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For a time-correlated channel, we consider the differential feedback of the geometrical mean decomposition (GMD) precoder, which is known to be optimal for a number of criteria. When the channel varies slowly, we can expect the optimal GMD precoders of consecutive channel uses to be close. We consider the feedback of the so-called differential precoder and show that it lies in a neighborhood of the identity matrix using matrix perturbation theory. Furthermore, the radius of the neighborhood is shown to be proportional to a time-correlation parameter. Such a characterization allows for subsequent efficient quantization of the differential precoder. We show how to design codewords for the prescribed radius by perturbing the identity matrix and applying QR decomposition on the perturbed matrix. Simulations are given to demonstrate that, with a small feedback rate, the performance of the proposed differential GMD comes close to the case when perfect channel state information is available to the transmitter for slowly time-varying channels like those in indoor and microcellular environments. [ABSTRACT FROM PUBLISHER]

In this paper, we consider variable-rate transmission over a slowly varying multiple-input multiple-output (MIMO) channel with a decision feedback receiver. The transmission rate is adapted to the channel by dynamically assigning bits to the subchannels of the MIMO system. Predictive quantization is used for the feedback of bit loading to take advantage of the time correlation inherited from the temporally correlated channel. Due to the use of decision feedback at the receiver, the bit loading is related to the Cholesky decomposition of the channel Gram matrix. Assuming the channel is modeled by a slowly varying Gauss–Markov process, we show that the nested submatrices generated during the process of Cholesky decomposition can be updated as time evolves. Based on the update, we derive the optimal predictor of the next bit loading for predictive quantization. Furthermore, we derive the statistics of the prediction error, which are then exploited to design the quantizer to achieve a smaller quantization error. Simulations are given to demonstrate that the proposed predictive quantization gives a good approximation of the desired transmission rate with a low feedback rate. [ABSTRACT FROM PUBLISHER]

In this paper we consider variable-rate transmission for time-correlated MIMO (multi-input multi-output) channels with limited feedback. The number of bits loaded on each subchannel of the MIMO system is dynamically assigned according to the current channel condition and fed back to the transmitter. As the channel is time-correlated, bit loading is a vector signal that is also time-correlated. We propose to feedback bit loading using predictive coding, which is known to be a powerful quantization technique when the underlying signal is correlated in time. Assuming the channel is a first-order Gauss-Markov random process, we derive the predictor for the bit loading to be coded and analyze the corresponding prediction error variance when the channel is varying slowly. By exploiting the prediction error variance, we adapt the quantizer of the prediction error to have a smaller quantization error. Furthermore we show that the prediction error variance is proportional to a term that depends only on the time-correlation coefficient. This leads to the conclusion that, a codebook that is designed for a particular time correlation coefficient can be easily modified to a codebook for a different correlation coefficient without redesign. Simulations are presented to demonstrate that the proposed predictive coding can achieve a very good approximation of the desired transmission rate with a very low feedback rate. [ABSTRACT FROM PUBLISHER]