TABLE OF CONTENTS To set a common framework for discussing various receiver configurations, we develop a baseband equivalent model of a passband data-transmission system. We start from a generic QAM system (Fig. 12.9) since it can be used to implement any linear modulation scheme.
The passband transmitted signal can be compactly written as:
where {x n } is the complex sequence of data symbols with I (real) and Q (imaginary) components, x r and x i respectively, such that x n= x rn+ jx in , a(t) is the transmit pulse shape and f c is the carrier frequency. We shall assume that the baseband transmit spectrum A(f) is bandlimited to f ?(1+ ?)/2T Hz where the roll-off factor ?, between 0 and 1, determines the excess bandwidth over the minimum f ?1/2 T. (Note that greater than 100% excess bandwidth is sometimes used in radio and baseband subscriber loop transmission systems).
The received signal is:
where h p (t) is the passband channel impulse response, n p (t) is passband Gaussian noise, and the operator * represents convolution. The in-phase and quadrature outputs of the receive LPFs, y r (t) and y i (t), may be represented in complex notation as y(t)=y r (t)+jy i (t):
where g(t) is the impulse response of the receive...
