On the Diversity Order of UW-OFDM

Abstract

International audienceUnique word (UW) OFDM is a multicarrier technique that follows a different approach than standard multicarrier techniques like cyclic prefix (CP) OFDM. It has been reported that UW-OFDM outperforms CP-OFDM in the sense that it performs better in fading channels [1, 2], and it has much lower out-of-band radiation [3] compared to CP-OFDM. However, a theoretical analysis of the error rate performance of UW-OFDM was never addressed in the literature. In this paper, we derive analytical expressions for the bit error rate for UW-OFDM, from which we can obtain the diversity order. It turns out that when the code generator matrix, needed to construct the UW-OFDM signal, is full rank, the UW-OFDM system reaches the maximum diversity order. This is in contrast with standard CP-OFDM, where only diversity order one can be reached, unless additional precoding is applied. Further, in the paper, we propose a construction method for the code generator matrix to achieve a (close to) maximum coding gain

Design and analysis of the UW-OFDM signal

“…In [1], it is shown that UW-OFDM outperforms cyclic prefix (CP-) OFDM with respect to the bit error rate in fading channels. This is confirmed in [2] where a theoretical analysis of the error rate performance shows that UW-OFDM is always able to achieve full diversity, whereas in CP-OFDM only a diversity one is obtained unless precoding is used. Further, it is shown in [3] that UW-OFDM has…”

“…To satisfy the constraints on the signal shape, the system parameters specify both the mapping matrix B and the null-space matrix U. The designer only has the freedom to select the linear combination matrix W. In [2], it is shown that, in order to achieve full diversity, the code generator matrix must be full rank. Hence also W should be full rank.…”

“…can be verified that maximization of the minimum Euclidean distance requires G H B H BG = I N d [2]. Besides the maximization of the minimum Euclidean distance, this requirement results in every data symbol being equally represented in the transmitted signal, i.e., assuming the energy per data symbol equals E s , the time-domain signal corresponding to a single data symbol has energy E s , and the transmit power [4] that this restriction results in the MSE of the BLUE and MMSE data detectors to be minimized, in frequency-flat channels.…”