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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]

Hybrid precoding that combines analog RF processing and digital baseband processing has been shown to be a promising technique for transceivers with limited number of RF chains. The RF processing, due to power and complexity issue, is typically done by using phase shifters. A recent study shows that hybrid precoding is no loss of generality if each coefficient of the analog precoder is implemented by using two phase shifters. In this paper, we consider two possible implementation structures that use Two pHase shIfters for each Coefficient (THIC). These two structures, having the same performance when the phases can take on continuum values, behave differently upon quantization, as the analysis shows. For a small number of quantization bits, the precoder implemented using THIC is a good approximation of the unquantized one. With 3-bit phase shifters, the performance is close to that of the unquantized system in multiuser communications, where the performance is more sensitive to quantization errors. While the analysis in this paper is done assuming high-resolution quantization, simulations show that the result is accurate even for coarse quantization. [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]

In this paper, we jointly consider statistical precoding and feedback of bit allocation (BA) for multiple-input–multiple-ouput (MIMO) systems over correlated channels. The proposed system will be termed a BA system. We assume that the statistics of the channel is known to the transmitter and a reverse link of very low rate is available so that the receiver can send back the quantized BA. Based on the statistics of the channel, we derive the statistical precoder so that bounds of the error rate averaged over the random correlated channel are minimized. Due to statistical precoding, the distribution of the BA is highly nonuniform. Treating BA as a vector signal, we quantize it using vector quantization (VQ), which is known to be particularly useful for quantizing signals with nonuniform distributions. As the distribution of BA is taken into consideration in the codebook design, a good tradeoff between performance and feedback rate can be achieved. Simulations show that the combination of statistical precoding and VQ-based quantization for BA leads to good performance with a small number of feedback bits. [ABSTRACT FROM PUBLISHER]

Bit rate and power are two commonly used optimality criteria for MIMO transceiver design. In the literature, bit rate maximization and power minimization problems are viewed as different problems and solved independently. In this paper, we derive the duality between these two problems for both the cases with and without integer constraint on bit allocation. We will show that if a transceiver is optimal for the power-minimizing problem, it is also optimal for the rate maximizing problem, and the converse is true. Such a duality has not been stated and proved in the literature to the best of our knowledge. The derivation does not involve any existing optimal solution and we can establish duality result even for the rate maximization problem with integer bit constraint, which the optimal solution is not known. The duality also allows us to develop an algorithm for finding the rate-maximizing transceiver with integer bit allocation using the solution of power-minimizing system. We will also consider some possible generalizations of the problem, for example, when there is a constraint on the maximal constellation size and when the subchannel bit error rates (BERs) are constrained. For each of these cases, we will see that the duality between the two problems continued to hold. In the simulations, we will compute the optimal solutions for these two problems and demonstrate the duality between these two. [ABSTRACT FROM PUBLISHER]

There have been many results on designing transceivers for MIMO channels. In early results, the transceiver is designed for a given bit allocation. In this paper we will jointly design the transceiver and bit allocation for maximizing bit rate. By using a high bit rate assumption, we will see that the optimal transceiver and bit allocation can be obtained in a closed form using simple Hadamard inequality and the Poincaré separation theorem. In the simulation, we will demonstrate the usefulness of the joint design. Simulation results, in which a high bit rate assumption is not used in allocating bits, show that a higher bit rate can be achieved compared to previously reported methods. [ABSTRACT FROM AUTHOR]