5 pages, 1 figure, journal version to appear in IEEE Transactions on Wireless Communications. Conference version appeared in NCC 2007, IIT Kanpur, India
Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.
Currently for the nt x nr MIMO channel, any explicitly constructed space-time (ST) designs that achieve optimality with respect to the diversity multiplexing tradeoff (DMT) are known to do so only when decoded using maximum likelihood (ML) decoding, which may incur prohibitive decoding complexity. In this paper we prove that MMSE regularized lattice decoding, as well as the computationally efficient lattice reduction (LR) aided MMSE decoder, allows for efficient and DMT optimal decoding of any approximately universal lattice-based code. The result identifies for the first time an explicitly co…
A recent result of the authors shows a so-called I-MMSE-like relationship that, for the two-user Gaussian interference channel, an I-MMSE relationship holds in the limit, as n $\to \infty$, between the interference and the interfered-with receiver, assuming that the interfered-with transmission is an optimal point-to-point sequence (achieves the point-to-point capacity). This result was further used to provide a proof of the "missing corner points" of the two-user Gaussian interference channel. This paper provides an information theoretic proof of the above-mentioned I-MMSE-like relationship w…
We consider the uplink of a Massive MIMO network with $L$ cells, each comprising a BS with $M$ antennas and $K$ single-antenna user equipments. Recently, [1] studied the asymptotic spectral efficiency of such networks with optimal multicell minimum mean-squared error (M-MMSE) processing when $M\to \infty$ and $K$ is kept fixed. Remarkably, [1] proved that, for practical channels with spatial correlation, the spectral efficiency grows unboundedly, even with pilot contamination. In this paper, we extend the analysis from [1] to the alternative regime in which $M,K\to \infty$ with a given ratio. …
Due to a large number of multipath components in a typical ultra wideband (UWB) system, selective Rake (SRake) receivers, which combine energy from a subset of multipath components, are commonly employed. In order to optimize system performance, an optimal selection of multipath components to be employed at fingers of an SRake receiver needs to be considered. In this paper, this finger selection problem is investigated for a minimum mean square error (MMSE) UWB SRake receiver. Since the optimal solution is NP hard, a genetic algorithm (GA) based iterative scheme is proposed, which can achieve …
Convex relaxations of the optimal finger selection algorithm are proposed for a minimum mean square error (MMSE) Rake receiver in an impulse radio ultra-wideband system. First, the optimal finger selection problem is formulated as an integer programming problem with a non-convex objective function. Then, the objective function is approximated by a convex function and the integer programming problem is solved by means of constraint relaxation techniques. The proposed algorithms are suboptimal due to the approximate objective function and the constraint relaxation steps. However, they can be use…
In this paper, a new matrix-based characterization of generalized-frequency-division-multiplexing (GFDM) transmitter matrices is proposed, as opposed to traditional vector-based characterization with prototype filters. The characterization facilitates deriving properties of GFDM (transmitter) matrices, including conditions for GFDM matrices being nonsingular and unitary, respectively. Using the new characterization, the necessary and sufficient conditions for the existence of a form of low-complexity implementation for a minimum mean square error (MMSE) receiver are derived. Such an implementa…
The minimum mean-square error (MMSE) achievable by optimal estimation of a random variable $Y\in\mathbb{R}$ given another random variable $X\in\mathbb{R}^{d}$ is of much interest in a variety of statistical settings. In the context of estimation-theoretic privacy, the MMSE has been proposed as an information leakage measure that captures the ability of an adversary in estimating $Y$ upon observing $X$. In this paper we establish provable lower bounds for the MMSE based on a two-layer neural network estimator of the MMSE and the Barron constant of an appropriate function of the conditional expe…
Linear receivers are considered as an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the performance of MMSE MIMO receivers in the limit of large antenna numbers in the presence of channel correlations. Using the replica method, we generalize our results obtained in arXiv:0810.0883 to Kronecker-product correlated channels and calculate the asymptotic mean and variance of the mutual information of a MIMO system of parallel MMSE subchannels. The replica method allows us to use the ties between the optimal receiver …
The problem of choosing the optimal multipath components to be employed at a minimum mean square error (MMSE) selective Rake receiver is considered for an impulse radio ultra-wideband system. First, the optimal finger selection problem is formulated as an integer programming problem with a non-convex objective function. Then, the objective function is approximated by a convex function and the integer programming problem is solved by means of constraint relaxation techniques. The proposed algorithms are suboptimal due to the approximate objective function and the constraint relaxation steps. Ho…
This paper investigates the diversity order of the minimum mean squared error (MMSE) based optimal transceivers in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems. While the diversity-multiplexing tradeoff (DMT) analysis accurately predicts the behavior of the MMSE receiver for the positive multiplexing gain, it turned out that the performance is very unpredictable via DMT for the case of fixed rates, because MMSE strategies exhibit a complicated rate dependent behavior. In this paper, we establish the diversity-rate tradeoff performance of MIMO AF relaying syst…
Minimum mean square error (MMSE) signal detection algorithm is near- optimal for uplink multi-user large-scale multiple input multiple output (MIMO) systems, but involves matrix inversion with high complexity. In this letter, we firstly prove that the MMSE filtering matrix for large- scale MIMO is symmetric positive definite, based on which we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion. The complexity can be reduced from O(K3) to O(K2), where K is the number of users. We also provide the convergence proof o…
We examine codes, over the additive Gaussian noise channel, designed for reliable communication at some specific signal-to-noise ratio (SNR) and constrained by the permitted minimum mean-square error (MMSE) at lower SNRs. The maximum possible rate is below point-to-point capacity, and hence these are non-optimal codes (alternatively referred to as "bad" codes). We show that the maximum possible rate is the one attained by superposition codebooks. Moreover, the MMSE and mutual information behavior as a function of SNR, for any code attaining the maximum rate under the MMSE constraint, is known …
