ission [66]. CHAPTER 9 The IEEE 802.16m Physical Layer (Part I) Ideal Linear Response Power Amplifier Response Input Amplitude (dB) FIGURE 9-7 An example of the AM/AM response of a power amplifier (saturation point = 6 dB) I Channel FIGURE 9-8 A 64 QAM signal constellation before and after power amplification Nsamples (AIR+AQ?) EVM = (9-14) Nsamples max Where Nsamples is the number of symbols used in the measurement period, AQ; refers to the In- phase (I) and Quadrature (Q) components of the ith error vector, and rmax denotes the maximum 9.3 SC-FDMA and OFDMA principles constellation amplitude. The EVM is measured over the continuous portion of a burst occupying at least one quarter of the transmission frame at maximum power settings. The permissible EVM can be esti- mated from the transmitter implementation margin, if the error vector is considered noise, which is added to the channel noise. The implementation margin is the excess power needed to maintain the carrier-to-noise ratio (C/N) intact when going from the ideal to the real transmitter. The EVM cannot be measured at the antenna connector, but should be measured by an ideal receiver with a certain carrier recovery loop bandwidth specified in a percentage of the symbol rate. The measured EVM include the transmitter filter accuracy, D/A-converter, modulator imbalances, untracked phase noise, and power amplifier nonlinearity. In practice, the sub-carrier spacing is not the same among different tones due to mismatched oscillators (i.e., frequency offset), Doppler shift, and timing synchronization errors, resulting in Inter- Carrier Interference (ICI) and loss of orthogonality. If the time-domain signals corresponding to sub- carriers k and k + m are represented by xk(t) and Xk+m(t), respectively, then the ICI is defined as the inner product between xk(t) and Xk+m(t) over the useful OFDM symbol duration Note that if the sub- carriers are ideally orthogonal, the inner product will be zero. xx(t) = ei2nkt/Tu (9-15) Clk=n(Tud)2 Where n is a constant, and 8 denote