Although the widely linear least mean square error (WLMMSE) receiver has been an appealing option for multiple-input-multiple-output (MIMO) wireless systems, a statistical understanding on its pose-detection signal-to-interference-plus-noise ratio (SINR) in detail is still missing. To this end, we consider a WLMMSE MIMO transmission system with rectilinear or quasi-rectilinear (QR) signals over the uncorrelated Rayleigh fading channel and investigate the statistical properties of its SINR for an arbitrary antenna configuration with $N_t$ transmit antennas and $N_r$ receive ones. We first derive an analytic probability density function (PDF) of the SINR in terms of the confluent hypergeometric function of the second kind, for WLMMSE MIMO systems with an arbitrary $N_r$ and $N_t=2, 3$. For a more general case in practice, i.e., $N_t>3$, we resort to the moment generating function to obtain an approximate but closed form PDF under some mild conditions, which, as expected, is more Gaussian-like as $2N_r-N_t$ increases. The so-derived PDFs are able to provide key insights into the WLMMSE MIMO receiver in terms of the outage probability, the symbol error rate, and the diversity gain, all presented in closed form. In particular, its diversity gain and the gain improvement over the conventional LMMSE one are explicitly quantified as $N_r-(N_t-1)/2$ and $(N_t-1)/2$, respectively. Finally, Monte Carlo simulations support the analysis.
We present a unified large system analysis of linear receivers for a class of random matrix channels. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. We derive expressions for the asymptotic signal-to-interference-plus-noise (SINR) of the MMSE receiver, and both the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms o…
A technique to compute the Cumulative Distribution Function (CDF) of the Signal-to-Interference-plus-Noise-Ratio (SINR) for a wireless link with a multi-antenna, Linear, Minimum-Mean-Square-Error (MMSE) receiver in the presence of interferers distributed according to a non-homogenous Poisson point process on the plane, and independent Rayleigh fading between antennas is presented. This technique is used to compute the CDF of the SINR for several different models of intensity functions, in particular, power-law intensity functions, circular-symmetric Gaussian intensity functions and intensity f…
Consider a multi-input multi-output (MIMO) downlink multi-user channel. A well-studied problem in such system is the design of linear beamformers for power minimization with the quality of service (QoS) constraints. The most representative algorithms for solving this class of problems are the so-called MMSE-SOCP algorithm [11-12] and the UDD algorithm [9]. The former is based on alternating optimization of the transmit and receive beamformers, while the latter is based on the well-known uplink-dowlink duality theory. Despite their wide applicability, the convergence (to KKT solutions) of both …
The problem of max-min signal-to-interference plus noise ratio (SINR) for uplink transmission of cell-free massive multiple-input multiple-output (MIMO) system is considered. We assume that the system is employed with local minimum mean square error (L-MMSE) combining. The objective is to preserve user fairness by solving max-min SINR optimization problem, by optimizing transmit power of each user equipment (UE) and weighting coefficients at central processing unit (CPU), subject to transmit power constraints of UEs. This problem is not jointly convex. Hence, we decompose original problem into…
In this paper, a new state-of-the-art multi-cell MMSE scheme is proposed for massive MIMO networks, which includes an uplink MMSE detector and a downlink MMSE precoder. The main novelty is that it exploits all available pilots for interference suppression. Specifically, let $K$ and $B$ denote the number of users per cell and the number of orthogonal pilot sequences in the network, respectively, where $β= B/K$ is the pilot reuse factor. Then our multi-cell MMSE scheme utilizes all $B$ channel directions, that can be estimated locally at each base station, to actively suppress both intra-cell an…
Base stations with a large number of transmit antennas have the potential to serve a large number of users at high rates. However, the receiver processing in the uplink relies on channel estimates which are known to suffer from pilot interference. In this work, making use of the similarity of the uplink received signal in CDMA with that of a multi-cell multi-antenna system, we perform a large system analysis when the receiver employs an MMSE filter with a pilot contaminated estimate. We assume a Rayleigh fading channel with different received powers from users. We find the asymptotic Signal to…