This paper characterizes the performance of cellular networks employing multiple antenna open-loop spatial multiplexing techniques. We use a stochastic geometric framework to model distance depended inter cell interference. Using this framework, we analyze the coverage and rate using two linear receivers, namely, partial zero-forcing (PZF) and minimum-mean-square-estimation (MMSE) receivers. Analytical expressions are obtained for coverage and rate distribution that are suitable for fast numerical computation. In the case of the PZF receiver, we show that it is not optimal to utilize all the r…
Cell-free massive multiple-input-multiple-output (mMIMO) is an emerging technology for beyond 5G with its promising features such as higher spectral efficiency and superior spatial diversity as compared to conventional multiple-input-multiple-output (MIMO) technology. The main working principle of cell-free mMIMO is that many distributed access points (APs) cooperate simultaneously to serve all the users within the network without creating cell boundaries. This paper considers the uplink of a cell-free mMIMO system utilizing the radio stripe network architecture with a sequential fronthaul bet…
Cell-free (CF) massive multiple-input multiple-output (MIMO) systems are expected to implement advanced cooperative communication techniques to let geographically distributed access points jointly serve user equipments. Building on the \emph{Team Theory}, we design the uplink team minimum mean-squared error (TMMSE) combining under limited data and flexible channel state information (CSI) sharing. Taking into account the effect of both channel estimation errors and pilot contamination, a minimum MSE problem is formulated to derive unidirectional TMMSE, centralized TMMSE and statistical TMMSE co…
This paper investigates the achievable sum rate of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) receivers. We present a new analytic framework which unveils an interesting connection between the achievable sum rate with MMSE receivers and the ergodic mutual information achieved with optimal receivers. This simple but powerful result enables the vast prior literature on ergodic MIMO mutual information to be directly applied to the analysis of MMSE receivers. The framework is particularized to various Rayleigh and Rician channel scenar…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting function computed on data without perturbation and the estimator that operates on the sorted noisy data. It is first shown that, under certain symmetry conditions, satisfied for example by the practically relevant Gaussian noise perturbation, the optimal estimator can be expressed as a linear combination of estimators on the unsorted data. Then, two suboptimal…
For vector Gaussian channels, a precise differential connection between channel capacity and a quantity termed normalized optimal detection error (NODE) is presented. Then, this C-NODE relationship is extended to continuous-time Gaussian channels drawing on a waterfilling characterization recently found for the capacity of continuous-time linear time-varying channels. In the latter case, the C-NODE relationship becomes asymptotic in nature. In either case, the C-NODE relationship is compared with the I-MMSE relationship due to Guo et al. connecting mutual information in Gaussian channels with …
This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE esti…
In multiple-input multiple-output (MIMO) spatially multiplexing (SM) systems, achievable error rate performance is determined by signal detection strategy. The optimal maximum-likelihood detection (MLD) that exhaustively examines all symbol candidates has exponential complexity and may not be applicable in many practical systems. In this paper, we consider a generalized minimum mean square error (MMSE) detection derived from conditional mean estimation, which in principle behaves equivalently to MLD but also includes a linear MMSE detection as a special case. Motivated by this fact, we propose…
In this paper we introduce a new right preprocessing method for the decoding of 2x2 algebraic STBCs, called algebraic reduction, which exploits the multiplicative structure of the code. The principle of the new reduction is to absorb part of the channel into the code, by approximating the channel matrix with an element of the maximal order of the algebra. We prove that algebraic reduction attains the receive diversity when followed by a simple ZF detection. Simulation results for the Golden Code show that using MMSE-GDFE left preprocessing, algebraic reduction with simple ZF detection has a lo…
For uplink large-scale MIMO systems, minimum mean square error (MMSE) algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss-Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose a approximated method to compute log-likelihood ratio…
The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the soft-limiter and the blanker, which are two popular suboptimal estimators characterized by very low complexity. The MMSE-optimum thresholds for such suboptimal estimators are obtained by practical iterative algorithms with fast convergence. The paper derives also the optimal thresholds according to a maximum-SNR (MSNR) criterion, and establishes connections with the M…
In this paper, a downlink multiple input multiple output (MIMO) non-orthogonal multiple access (NOMA) wireless communication system is considered. In NOMA systems, the base station has unicast data for all users, and multiple users in a group share the same resources. The objective is to design transmit precoders and power allocation coefficients jointly that provide max-min fairness (MMF) among the strongest users in each group, while maintaining minimum target rates for all the other users. The problem is solved via two main iterative approaches. The first method is based on semi-definite re…
The effects of quantization and coding on the estimation quality of Gauss-Markov processes are considered, with a special attention to the Ornstein-Uhlenbeck process. Samples are acquired from the process, quantized, and then encoded for transmission using either infinite incremental redundancy (IIR) or fixed redundancy (FR) coding schemes. A fixed processing time is consumed at the receiver for decoding and sending feedback to the transmitter. Decoded messages are used to construct a minimum mean square error (MMSE) estimate of the process as a function of time. This is shown to be an increas…
This paper provides a combinatorial characterization of weak algebraic manipulation detection (AMD) codes via a kind of generalized external difference families called bounded standard weighted external difference families (BSWEDFs). By means of this characterization, we improve a known lower bound on the maximum probability of successful tampering for the adversary's all possible strategies in weak AMD codes. We clarify the relationship between weak AMD codes and BSWEDFs with various properties. We also propose several explicit constructions for BSWEDFs, some of which can generate new optimal…
