TABLE OF CONTENTS We now consider the performance of the digital modulation techniques discussed in the previous chapter when used over AWGN channels and channels with flat fading. There are two performance criteria of interest: the probability of error, defined relative to either symbol or bit errors; and the outage probability, defined as the probability that the instantaneous signal-to-noise ratio falls below a given threshold. Flat fading can cause a dramatic increase in either the average bit error probability or the signal outage probability. Wireless channels may also exhibit frequency-selective fading and Doppler shift. Frequency-selective fading gives rise to intersymbol interference (ISI), which causes an irreducible error floor in the received signal. Doppler causes spectral broadening, which leads to adjacent channel interference (small at typical user velocities) and also to an irreducible error floor in signals with differential phase encoding (e.g. DPSK), since the phase reference of the previous symbol partially decorrelates over a symbol time. This chapter describes the impact on digital modulation performance of noise, flat fading, frequency-selective fading, and Doppler.
In this section we define the signal-to-noise power ratio (SNR) and its relation to energy per bit (E b ) and energy per symbol (E s ). We then examine the error probability on AWGN channels for different modulation techniques as parameterized by these energy metrics. Our analysis uses the signal space concepts of Section 5.1.
In an AWGN channel the modulated signal 
has noise n(t)
