Jamming-Resilient Sparse Delay-Doppler NOMA: Unitary Precoding, Randomized Active Sets, and Superincreasing Power Allocation

We propose a sparse delay-Doppler NOMA scheme resilient to intentional jamming. The transmitter places user data on a small random subset of delay-Doppler bins, spreads the result through a unitary precoder, and re-draws the active subset per frame from a pseudo-random seed shared with the receiver. The receiver detects and discards jammed bins, recovers the sparse signal by least squares, and decodes per bin via SIC. Hadamard, DFT, and Haar-random precoders all yield essentially the same BER, because a Marchenko-Pastur conditioning argument controls any random unitary submatrix. The closed-form BER has no jammer-induced floor, unlike the well-known partial-band floor of conventional OTFS-NOMA. The same argument shows that compromising the shared seed does not break the system: random unitary submatrices remain well-conditioned, so BER stays within the unjammed envelope. For more than two users we use a superincreasing power allocation (Merkle-Hellman knapsack) and prove the resulting low-complexity SIC matches maximum-likelihood detection exactly, removing the usual SIC propagation ceiling. For more than four users we partition them into pairs assigned to disjoint bin subsets; this OMA-friendly NOMA rule reaches floor BER at eight users by SNR around 20 dB. We extend the framework to Rician fading and show the jammer-independence property holds for arbitrary Rician K-factor. Monte Carlo simulations track the analytical predictions within 3 dB and show at least a 40 dB BER-ratio improvement against pattern-aware jammers, with about 24 dB of cumulative gain over conventional OTFS-NOMA under oracle jamming.