve higher time-averaged SINR and lower AFD but also significantly reduces the complexity required for subsequent signal processing.

Outage Probability of SIMO MRC Receivers With Correlated Poisson Field of Interferers

We study the performance of applying maximal ratio combining (MRC) in a single-input-multiple-output (SIMO) system with a Poisson field of interferers. Due to the correlated interference powers across different antennas, the derivation of the exact outage probability is highly involved. To tackle this problem, we take advantage of the mathematical property of the sub-Gaussian α-stable interference signal vector, and then derive an analytical lower bound of the outage probability, which is shown to be very tight through Monte Carlo simulations. Our results can be used to assist performance analysis and design of SIMO MRC receiver with random interferers.

MRC Receivers Under Multivariate Equal-Correlated Rician Fading

Novel single-integral functions of multivariate equal-correlated (equ.c.) Rician fading employing maximal ratio combining (MRC) are derived in this paper. It has been well known that theoretical progress under correlated fading cannot be given in closed-form, but single-integral. To the author's best knowledge, the single-integral proposed results are novel for MRC deployment under multivariate equ.c. Rician fading. Using underlying independent and identically distributed complex nonzero-mean Gaussian random variables, equ.c. Rician envelopes are constructed, leading to the proposed results. Outage probability and signal-to-noise-ratio gains are computed under selection-combining and MRC deployment for validation purposes. Detailed discussion are given. Monte Carlo simulation is shown to match theoretical predictions.

On the Performance of Massive MIMO Systems With Low-Resolution ADCs and MRC Receivers Over Rician Fading Channels

This article considers uplink massive multiple-input multiple-output (MIMO) systems with maximum-ratio-combining (MRC) receivers over Rician fading channels. Low-resolution analog-to-digital converters (ADCs) are considered for both data detection and channel estimation. Asymptotic approximations of the spectrum efficiency (SE) for large-scale MIMO systems are derived based on random matrix theory. With these closed-form expressions, we can provide insights into the tradeoffs between the SE and the ADC resolution and study the influence of the Rician K-factors on the performance. It is shown that a large value of K-factors may lead to a better performance and alleviate the influence of quantization noise on channel estimation. Moreover, we investigate the power-scaling laws for the system under imperfect channel state information and it shows that when the number of base station (BS) antennas is very large, without loss of the SE performance, the transmission power can be scaled by the number of BS antennas while the overall performance is limited by the resolution of ADCs. The asymptotic analysis is validated by numerical results. We also show that ADCs with intermediate resolutions lead to better energy efficiency than that with high-resolution or extremely low-resolution ADCs.

A Space-Time Correlation Model for MRC Receivers in Rayleigh Fading Channels

This paper presents a statistical model for maximum ratio combining (MRC) receivers in Rayleigh fading channels enabled with a temporal combining process. This means that the receiver effectively combines spatial and temporal branch components. Therefore, the signals that will be processed by the MRC receiver are collected not only across different antennas (space), but also at different instants of time. This suggests the use of a retransmission, repetition or space-time coding algorithm that forces the receiver to store signals in memory at different instants of time. Eventually, these stored signals are combined after a predefined or dynamically optimized number of time-slots or retransmissions. The model includes temporal correlation features in addition to the space correlation between the signals of the different components or branches of the MRC receiver. The derivation uses a frequency domain approach (using the characteristic function of the random variables) to obtain closed-form expressions of the statistics of the post-processing signal-to-noise ratio (SNR) under the assumption of equivalent correlation in time and equivalent correlation in space. The described methodology paves the way for the reformulation of other statistical functions as a frequency-domain polynomial root analysis problem. This is opposed to the infinite series approach that is used in the conventional methodology using directly the probability density function (PDF). The results suggest that temporal diversity is a good complement to receivers with limited spatial diversity capabilities. It is also shown that this additional operation could be maximized when the temporal diversity is adaptive (i.e., activated by thresholds of SNR), thus leading to a better resource utilization.

Uplink sum rate analysis of multi‐user massive MIMO–OFDM/OQAM systems in Ricean fading

This study investigates the uplink performance of offset quadrature amplitude modulation (OQAM)-based orthogonal frequency division multiplexing (OFDM) waveform in single-cell multi-user massive multiple-input multiple-output (MIMO) systems over Ricean fading. An uplink training-based minimum mean square error (MMSE) channel estimation by exploiting the inherent characteristics of OFDM/OQAM waveform is briefly presented. By leveraging the second-order statistical characteristics of the intrinsic interference, the achievable uplink sum rates and corresponding closed-form approximations are derived in the presence of MMSE channel estimate at the base station with zero-forcing (ZF) and maximum-ratio combining (MRC) receivers. Based on the above analytical results for the uplink rates, power scaling laws are also investigated. The effect of Ricean-K factor on the achievable uplink sum rate is also examined analytically for both the MRC and ZF receivers. Numerical results compare the performance of OFDM/OQAM and classic cyclic-prefix OFDM-based massive MIMO systems and also validate the various analytical expressions derived in this work.

Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO

We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the quantization error between adjacent antennas, the method shapes the spatial spectrum of the quantization noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the Sigma-Delta approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial quantization noise power spectrum are derived for the Sigma-Delta array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the Sigma-Delta approach for both MRC and zero-forcing receivers.

