Selecting FFT Word Length in OFDM systems with Undersampled Sparse Input

A critical module in telecommunication applications that are based on Orthogonal Frequency Division Multiplexing (OFDM) is the Fast Fourier Transform (FFT). Several FFT implementations have been proposed in the last 50 years aiming at the reduction of the required resources. The rounding error caused by the limited word length for the various FFT parameters has been extensively studied for many FFT implementation alternatives. In this paper, the minimum acceptable FFT word length is investigated for a specific OFDM architecture where undersampling is applied at the receiver when sparse data are exchanged. In the context of this paper, a configurable new FFT architecture has been developed in hardware description language in order to test various FFT sizes, word lengths and Quadrature Amplitude Modulation (QAM) levels. The simulation results show that the error floor caused by the undersampling in the specific OFDM system makes unnecessary the use of more than 8 bits as word length when 256-pt or 1024-pt FFT and 16QAM or 4QAM is used.