Ching-Chih Weng

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.

Block Diagonal GMD for Zero-Padded MIMO Frequency Selective Channels

In the class of systems with linear precoder and decision feedback equalizers (DFE) for zero-padded (ZP) multiple-input multiple-output (MIMO) frequency selective channels, existing optimal transceiver designs present two drawbacks. First, the optimal systems require a large number of feedback bits from the receiver to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as the bandwidth (BW) efficiency increases. In this paper, we propose using block diagonal geometric mean decomposition (BD-GMD) to design the transceiver. Two new BD-GMD transceivers are proposed: the ZF-BD-GMD system, where the receiver is a zero-forcing DFE (ZF-DFE), and the MMSE-BD-GMD system, where the receiver is a minimum- mean-square-error DFE (MMSE-DFE). The BD-GMD systems introduced here have the following four properties: a) They use the block diagonal unitary precoding technique to reduce the required number of encoding bits and simplify the computation. b) For any block size, the BD-GMD systems are optimal within the family of systems using block diagonal unitary precoders and DFEs. As block size gets larger, the BD-GMD systems produce uncoded bit error rate (BER) performance similar to the optimal systems using unitary precoders and DFEs. c) For the two ZF transceivers (ZF-Optimal and ZF-BD-GMD) and the two MMSE transceivers (MMSE-Optimal and MMSE-BD-GMD), the average BER degrades as the BW efficiency increases. d) In the case of single-input single-output (SISO) channels, the BD-GMD systems have the same performance as those of the lazy precoder transceivers. These properties make the proposed BD-GMD systems more favorable designs in practical implementation than the optimal systems.

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.

Nonuniform sparse array design for active sensing

Active sensing using multiple transmitting elements and independent waveforms has recently attracted much attention. Using M transmitting and N receiving elements, one can virtually simulate a physical array of MN elements by the sum co-array. Nonuniform sparse arrays can further be used in active sensing to produce the difference co-array of the given sum co-array with dramatically increased degree of freedom. However, current literature lacks an efficient design method for active sensing with nonuniform sparse arrays. In this paper, we address this problem and propose several systematic construction methods based on some classical results in number theory. By using these methods, we are able to construct active sensing sparse arrays, in which the difference co-array of the sum-co-array has aperture in the order of O(M2N2). Furthermore, it has no holes within this aperture. Several performance bounds on the maximum aperture of the sparse array are then provided. These can be used in the future to compare the performance of other suboptimal nonuniform sparse array geometries.1

Active beamforming with interpolated FIR filterin

The interpolated FIR (IFIR) radar was recently introduced in the context of MIMO radar theory. It was shown that this system has a signal to clutter ratio intermediate between those of the SIMO and MIMO radars. This paper considers the optimal design of the active IFIR beamformer in presence of jammers. It is shown that this beamformer can achieve beamwidths as sharp as those of colocated MIMO radars with full-length virtual arrays. At the same time, the extra complexity of MIMO radars, which arises from use of multiple transmitter waveforms and several sets of receiver matched filter banks, is not present in the IFIR realization. Design examples for IFIR radars which optimize the receiver beamforming weights in presence of jammers for fixed transmitter are also presented.1

MIMO Transceiver Optimization With Linear Constraints on Transmitted Signal Covariance Components

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.

The Role of GTD in Optimizing Perfect Reconstruction Filter Banks

Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we propose GTD (generalized triangular decomposition) filter banks as a subband coder for optimizing the theoretical coding gain. We focus on perfect reconstruction orthonormal GTD filter banks and biorthogonal GTD filter banks. We show that in both cases there are two fundamental properties in the optimal solutions, namely, total decorrelation and spectrum equalization. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can, with no loss of optimality, be used in the optimal biorthogonal GTD coders, which solves the granularity problem in the conventional optimum bit loading formula. We then extend the use of GTD filter banks to wireless communication systems, where linear precoding and zero-forcing decision feedback equalization is used in frequency selective channels. We consider the quality of service (QoS) problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints. Optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent GTD of the channel frequency response.

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.

Dithered GMD Transform Coding

The geometric mean decomposition (GMD) transform coder (TC) was recently introduced and was shown to achieve the optimal coding gain without bit loading under the high bit rate assumption. However, the performance of the GMD transform coder is degraded in the low rate case. There are mainly two reasons for this degradation. First, the high bit rate quantizer model becomes invalid. Second, the quantization error is no longer negligible in the prediction process when the bit rate is low. In this letter, we introduce dithered quantization to tackle the first difficulty, and then redesign the precoders and predictors in the GMD transform coders to tackle the second. We propose two dithered GMD transform coders: the GMD subtractive dithered transform coder (GMD-SD) where the decoder has access to the dither information and the GMD nonsubtractive dithered transform coder (GMD-NSD) where the decoder has no knowledge about the dither. Under the uniform bit loading scheme in scalar quantizers, it is shown that the proposed dithered GMD transform coders perform significantly better than the original GMD coder in the low rate case.

Per-antenna power constrained MIMO transceivers optimized for BER

This paper considers the linear transceiver optimization problem for multi-carrier multiple-input multiple-output (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.