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

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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.

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.

Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval---in which case there is a nonzero "outage capacity"---or multiple fading intervals---in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space-time signals are their own channel codes. We call this phenomenon space-time autocoding, and the accompanying capacity the space-time autocapacity. Let an M-transmitter-antenna, N-receiver-antenna Rayleigh flat fading channel be characterized by an M \Theta N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T -symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of ...

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We show that the Gaussian multiple-access channel and the Gaussian broadcast channel are fundamentally related and are essentially duals of each other. The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of a broadcast channel (both constant and fading) can be written in terms of the capacity region of the dual multiple-access channel, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the broadcast channel is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different notions of Shannon capacity for fading channels such as outage capacity and minimum rate capacity. Using duality, many results known for only one of the two channels are now known for the dual channel as well.

Abstract — This paper addresses cross-layer resource allocation in quasi-static fading multiple access channels (MAC) with no channel state information at the transmitters (CSIT). Under the cross-layer approach without CSIT, the power and rate are determined based on an outage rate region as well as the current queue state information (QSI). For heterogeneous quality-ofservice (QoS) requirements, an individual outage rate region results in better performance compared to the common outage rate region that is widely considered in the literature. This paper first reviews the recent notion of an individual outage rate region for the quasi-static fading MAC without CSIT. Individual outage rate regions are then used in two major types of scheduling policies: maximum weight matching scheduling (MWMS) and queue proportional scheduling (QPS). It is shown that MWMS and similar techniques based on weighted-sum-rate maximization require exponential complexity in the number of users because of the non-convex nature of the relevant optimization problems. By contrast, QPS can be very efficiently solved by using a successive feasibility check. Stochastic simulations show that compared to MWMS and the common outage rate region, significant throughput increase and delay reduction are possible by using the QPS scheduling policy with the individual outage rate region. I.

Consider a system with a xed number (K) of remote units and a single base transmitter with time varying (and perhaps correlated) connecting channels. Data to be transmitted to the remote units arrives according to some random process and is queued according to its destination. The forward link is treated. Power is to be allocated to the K channels in a queue and channel state dependent way to minimize some cost criterion. The modeling and control problem can be quite difficult. The channel time variations (fading) are fast and the bandwidth and data arrival rates are high. Owing to the complexity of the physical problem and the high speed of both the fading and arrival and service rates, an asymptotic or averaging method is promising. A heavy traffic analysis is done. By heavy traffic, we mean that on the average there is little server idle time and little spare power over the "average" requirements. Heavy traffic analysis has been very helpful in simplifying analysis of both controlled and uncontrolled problems in queueing and communications networks. It tends to eliminate unessential detail and focus on the fundamental issues of scaling and parametric dependencies. To illustrate the scope of the method, a variety of models are considered. The basic model assumes that the channel state is known or can be well estimated and that given the channel state there is a well defined rate of transmission per unit power. Then convergence of the controlled scaled queue lengths is shown. The scaling is different from the usual in heavy traffic work, and the limit Wiener process depends only on the channel state process and not on the...

Abstract We consider a non-ergodic multiple access Gaussian block-fading channel where a fixed number of independent identically distributed fading coefficients affect each codeword. Variable-rate coding with input power constraint enforced on a percodeword basis is examined. A centralized power and rate allocation policy is determined as a function of the previous and present fading coefficients. The power control policy that optimizes the expected rates is obtained through dynamic programming and the average capacity region and the average capacity region per unit energy are characterized. Moreover, we study the slope of spectral efficiency curve vs. (Eb=N0)dB, and we quantify the penalty incurred by TDMA over superposition coding in the low power regime.