We provide an overview of the extensive recent results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends

We show that the Gaussian multipleaccess channel (MAC) and broadcast channel (BC) are duals. The dual channels we consider have the same channel gains and the same noise power at all receivers. We nd an expression for the capacity region of the BC in terms of the capacity region of the dual MAC, and vice versa. Duality applies to many dierent channel models and capacity de nitions.

We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We present a unified theory for eight special cases of channel capacity and rate distortion with state information, which also extends existing results to arbitrary pairs of independent and identically distributed (i.i.d.) correlated state information @ I PA available at the sender and at the receiver, respectively. In particular, the resulting general formula for channel capacity a �— � @ A ‘ @ Y P A @ Y IA “ assumes the same form as the generalized Wyner–Ziv rate distortion function @ A a �� � @ A @ ” A ‘ @ Y I A @ Y PA“.

This paper considers the vector Gaussian broadcast channel where a single transmitter with multiple antennas sends independent information to multiple receivers. An achievable rate region is derived by decomposing the broadcast channel into a series of single-user channels with non-causal side information. The side information may be completely pre-subtracted using precoding techniques. A practical trellis precoding method is presented. Trellis precoding can be viewed as a generalization of the Tomlinson-Harashima precoder. By taking into account the entire non-causal side-information sequence, a trellis precoder gives an additional shaping gain up to 1.53dB compared to a Tomlinson precoder. I.

Multi-user diversity has attracted significant attention recently. In this paper, we propose a greedy algorithm based on QR decomposition of the channel and dirty paper precoding to exploit the multi-user diversity of the Gaussian vector broadcast channel. Simulations show the approach provides performance which is extremely close to a well-known upper bound on the sum rate. Further, exploiting multi-user diversity can provide large gain over approaches ignoring this resource.

It is known that some of the spectacular capacity gains of using multiple antennas on a point-to-point rich scattering channel, namely linear growth with the number of antennas, can also be obtained in a multi-user environment. We give the constant of proportionality of linear growth in the sum-capacity when the number of users and antennas grow simultaneously, but with fewer users than antennas. We assume that the transmitter and receivers know the channel. Because of the linear growth in sum-capacity, we can accommodate more users simply by adding more antennas, without increasing total transmitted power or bandwidth or lowering the rate to existing users. We dub any scheme that can achieve linear growth in this fashion a space-time multiple access scheme. Channel-hardening arguments show that a "channel-inversion" technique used in point-to-point multiple-antenna links achieves a large fraction of this linear growth in a multi-user environment without excessive transmitter power. Thus, multiple-antennas offer a tremendous advantage in designing scheduling, networking, and multiple-access protocols in rich scattering environments.

A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa’s strategies (i.e. by a random binning scheme induced by Costa’s auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies (“lattice precoding”) can achieve positive rates independent of the interferences, and in fact in some cases- which depend on the noise variance and power constraints- they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a “helper ” to the other user), and for the “common interference ” case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.

A Gaussian channel, when corrupted by an additive Gaussian interfering signal whose complete sample sequence is known non-causally to the transmitter but not to the receiver, has the same capacity as if the interfering signal were not present. This is true even when the noise and interference are not necessarily stationary or ergodic. 1

Abstract—We provide achievable rate regions for two-way relay channels (TRC). At first, for a binary TRC, we show that the subspace-sharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subset-sharing of lattice codes. In some cases, the proposed lattice coding scheme can achieve within 1/2-bit the capacity and is asymptotically optimal at high signal-to-noise ratio (SNR) regimes. I.

A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. Simulation results show that the proposed scheme performs well, and as compared to the more complex methods (such as the perturbation method [1]) has a negligible loss.