Comparative study of channel estimators for massive MIMO 5G NR systems

In this work, a comparative analysis is performed to study the bit error rate and error vector magnitude achieved with the least-squares (LS), the minimum mean squared error (MSE), and the Kalman filter (KF) channel estimators when these are applied to the maximum-ratio combining (MRC) and the regularised zero-forcing (RZF) receivers. The MSE achieved with the different channel estimators was also compared by varying the noise and interference power at the receiver. The proposed methodology relies on the characterisation of a massive multiple-input multiple-output (MIMO) channel with a quasi-deterministic radio channel generator and a cyclic prefix orthogonal frequency division multiplexing link-level radio simulation. The fifth-generation (5G) new radio (NR) frame structure was used to perform channel estimation and equalisation for operation frequencies below 6 GHz. Numerical results show that the MRC receiver achieves its maximum performance with the KF estimator, especially at low signal-to-noise ratio scenarios, while the RZF receiver achieves its maximum performance with the LS estimation even in high interference scenarios.

Capacity analysis of maximal ratio combining over Beaulieu-Xie fading

The present paper analyzes an L-branch maximal ratio combining (MRC) receiver over the Beaulieu-Xie (BX) fading channel. The expression of the probability density function (PDF) of the signal-to-noise ratio (SNR) of an MRC receiver in BX fading is derived by using the characteristic function approach. The obtained PDF is then utilized to calculate the various link-level and system-level parameters. This paper focuses on deriving closed-form expressions for different adaptive transmission techniques based on instantaneous channel state information in BX fading. The accuracy of our derived expressions is verified by comparing them with Monte Carlo simulations.

Performance Analysis of Coherent PLC With MPSK Signaling in Nakagami-$m$ Noise Environment

An $N$ -branch receive diversity power line communication (PLC) system subject to Rayleigh fading and corrupted by additive Nakagami- $m$ background noise is considered. A suboptimal maximal-ratio-combining (MRC), an optimal diversity combining, and a Gauss-optimal receiver are proposed for the PLC system. A closed form expression for the exact symbol error probability (SEP) and a union bound SEP expression are obtained for the proposed MRC and Gauss-optimal receivers, respectively, using a characteristic function (c.f.) approach for the system employing $M$ -ary phase-shift keying (MPSK) at the transmitter, conditioned to $mN$ being an integer. The asymptotic expression for the SEP obtained for the MRC receiver at high signal-to-noise (SNR) demonstrates that the diversity order of the system is independent of the shape parameter $m$ of the additive noise which is identical to the diversity order of the optimal and the Gauss-optimal receivers. Further, numerical studies justify the advantages of employing receive diversity to achieve superior SEP performance. The effect of increasing the diversity branches on the PLC system performance with varying $m$ and the power efficiency of the PLC system are also presented.

Performance analysis of relay-aided millimeter-wave communications with optimal and suboptimal combining at destination

We analyze the performance of a relay network in millimeter-wave (mmWave) band, in two cases when the optimal, Maximal-Ratio Combining (MRC), or a suboptimal, Selection Combining (SC), receiver is employed at destination. The recently proposed Fluctuating Two-Ray (FTR) channel model is applied to model communication in mmWave band. Unlike existing works on the topic which restrict their analysis to channels with integer-valued Nakagami-m fading figures, we extend the analysis to more practical cases, where the fading figure may take arbitrary real values greater than 0.5. We also derive equations which enables us to relate the FTR channel parameters to the underlying network parameters, namely distances between the nodes, and path loss exponents. We analyze the system in both cases where a line-of-sight link between the transmitting and receiving nodes is either present or absent. Distribution of the Signal-to-Noise Ratio (SNR) at combiner’s output, as well as system outage probability and spectral efficiency are analytically derived. Throughout extensive simulations, we study and compare the performance of MRC and SC receivers for different system setups. We also consider the effect of applying antenna arrays with different antenna patterns, as well as the effect of interference from other nodes, on the system performance. The results suggest that despite its simple and low-complexity structure, in most cases, SC receiver demonstrates an encouraging performance and shows small performance losses compared to the optimal MRC receiver.

Performance Analysis of Multi-User Massive MIMO Systems with Perfect and Imperfect CSI

A collection of independent terminals instantaneously transmits data streams to a compact array of antennas. With imperfect channel state information (CSI), the antenna makes use of transmitted pilots to find the knowledge about CSI and the power dissipated by the terminals can be made reciprocally proportional to the square root of the number of antennas without a reduction in performances used at the base station. In contrast, when the CSI is known at the base station, the transmitted power is inversely proportional to the number of used antennas. Lower capacity bounds for zero-forcing (ZF) and maximum-ratio combining (MRC) detection are derived. A ZF receiver outperforms the MRC. A power scaling law is being taken into consideration in the analysis of the uplink sum rate with perfect and imperfect CSI. It is analyzed that the uplink sum rate for MRC and ZR receiver with perfect and imperfect CSI, considering the power scaling law. As the number base station antennas increases, the difference between the uplink sum rate for ZF and MRC decreases and if the number of base station antenna is very high, then both of these lines coincide with each other. Especially at a very large number of base station antennas, all bounds are very tight. In comparison to a single antenna system, the uplink sum rate (or spectral efficiency) can be improved in order of several magnitudes by using moderately large antenna arrays in massive multiple input multiple output (MIMO) system.