Diversity order in ISI channels with single-carrier frequency-domain equalizers

Abstract

This paper analyzes the diversity gain achieved by single-carrier frequency-domain equalizer (SC-FDE) in frequency selective channels, and uncovers the interplay between diversity gain d, channel memory length ν, transmission block length L, and the spectral efficiency R. We specifically show that for the class of minimum means-square error (MMSE) SC-FDE receivers, for rates R ≤ log L ν full diversity of d = ν + 1 is achievable, while for higher rates the diversity is given by d = ⌊2 −R L⌋ + 1. In other words, the achievable diversity gain depends not only on the channel memory length, but also on the desired spectral efficiency and the transmission block length. A similar analysis reveals that for zero forcing SC-FDE, the diversity order is always one irrespective of channel memory length and spectral efficiency. These results are supported by simulations.

On Performance of Vector OFDM With Linear Receivers

“…It is still unknown how V-OFDM performs with linear receivers, i.e., the Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) receivers. As a special/extreme case of V-OFDM, there are several papers that discussed linear receivers for SC-FDE, see for example [18], [19] . V-OFDM has a more general structure, and thereby involves more parameters.…”

Single-Carrier Frequency-Domain Equalizer with Multi-Antenna Transmit Diversity

“…The analysis performed in [3] consists of two main steps. We first characterize the outage probability.…”

“…In this case, the system model is equivalent to a SISO ISI channel under CP transmission. If the equalizer is designed according to Hcir, it is known that in the SISO ISI CP transmission a rate-dependent diversity is observed [3], and due to equivalence of channel models this result can be directly lifted to the flat MISO CDD system. This result will be extended to the general case of the multipath MISO channel under CDD.…”

“…different choices for the set {δi}. Since these circulant matrices have different structures, the diversity analysis of [3] does not directly follow. We study the diversity of these systems and show that the L!−1 remaining choices {δi} yield the same diversity as shown in (20).…”

Single carrier frequency domain equalization and energy efficiency optimization for MIMO cognitive radio.

“…However, SC-FDE systems usually cannot take the full frequency diversity gain, which is a function of transmission rate and data block length (i.e. DFT size) [21].…”