General I/O Relations and Low-Complexity Universal MRC Detection for All OTFS Variants

Abstract

Orthogonal time frequency space (OTFS) is a recently proposed modulation scheme which multiplexes information symbols in the delay-Doppler domain to combat severe Doppler shifts in high mobility wireless communications. In this paper, we classify all the OTFS variants depending on whether a cyclic prefix (CP) or zero padding (ZP) is added to each block or to the entire frame. We then present the general input-output relations for integer and fractional delays and Doppler shifts. Further, we present a low-complexity universal maximum ratio combining (MRC) detector for all OTFS variants, which has the lowest complexity among other known OTFS detection schemes at no loss of performance. Finally, we derive the input-output relation for overspread channels, where the channel delay spreads can exceed the OTFS block duration. Simulation results demonstrate that the MRC detection offers same performance for all OTFS variants and can also be effectively used for overspread channels. 11 12 157 III. TIME-DOMAIN INPUT-OUTPUT RELATION 224 In this section, we present the time-domain input-output 225 relation in matrix form for RZP-OTFS and RCP-OTFS, 226 where RZP/RCP-OTFS appends/prepends a ZP/CP of length 227 L ≥ l max to an OTFS frame, as shown in Fig. 2 (a). 228 Both integer and fractional delays and Doppler shifts are 229 considered. Further, we present the general forms of channel 230 matrix G, valid for integer and fractional delays and Doppler 231 shifts. For simplicity, we do not include CP (or ZP) in the 232 derivation. Also, we omit noise term in the rest of the paper. 233 The time domain input-output relation in matrix form is 234 given as 235 r = G • s, (20) 236 where the time-domain channel matrix G ∈ C NM ×NM has 237 mostly zero entries except the diagonal entries 1238239 for all q and the l-th subdiagonal entries) 241 where b = NM − 1. 242 Next, we study the structure of matrix G for RZP-OTFS 243 and RCP-OTFS for integer and fractional delay and Doppler 244 shifts.

Low-Complexity Iterative Equalization for OTFS Based on Alternating Minimization

“…conditions of the optimization problem described by ( 21)−( 23) can be expressed completely by the K.K.T. conditions of the above two subproblems [24,26].…”

A New Micro-Subcarrier OFDM-Based Waveform for Delay Doppler Domain Communication

“…The resulting baseband input output (I/O) relation for OTFS modulation (with rectangular pulses) is a twisted convolution [1], [4], [11]. Although twisted convolution is a complicated relationship, the channel sparsity in the DD domain can be exploited for efficient equalization/detection [4], [5], [12], [13], [14], [15], [16].…”

A New Micro-Subcarrier OFDM-Based Waveform for Delay Doppler Domain Communication

“…The resulting baseband input output (I/O) relation for OTFS modulation (with rectangular pulses) is a twisted convolution [1], [4], [11]. Although twisted convolution is a complicated relationship, the channel sparsity in the DD domain can be exploited for efficient equalization/detection [4], [5], [12]- [16].…”