As an illustration, in Table 1 the values of the peak factor for BPSK are presented, while in Table 2 the values of the peak factor for QPSK are shown. BER penalty: In the process of reducing the PF, the amplitude of dm)(t) for some rn has been reduced. As a consequence the BER of x,(t) will increase. This is in fact the price paid for the reduction of the PF. In Fig. l a curves of BER for BPSK against SNR are shown: the broken line shows the BER for x(t), while the solid line shows the BER for x,(t). The SNR penalty at BER = is ~1 , 2 and 2.SdB for N = 4, 8 and 12, respectively. Conclusion: A method for MCM with low peak factor is presented for which the net bit rate remains the same as for standard MCM. However the BER is slightly higher than that in standard MCM. This BER degradation may be effectively improved by using FEC. The proposed method is very simple for on-line implementation: it is required only to measure the maximal value of the modulated signal for each symbol, and then to attenuate or amplify the signal accordingly. The off-line calculation of the value of the PF is very time consuming for large N.

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Practical applications in digital communication need non-maximally decimated filter banks to provide oversampled baseband signals for other necessary operations. The non-maximally decimated filter banks allow the required prototype filter to have wider transitional band to significantly reduce the required computational complexity. This Letter presents a non-maximally decimated filter bank structure derived by using multi-rate signal flow graphs.

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