Information Outage Probability Research Articles

Limiting performance of block-fading channels with multiple antennas

We derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas, a block-fading channel with additive white Gaussian noise (AWGN), delay and transmit-power constraints, and perfect channel-state information available at both the transmitter and the receiver. Because of a delay constraint, the transmission of a codeword is assumed to span a finite (and typically small) number M of independent channel realizations; therefore, the relevant performance limits are the information outage probability and the (or nonergodic) capacity. We derive the coding scheme that minimizes the information outage probability. This scheme can be interpreted as the concatenation of an optimal code for the AWGN channel without fading to an optimal beamformer. For this optimal scheme, we evaluate minimum-outage probability and delay-limited capacity. Among other results, we prove that, for the fairly general class of regular fading channels, the asymptotic delay-limited capacity slope, expressed in bits per second per hertz (b/s/Hz) per decibel of transmit signal-to-noise ratio (SNR), is proportional to min (t,r) and independent of the number of fading blocks M. Since M is a measure of the time diversity (induced by interleaving) or of the frequency diversity of the system, this result shows that, if channel-state information is available also to the transmitter, very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high-frequency diversity. Moreover, for a large number of antennas, delay-limited capacity approaches ergodic capacity.

Modulation and coding for the Gaussian collision channel

We study signal-space coding for coherent slow frequency-hopped communications over a Gaussian multiple-access collision channel (G-MACC). We define signal sets and interleavers having maximum collision resistance. The packet-error probability and the spectral efficiency obtained by these signal sets concatenated with outer block coding and hard (error-only) decoding is evaluated without assuming perfect interleaving. Closed-form expressions are provided and computer simulations show perfect agreement with analysis. The structure of good interleavers is also discussed. More generally, we present expressions for the information outage probability and for the achievable (ergodic) rate of the G-MACC at hand, under various assumptions on user coding and decoding strategies. The outage probability yields the limiting packet-error probability with finite interleaving depth (delay-limited systems). The achievable rate yields the limiting system spectral efficiency for large interleaving depth (delay-unconstrained systems). Comparisons with other classical multiple-access schemes are provided.

Optimum power control over fading channels

We study optimal constant-rate coding schemes for a block-fading channel with strict transmission delay constraint, under the assumption that both the transmitter and the receiver have perfect channel-state information. We show that the information outage probability is minimized by concatenating a standard Gaussian code with an optimal power controller, which allocates the transmitted power dynamically to the transmitted symbols. We solve the minimum outage probability problem under different constraints on the transmitted power and we derive the corresponding power-allocation strategies. In addition, we propose an algorithm that approaches the optimal power allocation when the fading statistics are not known. Numerical examples for different fading channels are provided, and some applications discussed. In particular, we show that minimum outage probability and delay-limited capacity are closely related quantities, and we find a closed-form expression for the delay-limited capacity of the Rayleigh block-fading channel with transmission over two independent blocks. We also discuss repetition diversity and its relation with direct-sequence or multicarrier spread-spectrum transmission. The optimal power-allocation strategy in this case corresponds to selection diversity at the transmitter. From the single-user point of view considered in this paper, there exists an optimal repetition diversity order (or spreading factor) that minimizes the information outage probability for given rate, power, and fading statistics.