A device for modulating communication signals comprises a transceiver for receiving and transmitting the signal, a storage medium storing computer implemented program code components to generate sequences and a processor in communication with the storage medium and transceiver. The processor executes computer implemented program code components to generate a family of shift sequences or arrays using exponential, logarithmic or index functions and a polynomial in i∈Zp−1 for a finite field Zp of prime p. Multiple columns of the arrays are substituted with pseudo-noise sequences in a cyclic shift equal to the shift sequence for the respective column to generate a substituted array. The substituted array, or a sequence unfolded using the CRT from the array when the array dimensions are relatively prime, is applied to a carrier wave of the communication signal to generate a modulated communication signal.