Sergey Loyka

Channel capacity of MIMO architecture using the exponential correlation matrix

Multiple-input multiple output (MIMO) communication architecture has recently emerged as a new paradigm for wireless communications in rich multipath environment, which has spectral efficiencies far beyond those offered by conventional techniques. The channel capacity of the MIMO architecture in independent Rayleigh channels scales linearly as the number of antennas. However, the correlation of a real-world wireless channel may result in a substantial degradation of the MIMO architecture performance. In this letter, we investigate the MIMO channel capacity in correlated channels using the exponential correlation matrix model. We prove that, for this model, an increase in correlation is equivalent to a decrease in signal-to-noise ratio (SNR). For example, r=0.7 is the same as 3-dB decrease in SNR.

Estimating MIMO system performance using the correlation matrix approach

The channel capacity of a multiple-input-multiple-output (MIMO) communication system depends substantially on correlation between individual receive branches. We investigate the MIMO capacity using the correlation matrix approach and the Salz-Winters (1994) spatial correlation model. It is shown that for a linear array, correlation has no impact on the MIMO channel capacity provided that the two-element array beamwidth is smaller than the angle spread of the incoming signals. Simple but accurate approximations for the correlation coefficient and the corresponding channel capacity are derived for different angular spreads.

New compound upper bound on MIMO channel capacity

MIMO channel capacity may be severely degraded due to correlation between individual sub-channels of the matrix channel. Several models, which are limited to some specific scenarios, have been developed to date to account for this effect. In this letter, we derive a new upper bound on the mean (ergodic) MIMO capacity, which is not limited to a particular scenario and accounts for both transmit (Tx) and receive (Rx) end correlations in such a way that their impact can be estimated separately and compared. Thus, a conclusion can be made as to which end contributes more to capacity reduction. In general, the higher correlated end has a dominant effect on the capacity.

On the Outage Capacity Distribution of Correlated Keyhole MIMO Channels

Keyhole multiple-input-multiple-output (MIMO) channels have recently received significant attention since they can model, to a certain extend, some practically important propagation scenarios and also relay channels in the amplify-and-forward mode. This paper investigates instantaneous signal-to-noise ratio (SNR) and outage capacity distributions of spatially correlated keyhole MIMO channels with perfect channel state information (CSI) at the receive end and with or without CSI at the transmit end. For a small number of antennas, the impact of correlation on the capacity distribution can be characterized by the effective average SNR. This SNR, as well as the outage capacity, decreases with correlation. For a large number of transmit (receive) antennas, the keyhole channel is asymptotically equivalent (in terms of capacity) to the Rayleigh diversity channel with a single transmit (receive) antenna and multiple receive (transmit) antennas. The outage capacity of the keyhole channel is upper-bounded by that of the equivalent Rayleigh diversity channel. When the number of both transmit and receive antennas is large, the outage capacity distribution of the keyhole channel is asymptotically Gaussian. In some cases, the asymptotic Gaussian approximation is accurate already for a reasonably small number of antennas. The perfect transmit CSI is shown to bring a fixed SNR gain. A more general channel model with multiple keyholes is proposed. For a large number of antennas, the capacity of a multikeyhole channel is a normally distributed sum of the capacities of single keyhole channels. The fact that, despite the strong degenerate nature of the keyhole channel, its outage capacity distribution is asymptotically normal indicates that Gaussian distribution has a high degree of universality for the capacity analysis of MIMO channels.

Exact capacity distributions for MIMO systems with small numbers of antennas

It is well known that multiple input multiple output (MIMO) systems offer the promise of achieving very high spectrum efficiencies (many tens of bit/s/Hz) in a mobile environment. The gains in MIMO capacity are sensitive to the presence of spatial correlation introduced by the radio environment. In this letter we consider the capacity outage performance of MIMO systems in correlated environments. For systems with large numbers of antennas Gaussian approximations are very accurate. Hence, we concentrate on systems with small numbers of antennas and derive exact densities and distribution functions for the capacity, which are simple and rapid to compute.

V-BLAST without optimal ordering: analytical performance evaluation for Rayleigh fading channels

The Bell Labs layered space-time (BLAST) algorithm is simple, and hence, a popular choice for a multiple-input multiple-output (MIMO) receiver. Its bit-error rate (BER) performance has been studied mainly using numerical (Monte Carlo) techniques, since exact analytical evaluation presents serious difficulties. Close examination of the problem of BLAST BER performance analysis reveals that the major difficulty for analytical evaluation is due to the optimal ordering procedure. Hence, we analyze the algorithm performance without optimal ordering. While this is a disadvantage of the analysis, there are certain advantages as well. Exact closed-form analytical evaluation is possible for arbitrary number of transmit and receive antennas in an independent, identically distributed Rayleigh fading channel, which provides deep insight and understanding that cannot be gained using the Monte Carlo approach alone. A result on the maximum ratio combining weights, which is used at each detection step, is derived to obtain a number of results: independence of noise, distribution of signal-to-noise ratio (SNR), and block- or bit-error rates. We present a detailed analysis and expressions for uncoded error rates at each detection step, which hold true for any modulation format and take simple closed form in some cases. Asymptotic form of these expressions for large SNRs is particularly simple. Extensive Monte Carlo simulations validate the analytical results and conclusions

Towards a Measure of Biometric Information

This paper addresses the issue of the information content of a biometric image or system. We define biometric information as the decrease in uncertainty about the identity of a person due to a set of biometric measurements. We then show that the biometric information for a person may be calculated by the relative entropy D(pparq) between the population feature distribution q and the persons feature distribution p. The biometric information for a system is the mean D(pparq) for all persons in the population. In order to practically measure D(pparq) with limited data samples, we introduce an algorithm which regularizes a Gaussian model of the feature covariances. An example of this method is shown for PCA and ICA based face recognition, with biometric information calculated to be 45.0 bits (PCA), 39.0 bits (ICA) and 46.9 bits (fusion of PCA and ICA features). Finally, we discuss general applications of this measure

On MIMO channel capacity, correlations, and keyholes: analysis of degenerate channels

It has been demonstrated that zero correlation of a random multiple-input multiple-output channel is not a guarantee of its high capacity. Degenerate channels exist, which have zero correlation and still low capacity. We provide a statistical analysis of this phenomenon, formulate the general condition for a channel to be degenerate, and propose a method to estimate its capacity.

Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multidimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER first and second derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels (¿fading is never good in low dimensions¿) and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates, and to coded systems.

Multiantenna capacities of waveguide and cavity channels

Multiple-input-multiple-output (MIMO) capacity of waveguide and cavity channels is investigated using the modal expansion technique. Rectangular and circular waveguides and cavities are studied in details. Approximate expressions for the number of modes and for the capacity are given. A MIMO system architecture is suggested for a waveguide channel, which achieves the full capacity by making use of the mode orthogonally (or near orthogonality) using an eigenmode modulator at the Tx end and a spatial correlation receiver at the Rx end. Various practical limitations (e.g., nonideal waveguides and modulators, using discrete sensors instead of continuous, one-dimensional sensors instead of two-dimensional, etc.) and their impact on the capacity are discussed. It is demonstrated that long cavities are equivalent to waveguides in terms of capacity. The concept of spatial capacity is introduced to characterize the limits on the transmission rates that are due to both electromagnetic and information-theoretic considerations, which can be evaluated in a closed form for ideal waveguides and cavities. It follows that the traditional single-mode transmission is optimum in terms of capacity in the small signal-to-noise ratio region only.