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This work analyzes a heterogeneous network ( HetNet), which comprises a macro base station ( BS) equipped with a large number of antennas and an overlaid dense tier of small cell access points ( SCAs) using a wireless backhaul for data traffic. The static and low mobility user equipments ( UEs) are associated with the SCAs while those with medium-to-high mobility are served by the macro BS. A reverse time division duplexing ( TDD) protocol is used by the two tiers. We evaluate and characterize the performance of the system through the power consumption of uplink ( UL) and downlink ( DL) transmissions under the assumption that target rates must be satisfied and imperfect channel state information is available. The large system analysis is used to provide concise formulae for the asymptotic UL and DL transmit powers and precoding vectors under the above assumptions. Numerical results are used to validate the analysis in different settings and to make comparisons with alternative network architectures.

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused to the distribution close to its most probable value, thus obtaining an asymptotically Gaussian distribution, we calculate the full distribution including its tails, which behave quite differently from the bulk of the distribution. Our resulting probability distribution seamlessly interpolates between the Gaussian approximation for rates R close to the ergodic value of the mutual information and the approach of Zheng and Tse [1], valid for large signal to noise ratios rho. This provides us with a tool to analytically calculate outage probabilities at any point in the (R, rho, N) parameter space, as long as the number of antennas N is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to R for a given rho. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities.

We investigate the emergence of rationality in repeated games where, at each iteration, the players’ payoffs are randombly perturbed (to account e.g. for the effects of fading or errors in the reading of one’s throughput). We see that even if players start out completely uneducated about the game, there is a simple learning scheme that enables them to eventually weed out the noise and identify suboptimal choices, regardless of the noise level. More precisely, we show that strategies that are strictly dominated (even iteratively) become extinct in the long run, i.e. players exhibit rational behavior. As an application, we model a number of users that are able to switch dynamically between multiple wireless nodes and see that they are able to pick up which node works best for them, even in the presence of high performance fluctuations.

The dynamics of handover between two coexisting Wireless standards and the consequent exploitation of the offered diversity by the use of multi standard terminals has been dis cussed. The potential capacity benefits of mobile initiated vertical handovers are substantial. However, it is important to choose the correct VHO criteria in order to achieve optimum load balancing and equilibrium states (global and social). Two fast handover schemes are presented, which exhibit fast convergence to the socially optimal states by allowing a subset of the necessary VHOs among the Als. In all cases the scheme with replicator dynamics, had the best performance at the cost of an increased vertical handover rate.

The so-called “replica method” of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. Focusing on discrete complex input alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. The energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. The limiting empirical distribution of the precoder’s output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a “zero-forcing” (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u is the channel input, X is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discrete-lattice alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high E-b/N-0 region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed.

While most literature on MIMO (Multiple-Input, Multiple-Output) multiantenna communications and space-time coding has considered optimal decoding, or bounded-distance approximations thereof, the current standardization trend in wireless local area network (WLAN) systems such as IEEE 802.11n, that will use MIMO as an integral component of their physical layer, focuses on simpler schemes, where a linear space-time equalizer is used to separate the signals from the M transmit antennas, thus creating a set of M “virtual” parallel channels. The output of these parallel channels is then fed to a standard SISO (Single-Input, Single-Output) decoder. Surprisingly, the Diversity-Multiplexing Tradeoff (DMT) of this simple scheme has not been fully characterized before. We provide such characterization in this work, where we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is equal to that of *one* of the parallel channels, even though coding and decoding is performed across the antennas. Hence, linear receivers incur a dramatic loss of diversity gain with respect to other non-linear schemes. Furthermore, we comment on the different behavior of the MMSE and ZF receivers at finite rate (zero multiplexing gain).

We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. 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 specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization i) 2-point lattice pre-coding and ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.