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1 is clearly a special case when cpk(t) = Chapter 3 PERFORMANCE OPTIMIZATION John M. Cioffi and Louise M. C. Hoo Optimization of an OFDM signal enables the highest data rates and/or most reliable performance in the bandwidth of transmission. , more bits/second/Hz in the given bandwidth allocated to the OFDM signal. Optimization can thus lead to better use of the scarce spectrum available for wireless transmission. As this chapter will show, use of every frequency is not always best and that shift of information and energy from channel frequencies of poor SNR to frequencies of comparatively higher SNR can be good and lead to higher performance.

1 Time-Varying lmpairments Both Doppler shift and frequency offset can be modelled as time-varying impairments. Here we first derive a general expression for the effect of the time-varying impairments and then discuss the effect of Doppler shift and frequency offset, respectively. Consider an OFDM signal, + where fa = f, kA f and sa is the signal transmitted over the k-th subchannel. 2. Impairments of Wireless Channels t o OFDM Signals 29 The demodulated signal will be where a1 is defined as a0 is usually a complex number, whose magnitude and phase represent the attenuation and the phase shift on the desired signal, respectively.

2. Power spectrum of OFDM Signal. Fig. 2 shows that, for an OFDM signal consisting of N subchannels, the signal bandwidth is about ( N l ) Af . , the total transmission rate of OFDM signal is $ symbol/sec. Therefore, the bandwidth efficiency of the OFDM system is + in symbols/sec/Hz. For most practical OFDM systems, N is much larger than 1 and the guard interval or cyclic extension is much smaller than the 24 BASIC CONCEPTS Chapter 2 OFDM symbol duration, so W = 1. If each symbol carries k bit information, the bandwidth efficiency will be k bits/sec/Hz.