Wideband fading channel capacity with training and partial feedback
IEEE Transactions on Information Theory
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A practical challenge in wireless communication systems is acquisition of channel state information at the transmitter and the receiver. In this thesis, we address the problem of training and limited-rate feedback optimization for fading channels. In a wideband (multi-carrier) channel, given limited coherence time and power, only a finite number of channel coefficients (each corresponding to a coherence band, or sub-channel) can be estimated. The achievable rate of such systems is therefore governed by the coherence time. A threshold based on-off transmission scheme, which requires only limited rate feedback, is assumed. For both single-user and a multiple access wideband channels, we optimize the training length and power, number of sub-channels probed, and the feedback threshold. For a correlated fading channel, we propose an adaptive training power control scheme, which can be implemented with limited rate channel state feedback (CSF). With this scheme, training power is reduced (increased) when the channel is faded (good). At low signal to noise ratios, or with fast fading, this scheme is shown to provide substantial gains. Next we consider the design of a limited CSF scheme for multi-carrier channels in which sub-channels randomly take on either a good or bad state. The problem is formulated as a vector quantization problem and performance bounds are obtained using rate-distortion theory. The results are then applied to Rayleigh fading sub-channels, which are reduced to two state sub-channels by comparing channel gains with a threshold. We also study the reliability of block codes over memoryless channels in which a fraction of received symbols are noiselessly fed back to the transmitter. We give an upper bound on the error exponent for this channel. In addition, for additive white Gaussian noise channels, we propose a coding scheme that exploits the partial feedback and achieves an error exponent that is close to the upper bound. Finally, we study the trade-off between CSF and receiver state feedback (RSF) over a multi-carrier block Rayleigh fading channel. RSF refers to the information about the decoder state, which can be used to improve reliability (e.g., through re-transmissions). Given a fixed forward rate we divide the feedback between CSF and RSF to maximize the error exponent. It is shown that the optimal trade-off depends critically on the coherence time.