We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading.

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

Multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels. This paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed. A compact model is developed for the multiple-input multiple-output (MIMO) dispersive spatially selective wireless communication channel. The multivariate information capacity is analyzed. For high signal-to-noise ratio (SNR) conditions, the MIMO channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components, the number of input antennas, or the number of output antennas. This desirable result is contrasted with the lower capacity slope of the well-studied case with multiple antennas at only one side of the radio link. A spatio-temporal vector-coding (STVC) communication structure is suggested as a means for achieving MIMO channel capacity. The complexity of STVC motivates a more practical reduced-complexity discrete matrix multitone (DMMT) space--frequency coding approach. Both of these structures are shown to be asymptotically optimum. An adaptive-lattice trellis-coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the DMMT channel. Experimental examples that support the theoretical results are presented. Index Terms---Adaptive arrays, adaptive coding, adaptive modulation, antenna arrays, broad-band communication, channel coding, digital modulation, information rates, MIMO systems, multipath channels. I.

This paper characterizes the sum capacity of a class of non-degraded Gaussian vectB broadcast channels where a singletransmitter with multiple transmit terminals sends independent information to multiple receivers. Coordinat+[ is allowed among the transmit teminals, but not among the different receivers. The sum capacity is shown t be a saddlepoint of a Gaussian mu al informat]R game, where a signal player chooses a tansmit covariance matrix to maximize the mutual information, and a noise player chooses a fictitious noise correlation to minimize the mutual information. This result holds fort he class of Gaussian channels whose saddle-point satisfies a full rank condition. Furt her,t he sum capacity is achieved using a precoding method for Gaussian channels with additive side information non-causally known at the transmitter. The optimal precoding structure is shown t correspond to a decision-feedback equalizer that decomposes t e broadcast channel into a series of single-user channels with intk ference pre-subtract] at the transmiter.

In this paper we introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed form solutions for transmission over frequency selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the sub-channels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER and symbol mean square error.

In this paper, Tomlinson-Harashima precoding for multiple-input/multiple-output systems including multiple-antenna and multi-user systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover, it outperforms decision-feedback equalization at the receiver side which is applicable if joint processing at the receiver side is possible, and which suffers from error propagation. A number of aspects of practical importance are studied. Loading, i.e., the optimum distribution of transmit power and rate is discussed in detail. It is shown that the capacity of the underlying MIMO channel can be utilized asymptotically by means of non-linear precoding.

Optimal finite impulse response (FIR) transmit and receive filterbanks are derived for block-based data transmissions over frequency-selective additive Gaussian noise (AGN) channels by maximizing mutual information subject to a fixed transmitpower constraint. Both FIR and pole-zero channels are considered. The inherent flexibility of the proposed transceivers is exploited to derive, as special cases, zero-forcing (ZF) and minimum mean-square error receive filterbanks. The transmit filterbank converts transmission over a frequency-selective fading channel, affected by additive colored noise, into a set of independent flat fading subchannels with uncorrelated noise samples. Two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels, while adhering to an upper bound on the bit error rate (BER). Reduction of the signal-to-noise ratio (SNR) margin required to satisfy the prescribed BER is achieved by coding each subchannel’s bit stream. The potential of the proposed transceivers is illustrated and compared to discrete multitone (DMT) with simulated examples.

In this paper, Tomlinson-Harashima precoding, a nonlinear pre-equalization technique, is proposed for transmission over multiple-input/multiple-output channels. Instead of equalizing intersymbol interference (temporal equalization) here spatial equalization, i.e., equalization of the multi-user interference, or combined spatial/temporal equalization is performed. It is shown that this MIMe precodinglike its sISe counterpart offers significant advantages over linear pre-equalization and over decisionfeedback equalization, as is done in BLAST-like schemes. Using channel coding, MIMe precoding is able to achieve higher power efficiencies at lower coding delays than competing schemes.

The availability of software radios and application of interference avoidance may offer a new perspective on communication over dispersive channels. By both lengthening the transmission interval so that ISI is almost inconsequential and by using combinations of channel eigenfunctions to convey the bits, communications over dispersive channels becomes (not surprisingly) a multiuser detection problem where each bit is assigned its own waveform. By choosing these waveforms to meet the Welch Bound with equality – through interference avoidance or some other numerical method – a uniform maximum SINR can be achieved for each bit. In addition by using Gaussian signaling and decoding with this codeword ensemble, the channel capacity can be (theoretically) met. A trivial extension of the single user case can be used for multiple users over identical channels. Multiple users with non-identical channels is more subtle and is discussed in the interference avoidance context with suggestions for future work. 1

By both lengthening the transmission interval so that ISI is almost inconsequential and by using combinations of channel eigenfunctions to convey the bits, communications over dispersive channels can be cast as a multiuser detection problem where each bit is assigned its own waveform. For a single dispersive channel -- through interference avoidance or some other numerical method -- a uniform maximum signal-to-interference plus noiseratio (SINR) can be achieved for each bit. These codeword ensembles also maximize the mutual information between the channel input and channel output assuming Gaussian signaling (sum capacity). For the multiple access case where different signals are received at a common base over different dispersive channels, we show that application of interference avoidance again yields an information theoretically optimal ensemble of codewords. Popescu and Rose: Multiaccess Dispersive Channels and IA 2 1 Introduction Wireless communication channels are generally di...