Improving the Spectral Efficiency of Zak-OTFS via Mutually Unbiased Bases

Orthogonal signaling or Nyquist signaling limits the number of information symbols transmitted in bandwidth $B$ and time $T$ to be $BT$, the time-bandwidth product. Transmitting more than $BT$ symbols leads to loss of orthogonality. The standard approach is to reduce the symbol interval and resolve the resulting inter-symbol interference. This requires changing the sampling frequency and possibly the sampling clock. This paper shows that it is possible to improve spectral efficiency on doubly spread channels without changing the sampling frequency. The idea is to superimpose the information symbols using mutually unbiased bases (MUB) while maintaining the original spacing. We carry this out in the delay-Doppler domain using Zak-transform based orthogonal time frequency space (Zak-OTFS) modulation as it allows construction of MUB. We also construct a precoder that mitigates the effect of the doubly-spread channel. This simplifies receiver processing to detection in Gaussian noise since each basis appears to the other as Gaussian noise. This reduction makes it possible to use trellis coded modulation to further improve the bit-error performance. Numerical results demonstrate that the proposed signaling scheme using MUB achieves good bit-error performance.