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

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

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

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

Simultaneous wireless information and power transfer based on generalized triangular decomposition

In this paper, a new approach, based on the generalized triangular decomposition (GTD), is proposed for simultaneous wireless information and power transfer (SWIPT) in the spatial domain for a point-to-point multiple-input multiple-output (MIMO) system. The proposed approach takes advantage of the GTD structure to allow the transmitter to use the strongest eigenchannel jointly for energy harvesting and information exchange while these transmissions can be separated at the receiver. The optimal structure of the GTD that maximizes the total information rate constrained by a given power allocation and a required amount of energy harvesting is derived. An algorithm is developed that minimizes the total transmitted power for given information rate and energy harvesting constraints with a limited total power at the transmitter. Both theoretical and simulation results show that our proposed GTD based SWIPT outperforms singular value decomposition (SVD) based SWIPT. This is due to the flexibility introduced by the GTD to increase the energy harvested via interstream interference

Modulation-mode and power-assignment for SVD-and GMD-assisted downlink MIMO systems

Multiuser multiple-input multiple-output (MIMO) downlink (DL) transmission schemes experience both multiuser interference (MUI) as well as inter-antenna interference. However, instead of treating all the users jointly as in zero-forcing (ZF) multiuser transmission techniques, the investigated singular value decomposition (SVD) and geometric mean decomposition (GMD) assisted DL multiuser MIMO systems take the individual user's channel characteristics into account. The performed joint optimization of the number of activated MIMO layers and the number of bits per symbol along with the appropriate allocation of the transmit power shows that not necessarily all user-specific MIMO layers have to be activated in order to minimize the overall BER under the constraint of a fixed data throughpu

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio

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