Pulse shaping

Electrical engineering

Optics

Physics

Channel (broadcasting)

Engineering

Philosophy

Prefix

Voltage

Materials science

Waveform

Electronic engineering

Cyclic prefix

Pulse (music)

Orthogonal frequency-division multiplexing

Computer science

Linguistics

Laser

Radar

Telecommunications

IEEE Transactions on Vehicular Technology

In this paper, we model null null $M\times N$ null null orthogonal time frequency space modulation (OTFS) over a null null $P$ null -path doubly dispersive channel with delays less than null null $\tau _{\max }$ null null and Doppler shifts in the range null null $(\nu _{\min },\nu _{\max })$ null . We first derive in a simple matrix form the input–output relation in the delay-Doppler domain for practical (e.g., rectangular) pulse-shaping waveforms, next generalize it to arbitrary waveforms. This relation extends the original OTFS input–output approach, which assumes ideal pulse-shaping waveforms that are bi-orthogonal in both time and frequency. We show that the OTFS input–output relation has a simple sparse structure that enables one to use low-complexity detection algorithms. Different from previous work, only a single cyclic prefix is added at the end of the OTFS frame, significantly reducing the overhead, without incurring any penalty from the loss of bi-orthogonality of the pulse-shaping waveforms. Finally, we compare the OTFS performance with different pulse-shaping waveforms, and show that the reduction of out-of-band power may introduce nonuniform channel gains for the transmitted symbols, thus impairing the overall error performance.

Practical Pulse-Shaping Waveforms for Reduced-Cyclic-Prefix OTFS