Efficient Offline Waveform Design Using Quincunx/Hexagonal Time-Frequency Lattices

Algorithm 1

Optimization approach.

Initialization stage: At this stage, we initialize and introduce a precision parameter and the maximum number of

allowed iterations.

Iterative stage: At the th iteration, , we successively estimate the receiver waveform and the transmitter

waveform as follows:

    Compute the Kernels and

    Calculate the Kernels and

Stop condition: and or the maximum number of

allowed iterations is reached.