Channel Protection Using Random Modulation

This paper shows that modulation protects a bandlimited signal against convolutive interference. A signal , bandlimited to BHz, is modulated (pointwise multiplied) with a known random sign sequence , alternating at a rate , and the resultant spread spectrum signal is convolved against an M-tap channel impulse response to yield the observed signal , where and denote pointwise multiplication, and circular convolution, respectively.We show that both , and can be provably recovered using a simple gradient descent scheme by alternating the binary waveform at a rate (to within factors and a signal coherences) and sampling at a rate . We also present a comprehensive set of phase transitions to depict the trade-off between , , and for successful recovery. Moreover, we show stable recovery results under noise.