Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decode-and-forward the source message to the destination, or they compress-and-forward their channel outputs to the destination. The decode-and-forward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compress-and-forward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination’s channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, single-bounce fading, certain quasi-static fading problems, cases where partial channel knowl-edge is available at the transmitters, and cases where local user co-operation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels.

This paper provides an overview of state-of-the-art radio propagation and channel models for wireless multiple-input multiple-output (MIMO) systems. We distinguish between physical models and analytical models and discuss popular examples from both model types. Physical models focus on the double-directional propagation mechanisms between the location of transmitter and receiver without taking the antenna configuration into account. Analytical models capture physical wave propagation and antenna configuration simultaneously by describing the impulse response (equivalently, the transfer function) between the antenna arrays at both link ends. We also review some MIMO models that are included in current standardization activities for the purpose of reproducible and comparable MIMO system evaluations. Finally, we describe a couple of key features of channels and radio propagation which are not sufficiently included in current MIMO models. I. INTRODUCTION AND OVERVIEW Within roughly ten years, multiple-input multiple-output (MIMO) technology has made its way from purely theoretical performance analyses that promised enormous capacity gains [1], [2] to actual products for the wireless market (e.g., [3], [4], [5]). However, numerous MIMO techniques still have not been sufficiently tested under realistic propagation conditions and hence their integration into real applications can be considered to

The problem of energy-efficient precoding is investigated when the terminals in the system are equipped with multiple antennas. Considering static and fast-fading multiple-input multiple-output (MIMO) channels, the energy-efficiency is defined as the transmission rate to power ratio and shown to be maximized at low transmit power. The most interesting case is the one of slow fading MIMO channels. For this type of channels, the optimal precoding scheme is generally not trivial. Furthermore, using all the available transmit power is not always optimal in the sense of energy-efficiency [which, in this case, corresponds to the communication-theoretic definition of the goodput-to-power (GPR) ratio]. Finding the optimal precoding matrices is shown to be a new open problem and is solved in several special cases: 1. when there is only one receive antenna; 2. in the low or high signal-to-noise ratio regime; 3. when uniform power allocation and the regime of large numbers of antennas are assumed. A complete numerical analysis is provided to illustrate the derived results and stated conjectures. In particular, the impact of the number of antennas on the energy-efficiency is assessed and shown to be significant.

Abstract — Recent advances in multi-hopping are extended to relay networks having multiple antennas and multiple sources. As for the single-antenna and single-source case, one can achieve the ergodic capacity of wireless relay networks with phase fading if the relays are in a region near the source terminal, and if phase information is available only locally. The capacity results further generalize to Rayleigh fading, single-bounce fading, certain quasistatic fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The multi-source networks considered are the multi-access and broadcast relay channels. I.

The general framework of Mobile Flexible Networks is to design self-organizing secure networks where terminals and base stations interact and self-adapt in an intelligent manner without the need of a central controller (or with the right amount of regulation...just enough to let the agents in the network exploit fully the degrees of freedom). Of course, the design depends on the mobility pattern and delay tolerance as in highly mobile environments, exchange of control signaling bears a huge cost whereas for fixed (non-mobile) networks, the designer can dedicate a fraction of the rate (which is negligible in terms of overhead) to optimize the system. One of the big challenges is to find how to optimally split the intelligence between cognitive terminals and cognitive networks. In this paper, we discuss the challenges ahead and provide some research directions to develop the theoretical foundations of these networks.

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Abstract—The potential benefits of multiple-antenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multiple-input multiple-output (MIMO) systems, with an emphasis on orthogonal space–time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signal-to-noise ratio (SNR). In particular, we consider a general family of MIMO chan-nels known as double-scattering channels—i.e., Rayleigh product MIMO channels—which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rank-deficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order

In this contribution, models of wireless channels are derived from the maximum entropy principle, for several cases where only limited information about the propagation environment is available. First, analytical models are derived for the cases where certain parameters (channel energy, average energy, spatial correlation matrix) are known deterministically. Frequently, these parameters are unknown (typically because the received energy or the spatial correlation varies with the user position), but still known to represent meaningful system characteristics. In these cases, analytical channel models are derived by assigning entropy-maximizing distributions to these parameters, and marginalizing them out. For the MIMO case with spatial correlation, we show that the distribution of the covariance matrices is conveniently handled through its eigenvalues. The entropy-maximizing distribution of the covariance matrix is shown to be a Wishart distribution. Furthermore, the corresponding probability density function of the channel matrix is shown to be described analytically by a function of the channel Frobenius norm. This technique can provide channel models incorporating the effect of shadow fading and spatial correlation between antennas without the need to assume explicit values for these parameters. The results are compared in terms of mutual information to the classical i.i.d. Gaussian model.

We apply the replica method to analyze vector precoding, a method to reduce transmit power in antenna array communications. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We find that vector precoding performs much better for complex than for real alphabets. As a byproduct, we find a nonlinear precoding method with polynomial complexity that outperforms NP-hard Tomlinson-Harashima precoding for binary modulation on complex channels if the number of transmit antennas is slightly larger than twice the number of receive antennas. Index Terms Multiple-antenna wireless, multiple-input multiple-output (MIMO), spatial equalization, Tomlinson-Harashima precoding, replica method, random matrices, R-transform. I.

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