Cell-Free Massive MIMO comprises a large number of distributed single-antenna access points (APs) serving a much smaller number of users. There is no partitioning into cells and each user is served by all APs. In this paper, the uplink performance of cell-free systems with minimum mean squared error (MMSE) and large scale fading decoding (LSFD) receivers is investigated. The main idea of LSFD receiver is to maximize achievable throughput using only large scale fading coefficients between APs and users. Capacity lower bounds for MMSE and LSFD receivers are derived. An asymptotic approximation f…
The expected operating scenarios of 5G pose a great challenge to orthogonal frequency division multiplexing (OFDM) which has poor out of band (OoB) spectral properties, stringent synchronization requirements, and large symbol duration. Generalized frequency division multiplexing (GFDM) which is the focus of this work, has been suggested in the literature as one of the possible solutions to meet 5G requirements. In this work, the analytical performance evaluation of MMSE receiver for GFDM is presented. We also proposed precoding techniques to enhance the performance of GFDM. A simplified expres…
A technique is presented to characterize the Signal-to-Interference-plus-Noise Ratio (SINR) of a representative link with a multiantenna linear Minimum-Mean-Square-Error receiver in a wireless network with transmitting nodes distributed according to a doubly stochastic process, which is a generalization of the Poisson point process. The cumulative distribution function of the SINR of the representative link is derived assuming independent Rayleigh fading between antennas. Several representative spatial node distributions are considered, including networks with both deterministic and random clu…
Orthogonal time-frequency space (OTFS) scheme, which transforms a time and frequency selective channel into an almost non-selective channel in the delay-Doppler domain, establishes reliable wireless communication for high-speed moving devices. This work designs and analyzes low-complexity zero-forcing (LZ) and minimum mean square error (LM) receivers for multiple-input multiple-output (MIMO)-OTFS systems with perfect and imperfect receive channel state information (CSI). The proposed receivers provide exactly the same solution as that of the conventional counterparts, and reduce the complexity…
In this paper, we consider the joint design of the transceivers for a multiple access Multiple Input and Multiple Output (MIMO) system having Inter-Symbol Interference (ISI) channels. The system we consider is equipped with the Minimum Mean Square Error (MMSE) Decision-Feedback (DF) detector. Traditionally, transmitter designs for this system have been based on constraints of either the transmission power or the signal-to-interference-and-noise ratio (SINR) for each user. Here, we explore a novel perspective and examine a transceiver design which is based on a fixed sum mutual information cons…
In this paper, a new multi-cell MMSE detector is proposed for massive MIMO systems. Let $K$ and $B$ denote the number of users in each cell and the number of available pilot sequences in the network, respectively, with $B = βK$, where $β\ge 1 $ is called the pilot reuse factor. The novelty of the multi-cell MMSE detector is that it utilizes all $B$ channel directions that can be estimated locally at a base station, so that intra-cell interference, parts of the inter-cell interference and the noise can all be actively suppressed, while conventional detectors only use the $K$ intra-cell channels…
Linear receivers offer a low complexity option for multi-antenna communication systems. Therefore, understanding the outage behavior of the corresponding SINR is important in a fading mobile environment. In this paper we introduce a large deviations method, valid nominally for a large number M of antennas, which provides the probability density of the SINR of Gaussian channel MIMO Minimum Mean Square Error (MMSE) and zero-forcing (ZF) receivers, with arbitrary transmission power profiles and in the presence of receiver antenna correlations. This approach extends the Gaussian approximation of t…
In this paper, a new multi-cell MMSE precoder is proposed for massive MIMO systems. We consider a multi-cell network where each cell has $K$ users and $B$ orthogonal pilot sequences are available, with $B = βK$ and $β\ge 1$ being the pilot reuse factor over the network. In comparison with conventional single-cell precoding which only uses the $K$ intra-cell channel estimates, the proposed multi-cell MMSE precoder utilizes all $B$ channel directions that can be estimated locally at a base station, so that the transmission is designed spatially to suppress both parts of the inter-cell and intra-…
