Differential Space-Frequency Modulation and Fast 2-D Multiple-Symbol Differential Detection for MIMO-OFDM

Abstract

The combination of differential space-frequency modulation (DSFM) with orthogonal frequency division multiplexing (OFDM) is attractive for transmission over time-and frequency-selective multiple-input multiple-output (MIMO) channels and detection without the need for channel state information (CSI) at the receiver. It is well known that simple differential detection results in a high error floor already for moderate time and frequency selectivity of the channel. More sophisticated multiple-symbol differential detection (MSDD), which jointly processes multiple received symbols, overcomes this limitation, usually at the price of higher detection complexity. In this paper we consider DSFM for MIMO-OFDM transmission and MSDD at the receiver. Inspired by previous work presented in the literature, we devise a novel DSFM scheme, which makes use of spatial and/or spectral (multipath) diversity and is particularly suited for MIMO-OFDM and power-efficient, low-delay MSDD. We further investigate the application of a two-dimensional (2D) observation window to MSDD (2D-MSDD) in order to exploit channel correlations in both time and frequency direction. We develop a representation of the detection problem that is amenable to tree-search decoding, whose application leads to a tremendous reduction in MSDD complexity or "fast" MSDD. An analytical approximation of the symbol-error rate of 2D-MSDD for MIMO-OFDM under spatially correlated fading is derived, which enables quick and accurate performance evaluations. Numerical and simulation results corroborate the efficacy of our approach and show that power efficiency close to that of coherent detection with perfect CSI is feasible in all standard fading scenarios at reasonable decoder complexity. Index TermsOrthogonal frequency division multiplexing (OFDM), multiple-input multiple-output (MIMO) transmission, differential space-frequency modulation (DSFM), differential space-time modulation (DSTM), multiple-symbol differential detection (MSDD), tree-search decoding, sphere decoding.

Multiple-Symbol Differential Sphere Detection and Decision-Feedback Differential Detection Conceived for Differential QAM

“…As a result, the SD's Partial Euclidean Distance (PED) d v based on (19) and (24) is defined as (25), and the PED increment ∆ v−1 is given by (26), where the coef-…”

“…Based on the PED defined in (25), the MSDSD algorithm of [19] may be invoked, but its "sortDelta" subfunction formulated for the Schnorr-Euchner search strategy [34] should be revised as summarized in Table I 2 . Owing to the fact that the MSDD model of (10) stores the received samples in a reverse order compared to [19], the MSDSD algorithm should commence from index v = 1, and the sphere radius is updated at index v = N w .…”

“…The price paid is that the detection complexity of DQAM relying on M A -ring Star QAM constellation is at least about M A times higher than that of its DPSK counterpart, when the proposed hard-decision MSDSD and DFDD are employed. Without loss of generality, we may readily assume that the OFDM technique and/or interference surpression filters are employed in the scenarios of frequency-selective fading and/or multi-user scenarios, respectively, like within [25]- [27]. As a result, when the proposed MSDSD and DFDD aided DQAM schemes are employed for the sake of mitigating the potential error-floor imposed by a high Doppler frequency, the assumption of having an interference-free flat fading channel model is used.…”

Unitary Space-Time Modulation for Single-Carrier Transmission Over Frequency-Selective Channels

“…With CSI assumed known to receiver, spatial and frequency diversity gains can be realized by precoding cascaded with space-frequency (SF) encoding [10]. Without channel estimation at receiver, noncoherent SF codes and differential SF codes were addressed in [13] and [11][12], respectively. The noncoherent SF code in [13] follows the design of the unitary ST code proposed in [7], which suffers from decoding complexity for its exponential increase with code size, and exhibits a diversity gain by the product of the number of transmit antennas, size of receive antennas and channel length.…”

“…The noncoherent SF code in [13] follows the design of the unitary ST code proposed in [7], which suffers from decoding complexity for its exponential increase with code size, and exhibits a diversity gain by the product of the number of transmit antennas, size of receive antennas and channel length. Frequency-domain differential SF code [12] trades the aforementioned complexity for error floor when subject to large delay spread. Compared to OFDM, SC counterpart enjoys the advantages of lower peak-to-average power ratio, less susceptibility to amplifier nonlinearity, and lower sensitivity to carrier frequency offset.…”