Abstract-Inspired by multiaccess in dense cellular systems, the paper first considers minimizing the determinant of the sum of a subset of n i.i.d. central Wishart matrices, for any given size. When n goes to infinity, the exact scaling for more general case, selecting a subset to minimize the product-determinant-sum of n i.i.d. central Wishart matrix vectors, is provided. Specifically, suppose each vector has K Wishart matrices of format GG with G of dimension Nr× Nt. Then for any subset of size nα, the K determinants, each being the sum over one of the vector elements, will have a product no less than exp{K Nr(1+ 1/K NrNt)(α - α*) log n}, for all a between α* := 1/(1 + K NrNt) and 1. The paper then applies the results to study multiaccess with cross-cell collaborations in dense environment. When each cell allows multi-users to be on and decodes by treating signals from neighboring cells as noise, the maximum throughput is characterized and achieved by selecting users based on their channels. Specifically, if every cell allows same number of nodes to be on and decodes by successive interference cancellation for in-cell nodes, the maximum throughput is Nr/1 + K NrNtlog n bit/s/Hz/cell when n goes to infinity, where n,K, Nr, Ntare numbers of nodes per cell, neighbors per cell, receive antennas per user and transmit antennas per base station, respectively. It is also shown that time-sharing across cells achieves higher throughput, determined by the chromatic number of the interference graph.

We consider multiaccess in cell-based dense wireless networks (e.g., cellular and WiFi with access points) when the communications are interference-limited. The purpose is to understand, in a dense network, how MIMO, user diversity, network topology and limited cooperation influence the uplink cell throughput. Each cell has n Nt-antenna users and K neighboring Nr-antenna cells, and the channels are i.i.d. Rayleigh. Multi-users are allowed to transmit in one cell simultaneously, and each cell decodes by treating signals coming from other cells as noise. We assume that only the receivers have channel state information (CSI), and every cell has a common number of active users. It is shown that Nr/1+KNtNrlog n bit/s/Hz is achievable for every cell by selecting exp{ 1/1+KNtNrlog n} users per cell according to a simple threshold rule, and decoding using successive interference cancelation. On the other hand, this is also shown to be an upper bound on the per cell throughput, no matter how users are chosen. Furthermore, simulations are provided to verify the results.

We consider a multi-user MIMO downlink where the transmitter has only estimates of the channel while the receivers have perfect channel information. The impact of channel estimation error on the sum rate is studied. It is shown that the sum rate saturates due to the inaccurate channel information. In order to maintain full multiplexing gain, the channel estimation quality has to increase with at least the square root of data SNR but there is no need to increase more than linearly with the SNR. With user scheduling, the sum rate scales at leastM/2loglogK, whereKis the number of users and M is the number of transmit antennas.

Based on random codes and typical set decoding, an alternative proof of Root and Varaiya's compound channel coding theorem for linear Gaussian channels is presented. The performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation. Although the theorem promises uniform convergence of the probability of error as the block length approaches infinity, with short block lengths the performance can differ considerably for individual channels. Simulation results show that universal performance can be a practical goal as the block lengths become large.

We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks

We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, l terminals, and n relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.) /spl sim/X, the maximum flow between the source and the terminals is approximately nE[X] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area.

A channel-eigenvector invariant space-time constellation (CEI-STC) is a set of matrices such that the product of any pairwise difference matrix and its complex conjugate transpose is a scalar matrix. The pairwise error probability of a multi-antenna system equipped with the CEI-STC does not depend on the eigenvectors of the channel matrix. It may, however, depend on the eigenvalues of the channel. The maximum cardinality of a CEI-STC whose entries are restricted to a finite set is studied. A lower bound and an upper bound on the maximum cardinality are obtained.

The rotationally invariant space time constellation (RISTC) is defined. Both linear and affine constellations are studied. The RISTC is shown to be generalization of space time codes from the orthogonal design. A space time constellation is said rotationally invariant if for any pair in the set, the squared Euclidean distance is independent of the eigenvectors.

For trellis codes, generating function techniques provide the distance spectrum and a union bound on bit-error rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using low-complexity approaches. The second stage produces the generating function from the reduced-state diagram through some form of matrix inversion, which has a relatively high complexity. In this paper, we improve on the amount of state reduction possible during the low-complexity first stage. We also show that for a trellis code that is a linear convolutional code followed by a signal mapper, the number of states may always be reduced from N/sup 2/ to ((N/sup 2/-N)/2)+1 using low-complexity techniques. Finally, we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two-stage approach we propose has the lowest complexity. In an example, the new technique produced the union bound in about half the time required by the best algorithm already in the literature.

Biglieri showed that a diagram with N/sup 2/ states can be used to compute the generating function for any trellis code with N states. Rouanne & Costello and Zehavi & Wolf showed that for quasi-regular trellis codes, an N-state diagram produces the correct generating function. Schlegel showed that application of a standard FSM (finite-state-machine) minimization algorithm reduces quasi-regular trellis code diagrams to at most N states and often reduces the number of states for non-quasi-regular trellis codes as well. In this paper we show that performing iteratively both a forward and a backward application of Schlegel's state reduction operation can further reduce the diagram produced by Schlegel's algorithm. We also found that the maximum required diagram size for linear trellis codes to be [(N/sup 2/ - N)/2] + 1.

Foschini's (1996) diagonally layered space-time transmission system known as D-BLAST is an advanced architecture designed for a Rayleigh fading environment using multiple element antenna arrays at both the transmit and receive sites to achieve very high spectral efficiencies. In this paper we examine the performance of trellis codes that are designed to have a distance structure that is matched to the periodic signal-to-noise ratio variation of the channel created by D-BLAST, under the assumption that the channel is static during one burst but may change from burst to burst. We show that trellis coding comes within 2 dB of the best theoretical outage curve possible with D-BLAST.