Error rates for a class of multiple position modulation schemes

A class of multiple position modulation schemes is presented and analyzed. These modulation schemes generalize m-ary bi-orthogonal signaling by allowing exactly k binary (±1) pulses to appear in any of m possible positions. Such modulation schemes have been implemented in time-modulated ultra wide band communications systems. In high signal-to-noise ratio environments, these schemes offer the possibility of more efficient communications than ordinary BPSK-type modulation provides. In this paper we define these modulation schemes, and derive their symbol and bit error rates in the additive white Gaussian noise (AWGN) channel as a function of E_b/N_o.