Linear precoding and post-processing schemes are ubiquitous in wireless multi-input-multi-output (MIMO) settings, due to their reduced complexity with respect to optimal strategies. Despite their popularity, the performance analysis of linear MIMO receivers is mostly not available in closed form, apart for the canonical (uncorrelated Rayleigh fading) case, while for more general fading conditions only bounds are provided. This lack of results is motivated by the complex dependence of the output signal-to-interference and noise ratio (SINR) at each branch of the receiving filter on both the squ…
Consider a multiuser system where an arbitrary number of users communicate with a distributed receive array over independent Rayleigh fading paths. The receive array performs minimum mean squared error (MMSE) or zero forcing (ZF) combining and perfect channel state information is assumed at the receiver. This scenario is well-known and exact analysis is possible when the receive antennas are located in a single array. However, when the antennas are distributed, the individual links all have different average signal to noise ratio (SNRs) and this is a much more challenging problem. In this pape…
A technique is presented to evaluate the performance of a wireless link with a multi-antenna linear Minimum-Mean-Square Error (MMSE) receiver in the presence of interferers distributed according to non-homogeneous Poisson processes or Poisson cluster processes on the plane. The Cumulative Distribution Function (CDF) of the Signal-to-Interference-plus-Noise Ratio (SINR) of a representative link is derived for both types of networks assuming independent Rayleigh fading between antennas. Several representative spatial node distributions are considered, for which the derived CDFs are verified by n…
We consider a multiple-input multiple-output (MIMO) multiple access channel (MAC), where the channel between each transmitter and the receiver is modeled by the doubly-scattering channel model. Based on novel techniques from random matrix theory, we derive deterministic approximations of the mutual information, the signal-to-noise-plus-interference-ratio (SINR) at the output of the minimum-mean-square-error (MMSE) detector and the sum-rate with MMSE detection which are almost surely tight in the large system limit. Moreover, we derive the asymptotically optimal transmit covariance matrices. Ou…
We analyze scheduling algorithms for multiuser communication systems with users having multiple antennas and linear receivers. When there is no feedback of channel information, we consider a common round robin scheduling algorithm, and derive new exact and high signal-to-noise ratio (SNR) maximum sum-rate results for the maximum ratio combining (MRC) and minimum mean squared error (MMSE) receivers. We also present new analysis of MRC, zero forcing (ZF) and MMSE receivers in the low SNR regime. When there are limited feedback capabilities in the system, we consider a common practical scheduling…
This paper investigates the spectral efficiency of multi-cell massive multiple-input multiple-output systems with Ricean fading that utilize the linear maximal-ratio combining detector. We firstly present closed-form expressions for the effective signal-to-interference-plus-noise ratio (SINR) with the least squares and minimum mean squared error (MMSE) estimation methods, respectively, which apply for any number of base-station antennas $M$ and any Ricean $K$-factor. Also, the obtained results can be particularized in Rayleigh fading conditions when the Ricean $K$-factor is equal to zero. In t…
Massive multiple-input multiple-output (MIMO) promises improved spectral efficiency, coverage, and range, compared to conventional (small-scale) MIMO wireless systems. Unfortunately, these benefits come at the cost of significantly increased computational complexity, especially for systems with realistic antenna configurations. To reduce the complexity of data detection (in the uplink) and precoding (in the downlink) in massive MIMO systems, we propose to use conjugate gradient (CG) methods. While precoding using CG is rather straightforward, soft-output minimum mean-square error (MMSE) detect…
Spatial multiplexing (SM) gains in multiple input multiple output (MIMO) cellular networks are limited when used in combination with ultra-dense small cell networks. This limitation is due to large spatial correlation among channel pairs. More specifically, it is due to i) line-of-sight (LOS) communication between user equipment (UE) and base station (BS) and ii) in-sufficient spacing between antenna elements. We propose to shape transmit signals at adjacent antennas with distinct interpolating filters which introduces pulse shaping diversity eventually leading to improved SINR and throughput …
We study a multiple-input multiple-output (MIMO) multiple access channel (MAC) from several multi-antenna transmitters to a multi-antenna receiver. The fading channels between the transmitters and the receiver are modeled by random matrices, composed of independent column vectors with zero mean and different covariance matrices. Each transmitter is assumed to send multiple data streams with a random precoding matrix extracted from a Haar-distributed matrix. For this general channel model, we derive deterministic approximations of the normalized mutual information, the normalized sum-rate with …
