GTD-based transceivers for decision feedback and bit loading

We consider new optimization problems for transceivers with DFE receivers and linear precoders, which also use bit loading at the transmitter. First, we consider the MIMO QoS (quality of service) problem, which is to minimize the total transmitted power when the bit rate and probability of error of each data stream are specified. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It is shown that under some multiplicative majorization conditions there exists a custom GTD-based transceiver which achieves the minimal power. The problem of maximizing the bit rate subject to the total power constraint and given error probability is also considered in this paper. It is shown that the GTD-based systems also give the optimal solutions to the bit rate maximization problem

MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization

This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zero-forcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities for the symbol streams. The precoder and DFE matrices are optimized jointly with bit allocation. It is shown that the generalized triangular decomposition (GTD) introduced by Jiang, Li, and Hager offers an optimal family of solutions. The optimal linear transceiver (which has a linear equalizer rather than a DFE) with optimal bit allocation is a member of this family. This shows formally that, under optimal bit allocation, linear and DFE transceivers achieve the same minimum power. The DFE transceiver using the geometric mean decomposition (GMD) is another member of this optimal family, and is such that optimal bit allocation yields identical bits for all symbol streams—no bit allocation is necessary—when the specified error probabilities are identical for all streams. The QR-based system used in VBLAST is yet another member of the optimal family and is particularly well-suited when limited feedback is allowed from receiver to transmitter. Two other optimization problems are then considered: a) minimization of power for specified set of bit rates and error probabilities (the QoS problem), and b) maximization of bit rate for fixed set of error probabilities and power. It is shown in both cases that the GTD yields an optimal family of solutions

Joint optimization of transceivers with decision feedback and bit loading

The transceiver optimization problem for MIMO channels has been considered in the past with linear receivers as well as with decision feedback (DFE) receivers. Joint optimization of bit allocation, precoder, and equalizer has in the past been considered only for the linear transceiver (transceiver with linear precoder and linear equalizer). It has also been observed that the use of DFE even without bit allocation in general results in better performance that linear transceivers with bit allocation. This paper provides a general study of this for transceivers with the zero-forcing constraint. It is formally shown that when the bit allocation, precoder, and equalizer are jointly optimized, linear transceivers and transceivers with DFE have identical performance in the sense that transmitted power is identical for a given bit rate and error probability. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It will be shown that a broad class of GTD-based systems solve the optimal DFE problem with bit allocation. The special case of a linear transceiver with optimum bit allocation will emerge as one of the many solutions

A novel structure for MMSE transceivers over slowly time-varying channels

This paper addresses the design problem of decision feedback (DF) transceiver without zero-forcing constraint over slowly time-varying narrowband multi-input multi-output (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) is applied for the design of minimum mean square error (MMSE) DF transceiver. With space-time powerloading, the proposed space-time geometric mean decomposition (ST-GMD) MMSE transceiver maximizes Gaussian mutual information over the equivalent channel seen by each space-time block. For practical applications, the causal ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic bit error rate (BER) performance with the ST-GMD MMSE system is also developed. In high signal to interference plus noise ratio (SINR) region, our results show that the proposed MMSE transceivers have better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are a non-increasing function of the ST-block size

Zero-Forcing DFE Transceiver Design Over Slowly Time-Varying MIMO Channels Using ST-GTD

This paper considers the optimization of transceivers with decision feedback equalizers (DFE) for slowly time-varying memoryless multi-input multi-output (MIMO) channels. The data vectors are grouped into space-time blocks (ST-blocks) for the spatial and temporal precoding to take advantage of the diversity offered by time-varying channels. The space-time generalized triangular decomposition (ST-GTD) is proposed for application in time-varying channels. Under the assumption that the instantaneous channel state information at the transmitter (CSIT) and receiver (CSIR), and the channel prediction are available, we also propose the space-time geometric mean decomposition (ST-GMD) system based on ST-GTD. Under perfect channel prediction, the system minimizes both the arithmetic MSE at the feedback detector, and the average un-coded bit error rate (BER) in moderate high signal to noise ratio (SNR) region. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD system is also proposed. At the moderate high SNR region, our analysis and numerical results show that all the proposed systems have better BER performance than the conventional GMD-based systems over time-varying channels; the average BERs of the proposed systems are non-increasing functions of the ST-block size

Generalized Triangular Decomposition in Transform Coding

A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang This family includes the Karhunen-Loeve transform (KLT) and the generalized version of the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to that of the KLT and the PLT. Even though the original PLT introduced by Phoong is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes, the GTD-based family includes members that are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT, which has the unit noise-gain property. Other special cases of the GTD-TC are the geometric mean decomposition (GMD) and the bidiagonal decomposition (BID) transform coders. The GMD-TC in particular has the property that the optimum bit allocation is a uniform allocation; this is because all its transform domain coefficients have the same variance, implying thereby that the dynamic ranges of the coefficients to be quantized are identical

Transceiver design with vector perturbation technique and iterative power loading

In this paper we consider the optimization of transceivers which use the nonlinear vector perturbation technique at the transmitter. Since the perturbation vector can be almost totally removed at the receiver, the transmitter can use this extra freedom to reduce the transmitted power while maintaining the performance. The two cases considered in this paper are linear transceivers and transceivers with decision feedback (DFE). For both cases, efficient iterative power loading algorithms are developed to reduce the average bit error rate under the total transmitted power constraint. We present simulation results showing that the proposed technique performs better than the existing state-of-the-art uniform channel decomposition (UCD) system and the vector perturbation (VP) precoder

Frequency dependent GTD coders

This paper proposes the frequency dependent generalized triangular decomposition (FDGTD) coder family for wide-sense-stationary (WSS) vector processes. Under the uniform bit allocation constraint, a set of necessary and sufficient conditions for FDGTD's coding gain optimality is derived. It is shown that one member in the FDGTD family, the frequency dependent geometric mean decomposition (FDGMD) coder, satisfies these conditions and thus is optimal. It is also demonstrated that the FDGMD coders use a simpler uniform quantizer structure and yet achieve a better performance than the conventional optimal orthonormal subband coders with sophisticated bit allocation scheme