We study the problem of maximizing the expected rate over a slowly fading channel with quantized channel state information at the transmitter (CSIT). This problem has been recently studied in the literature assuming a noiseless feedback link. In this work, we consider a more realistic model, where the feedback link suffers from fading, as well as the limited power allocated to the feedback signals. Our scheme considers a finite-state model to capture the fading in the feedback link. We solve the rate maximization problem with different power control strategies at the transmitter. A channel optimized scaler quantizer (COSQ) is designed to incorporate feedback in our transmission scheme. Unlike the conventional COSQs where the objective is to reconstruct the source, our proposed quantizer is designed to optimize the expected rate of the forward link. For a high quality feedback channel, the proposed system performs close to the noiseless feedback case, while its performance converges to the nofeedback scenario as the feedback channel quality degrades.
We consider the problem of transmitting an analog source over a quasi-static fading channel. This problem is motivated by the recent demand for multimedia content over wireless channels. The goal is to minimize the expected distortion of the received signal. Over slowly fading channels, the delay sensitivity of multimedia applications limits channel coding to a single fading realization. Due to the non-ergodicity of the channel, Shannon's separation theorem does not hold and a joint source-channel coding approach is more appropriate. When no channel state information is available at the transmitter, a multiple-antenna fading channel with either one receive or one transmit antenna can be modeled as a degraded broadcast channel where each channel realization corresponds to a user. The optimal transmission strategy for the degraded broadcast channel is superposition coding. Codewords of different rates and powers are superimposed and transmitted over the channel. At the receiver, the fading channel realization allows the layers up to a certain level to be decoded, while considering the undecodable layers as interference. The problem is to find the optimal rate and power allocations that minimize the expected distortion. In [1], the optimal distortion exponent for this system is derived that is defined as the slope of the expected distortion curve with respect to the channel signal to noise ratio (SNR) for asymptotically high SNRs. In our work, we propose an efficient numerical technique to explicitly solve the rate and power allocation problems at a finite SNR. Our proposed algorithm iteratively optimizes the rates for a given power allocation and vice versa, and is guaranteed to converge. Fig. 1(a) shows the results for a complex Gaussian source and one-transmit, one-receive antenna (1x1), and 4x1 systems with different number of layers (N). The bandwidth expansion ratio, b, is the number of channel symbols transmitted per source symbol. It is seen that 5 layers achieves almost all the gain associated with layering. Fig. 1(b) represents the gain of superposition coding with respect to time-sharing [2]. Fig. 1(c) shows that for very small N (N=2) and large b (b=10), unequal rate allocation provides gains up to 1.8dB. For other scenarios, however, optimal power allocation with equal rate assignment is nearly optimal. 0 20 40 0 0.2 0.4 0.6 0.8 1 1.2
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