This paper presents unitary-precoded single-carrier (USC) modulation as a family of waveforms based on multiplexing the information symbols on time domain unitary basis functions. The common property of these basis functions is that they span the entire time and frequency plane. The recently proposed orthogonal time frequency space (OTFS) and orthogonal time sequency multiplexing (OTSM) based on discrete Fourier transform (DFT) and Walsh Hadamard transform (WHT), respectively, fall in the general framework of USC waveforms. In this work, we present channel estimation and detection methods that work for any USC waveform and numerically show that any choice of unitary precoding results in the same error performance. Lastly, we implement some USC systems and compare their performance with OFDM in a real-time indoor setting using an SDR platform.

This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations that OTSM offers high performance gains over orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS), but at lower complexity owing to WHT. Then we propose a low complexity time-domain channel estimation method. Finally, we show how to include an outer error control code and a turbo decoder to improve error performance of the coded system.

This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme based on the well known Walsh-Hadamard transform (WHT) combined with row-column interleaving, and zero padding (ZP) between blocks in the time-domain. The information symbols in OTSM are multiplexed in the delay and sequency domain using a cascade of time-division and Walsh-Hadamard (sequency) multiplexing. By using the WHT for transmission and reception, the modulation and demodulation steps do not require any complex multiplications. We then propose two low-complexity detectors: (i) a simpler non-iterative detector based on a single tap minimum mean square time-frequency domain equalizer and (ii) an iterative time-domain detector. We demonstrate, via numerical simulations, that the proposed modulation scheme offers high performance gains over orthogonal frequency division multiplexing (OFDM) and exhibits the same performance of orthogonal time frequency space (OTFS) modulation, but with lower complexity. In proposing OTSM, along with simple detection schemes, we offer the lowest complexity solution to achieving reliable communication in high mobility wireless channels, as compared to the available schemes published so far in the literature.

This paper presents a linear complexity iterative rake detector for the recently proposed orthogonal time frequency space (OTFS) modulation scheme. The basic idea is to extract and coherently combine the received multipath components of the transmitted symbols in the delay-Doppler grid using maximal ratio combining (MRC) to improve the SNR of the combined signal. We reformulate the OTFS input-output relation in simple vector form by placing guard null symbols or zero padding (ZP) in the delay-Doppler grid and exploiting the resulting circulant property of the blocks of the channel matrix. Using this vector input-output relation we propose a low complexity iterative decision feedback equalizer (DFE) based on MRC. The performance and complexity of the proposed detector favorably compares with the state of the art message passing detector. An alternative time domain MRC based detector is also proposed for even faster detection. We further propose a Gauss-Seidel based over-relaxation parameter in the rake detector to improve the performance and the convergence speed of the iterative detection. We also show how the MRC detector can be combined with outer error-correcting codes to operate as a turbo DFE scheme to further improve the error performance. All results are compared with a baseline orthogonal frequency division multiplexing (OFDM) scheme employing a single tap minimum mean square error (MMSE) equalizer.