Computationally Efficient IFFT/FFT Approximations for OFDM

Both the modulation and demodulation of an OFDM signal involves a Fourier transform in which the implementation requires several multiplications. These multiplications require significant hardware resources in FPGA and ASIC devices. Significant cost and speed improvements would follow if the number of multiplications could be reduced. Our approach eliminates the multiplications and is based on three observations that are somewhat independent of each other. First, the subcarrier modulation must be QAM, including QPSK and BPSK. Secondly, an approximation of the sin/cos basis waveforms by square type pulses transforms the multiplications by sin/cos to simple additions. Thirdly, over sampling of the signals puts the harmonics of the square type pulses outside the bandwidth of the OFDM signal. Limiting the scope to QAM signals has the benefit of the input signal having only N levels which can be decomposed into binary pulses. Hence, the Fourier transform can be transformed into simple multiplies of type +/-2ⁿ, which are further reduced to logic shifts and additions. Since most practical OFDM systems use QAM modulation, this restriction is of little concern. The proposed method can be used to approximate any OFDM modulation to any degree of precision and it can be used both in transmitters and receivers.