Signal Design for PAM Data Transmission to Minimize Excess Bandwidth

To fix ideas, consider the following conventional (baseband) PAM data-transmission scheme (see, for example, Ref. 1). T h e data to be transmitted is a sequence T h e ak are independent identically distributed copies of the random variable a, which is uniformly distributed on the set (±1, ±3, · · ·, ±2L -- 1}. Thus, a takes 2 L equally likely values, where L = 1, 2, · · ·, is a fixed parameter. The modulated signal is £ akg0(t-kT0), k=-°= where go(-) is a real-valued "Nyquist pulse"--i.e., go(0) ^ 0, x0(t)= (1)