Advanced Modulation

Abstract

In baseband PAM, symbols {ak} modulate the amplitude of a pulse train according to: (6.1) A single pulse shape g(t) is used in one signaling interval, and its amplitude is modulated by a data symbol. In this chapter we generalize the PAM model to M-ary modulation by allowing the pulse shape in any signaling interval to be chosen from a set of M possibilities, {gi(t); 0 ~ i ~ M-I}, to represent log2Mbits of information. The transmitted signal is then: (6.2) where ak takes on values in the set {O, 1, ... , M-I}. The data symbol thus indexes which pulse is transmitted in the k-th symbol interval, rather than the amplitude of the pulse that is transmitted.In Chapter 5 the 8-PAM signal set was defined as {ag(t) : a E.9l.} with alphabet .9l. = {±1, ±3, ±5, ±7}. In tenus of the new notation of (6.2), the 8-PAM signal set is go(t) =-7g(t), gl (t) =-5g(t), ... , g7(t) = 7g(t), as sketched below for a rectangular pulse: lIT 6.1.1. Baseband Equivalent Model For passband systems, the pulses {gi(t); 0 ~ i ~ M-I} often represent the complex envelopes of the transmitted signal. In that case, the transmitted passband signal will be x(t) = J2 Re{ei21tfcts(t)}. An alternative viewpoint is to define the passband equivalent pulses gi(t) = J2Re{ei21tfctgi(t)}. These can then be used to form directly the passband signal x(t)=~OO ga(t-kT). £.Jk =- k Both interpretations will be useful. (6.3) (6.4) (6.5)