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.

Abstract — 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. 1

Abstract—A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang et al. 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 et al. 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. Index Terms—Bit allocation, generalized triangular decomposition, geometric mean decomposition, linear prediction, majorization, Schur convexity.

Abstract — 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. 1

Abstract—This correspondence revisits the joint transceiver optimization problem for multiple-input multiple-output (MIMO) channels. The linear transceiver as well as the transceiver with linear precoding and decision feedback equalization are considered. For both types of transceivers, in addition to the usual total power constraint, an individual power constraint on each antenna element is also imposed. A number of objective functions including the average bit error rate, are considered for both of the above systems under the generalized power constraint. It is shown that for both types of systems the optimization problem can be solved by first solving a class of MMSE problems (AM-MMSE or GM-MMSE depending on the type of transceiver), and then using majorization theory. The first step, under the generalized power constraint, can be formulated as a semidefinite program (SDP) for both types of transceivers, and can be solved efficiently by convex optimization tools. The second step is addressed by using results from majorization theory. The framework developed here is general enough to add any finite number of linear constraints to the covariance matrix of the input. Index Terms—BER optimization, MIMO transceivers, per-antenna constraints, Schur convexity, semidefinite programming. I.

Abstract — This paper considers the linear transceiver optimization problem for multi-carrier multiple-input multipleoutput (MIMO) channels with per-antenna power constraints. Because in practical implementations each antenna is limited individually by its equipped power amplifier, this paper adopts the more realistic per-antenna power constraints, in contrast to the conventional sum-power constraint on the transmitter antennas. Assuming perfect channel knowledge both at the transmitter and the receiver, the optimization problem can be transformed into a semi-definite program (SDP), which can be solved by convex optimization tools. Furthermore, several objective functions of the MIMO system, including average bit error rate, can also be optimized by the introduction of the majorization theory. 1

Abstract — 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. 1

Abstract — In this paper we propose a method for joint optimization of transceivers with fractionally spaced equalization (FSE). We use the effective single-input multiple-output (SIMO) model for the fractionally spaced receiver. Since the FSE is used at the receiver, the optimized precoding scheme should be changed correspondingly. Simulation shows that the proposed method demonstrates remarkable improvement for jointly optimal linear transceivers as well as transceivers with decision feedback. 1