Algebraic Differential Spatial Modulation is Capable of Approaching the Performance of its Coherent Counterpart

Abstract

Abstract-We show that certain signal constellations invoked for classic differential encoding result in a phenomenon we term as the unbounded differential constellation size (UDCS). Various existing differential transmission schemes that suffer from this issue are identified. Then, we propose an enhanced algebraic field extension based differential spatial modulation scheme (AFE-DSM) and its enhanced counterpart that strikes a diversity-rate trade-off (AFE-DSM-DR), both of which overcome the UDCS issue without compromising its full transmit diversity advantage. Furthermore, the proposed schemes are extended to incorporate amplitude and phase shift keying (APSK) in order to exploit all the available degrees of freedom. Additionally, we propose a pair of detection schemes specially designed for APSK aided differential transmission schemes. Explicitly, we conceive the buffered minimum mean squared error (B-MMSE) detector and buffered maximum likelihood (B-ML) detector, which exploit the knowledge of previously detected symbols in order to further improve the detection performance. Our simulation results have shown that the proposed detectors are capable of bridging the performance gap between the conventional differential detector (CDD) and the coherent detector that has full channel state information. Specifically, when employing the proposed APSK aided AFE-DSM scheme operating at a rate of 2 bits per channel use (bpcu), the B-MMSE and B-ML detectors are observed to give about 3 dB and 3.5 dB signal-to-noise ratio gain with respect to their CDD counterpart at a bit error ratio of 10 −5 .Index Terms-Differential spatial modulation, finite input constellation, diversity, minimum mean squared error, maximum likelihood detector.

50 Years of Permutation, Spatial and Index Modulation: From Classic RF to Visible Light Communications and Data Storage

“…Hence, the DSM scheme is capable of enabling single-RF operation, as well as dispensing with the channel estimation overhead. Furthermore, because the number of non-zero elements in each column is limited in the DSM codewords, the transmitter complexity can be further improved by limiting the phase of non-zero elements [181], [182], [184]. Note that the concept of sparse space-time codewords was proposed in [16], [178] before the invention of the DSM concept.…”

“…Note that this scheme is different from that of [108] because it depends on square matrices instead of rectangular matrices. Rajashekar et al [181] Proposed an enhanced DSM scheme based on [23], which is capable of avoiding the issue raised in [182]. Two novel buffer-based low-complexity detectors were conceived, where the successive codewords were used to improve the error rate.…”

Differential Space-Time Coding Dispensing With Channel Estimation Approaches the Performance of Its Coherent Counterpart in the Open-Loop Massive MIMO-OFDM Downlink

“…Differential space-time coding (DSTC) has been investigated since 2000 [15][16][17]. In parallel to the development of coherent SM [4,8], its differential counterpart has been studied [18][19][20][21][22][23] within the DSTC framework, in which neither transmitter nor receiver needs CSI. The differential counterpart of the SM scheme has been termed as differential spatial modulation (DSM) [18,20], which relies on sophisticated square-shaped sparse-matrix multiplications termed as unitary differential encoding [15,16].…”

“Near-Perfect” Finite-Cardinality Generalized Space-Time Shift Keying

“…The DR arrangement in [21], [62], [63] was originally conceived for the square-shaped signal matrix. In this work, however, we opt for using the rectangular-shaped signal matrix setup of (T < M ), so that the signal construction for large M is based on the smaller (T × T ) constituent matrices.…”

“…The new FC-GSTSK subsumes the single-RF STSK [21], which was proposed in the differential MIMO scenario and was shown to outperform Differential SM (DSM) [18], [19], [56], [57] and its diversity-oriented counterparts [20], [58]- [63]. Moving forward from [21], this work activates multiple RF chains and further improves the methodology of the diversity gain optimization, so that the new FC-GSTSK becomes capable of achieving the best MIMO performance.…”