On Performance of Vector OFDM With Linear Receivers

Abstract

Vector Orthogonal Frequency Division Multiplexing (OFDM) for single transmit antenna systems is a general transmission scheme, where OFDM and Single-Carrier Frequency Domain Equalization (SC-FDE) can be treated as two special/extreme cases. Due to its flexibility, it has drawn more and more attention recently. So far, all the studies about Vector OFDM assume the Maximum Likelihood (ML) receiver. In this paper, we investigate the performance of Vector OFDM with linear receivers, i.e., the Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) receivers. We first show that the detection SNR gap between the MMSE and ZF receivers increases with both channel SNR and the vector blocks (VB) size defined in Vector OFDM. Then, it is proved that for both ZF and MMSE receivers, all the transmitted symbols have equal performance. This is different from the Vector OFDM with ML receiver, where different VBs may have different coding gain, and thus may have different performances. We analyze the diversity order for Vector OFDM with MMSE receiver, and show that, regardless of the Vector OFDM symbol length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> , the diversity order can be represented as min{[ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-R</sup> ], <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> }+1, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> is the VB size, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> is the spectrum efficiency in bits/symbol, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> is the maximum delay of the multipath channel. For Vector OFDM with ZF receiver, we show that the diversity order equals 1 and the performance is the same as the conventional OFDM at high SNR.