Unitary and Non-Unitary Precoders for a Limited Feedback Precoded OSTBC System

Abstract

In this paper, a multiple-input-multiple-output (MIMO) system with finite-bit feedback first proposed by Love-Heath is considered, where a transmitted signal consists of a precode followed by an orthogonal space-time block code (OSTBC), such as Alamouti code. A new design criterion and a corresponding design method of precoders are proposed. Simulations show that the precoders obtained by our proposed criterion and method perform better than the existing ones. Furthermore, since our proposed precoders have a layered structure, their designs can be implemented in the simplest Grassmannian manifold. Moreover, a fast encoding algorithm can be applied, which can greatly reduce the complexity of codeword selection. In this paper, we also propose non-unitary precoders and their design criterion and method based on the performance analysis and the special property of an OSTBC. Interestingly, non-unitary precoders can significantly improve performance over unitary precoders.

Distortion-Free Golden-Hadamard Codebook Design for MISO Systems

“…The selected precoding matrix W sel D,i can be treated as the distortion due to non-ideal precoding W D,i . Therefore, a packing can be described by its MCD [4], [5], [7] as following:…”

“…, the rotation vector u=[1 7] uses the IEEE 802.16e parameters, Θ D = diag( e jπ/2 , e j7π/2 ), W D,1 is the 2 × 2 DFT first precoding matrix, S k is the k-th entry of the 2 × 2 complex Alamouti code, symbols s 11 and s 21 belong to a quadrature amplitude modulation (QAM) constellation, and (•) * is the complex conjugate operator. Now, we increase the size of the DFT precoding in (5). Let i = 3, M = 2, and N T = 4 in ( 5); and we obtain the 4 × 2 DFTC-A third codeword as follows.…”

“…Thus, precoded OSTBC (POSTBC), such as the discrete Fourier transform codebook with Alamouti (DFTC-A) coding, has been proposed [4] to improve array gain and attain low average codeword distortion using a matrix search method. In contrast, in another study, a vector search method with unitary and non-unitary POSTBC [5] to minimize codebook selection complexity. Additionally, Suh et al proposed using the DFTC [6] to achieve high eigenvectors with a high resolution.…”

A Beamforming-Aided Full-Diversity Scheme for Low-Altitude Air-to-Ground Communication Systems Operating With Limited Feedback

“…When using uniform bit-loading across all the sub-channels, the effective bit error ratio (BER) performance will be dominated by the sub-channels having low SNRs. Some of the existing solutions that attempt to address this issue include the popular geometric mean decomposition (GMD) based beamforming [19], [20], the uniform channel decomposition (UCD) based beamforming [21], and the space-time block coding (STBC) aided beamforming schemes [22]- [26]. The GMD based beamforming provides identical SNRs across the subchannels, but does not provide any transmit diversity gain, while the UCD based beamforming overcomes this impediment, but at a high computational complexity.…”

“…3) In contrast to the existing beamforming schemes [19]- [26] discussed earlier, we propose a full-diversity rotation (FDR) [39]- [41] aided beamformer (FDR-BF) that attains the maximum achievable transmit diversity gain without compromising the multiplexing gain. Furthermore, the proposed scheme is shown to attain a significant performance gain over the existing schemes.…”