Widely adopted at home, business places, and hot spots, wireless ad-hoc networks are expected to provide broadband services parallel to their wired counterparts in near future. To address this need, MIMO techniques, which are capable of offering several-fold increase in capacity, hold significant promise. Most previous work on capacity analysis of ad-hoc networks is based on an implicit assumption that each node has only one antenna. Core to the analysis therein is the characterization of a geometric area, referred to as the exclusion region, which quantizes the amount of spatial resource occu…
Cell-Free Massive Multiple-input Multiple-output (mMIMO) consists of many access points (APs) in a coverage area that jointly serve the users. These systems can significantly reduce the interference among the users compared to conventional MIMO networks and so enable higher data rates and a larger coverage area. However, Cell-Free mMIMO systems face multiple practical challenges such as the high complexity and power consumption of the APs' analog front-ends. Motivated by prior works, we address these issues by considering a low complexity hybrid beamforming framework at the APs in which each A…
We consider a multiple-input multiple-output (MIMO) relaying boardcast channel in downlink cellular networks, where the base station and the relay stations are both equipped with multiple antennas, and each user terminal has only a single antenna. In practical scenarios, channel estimation is imperfect at the receivers. Aiming at maximizing the SINR at each user, we develop two robust linear beamforming schemes respectively for the single relay case and the multi-relay case. The two proposed schemes are based on sigular value decomposition (SVD), minimum mean square error (MMSE) and regularize…
Linear data-detection algorithms that build on zero forcing (ZF) or linear minimum mean-square error (L-MMSE) equalization achieve near-optimal spectral efficiency in massive multi-user multiple-input multiple-output (MU-MIMO) systems. Such algorithms, however, typically rely on centralized processing at the base-station (BS) which results in (i) excessive interconnect and chip input/output (I/O) data rates and (ii) high computational complexity. Decentralized baseband processing (DBP) partitions the BS antenna array into independent clusters that are associated with separate radio-frequency c…
Extremely large-scale multiple-input multiple-output (XL-MIMO) communication aims to further boost the antenna size significantly than current massive MIMO systems, for which conventional far-field assumption with uniform plane wave (UPW) model may become invalid. This paper studies the modelling and performance analysis for multi-user XL-MIMO communication. With the spherical wavefront phase modelling, and also by taking into account the variations of signal amplitude and projected aperture across array elements, the performance of the three typical beamforming schemes are analyzed, namely th…
In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-di…
Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency-flat fading. Signal to interference and noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean square error (MMSE) detectors, are derived. The approach is general and optionally allows even for statistics obtained by under-sampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit…
The performance of linear receivers in the presence of co-channel interference in Rayleigh channels is a fundamental problem in wireless communications. Performance evaluation for these systems is well-known for receive arrays where the antennas are close enough to experience equal average SNRs from a source. In contrast, almost no analytical results are available for macrodiversity systems where both the sources and receive antennas are widely separated. Here, receive antennas experience unequal average SNRs from a source and a single receive antenna receives a different average SNR from each…
Orthogonal time frequency space (OTFS) is being pursued in recent times as a suitable wireless transmission technology for use in high mobility scenarios. In this work, we propose nonorthogonal multiple acess (NOMA) based OTFS which may be called NOMA-OTFS system and evaluate its performance from system level and link level perspective. The challenge lies in the fact that while OTFS transmission technology is known for its resilience to high mobility conditions, while NOMA is known to yield high spectral efficiency in low mobility scenarios in comparison to orthogonal multiple access (OMA). We…
