The identification of maximum tolerable levels for potential mismatches is critical when designing communication systems. In this paper, we derive maximum tolerable levels for time-interleaved analog-to-digital-converter (TI-ADC) gain mismatch in orthogonal frequency-division multiplexing (OFDM) systems. To this end, we first analytically evaluate the bit error rate (BER) for square quadrature amplitude modulated-OFDM systems that are impaired by: 1) the gain mismatch of a TI-ADC and 2) the channel estimation errors (CEEs) of a zero-forcing equalizer. Our analysis includes the cases of a frequency-selective Rayleigh fading channel and a wired channel. Next, built on the obtained BER expressions, a threshold is established on the gain mismatch level, at which an error floor caused by the gain mismatch is below a given BER value at high signal-to-noise ratios in the absence of CEEs. Finally, numerical results further show that if and only if we set the gain mismatch level below 0.25 of this threshold, there is essentially no BER performance degradation compared with the mismatch-free case.

This paper presents an efficient procedure to numerically evaluate the exact bit error rate of a rectangular quadrature amplitude modulated-orthogonal frequency division multiplexing (OFDM) system that is impaired by the gain mismatch of a time-interleaved analog-to-digital converter. As opposed to previous contributions, no approximations are involved in this procedure. The obtained results allow to accurately analyze the effect of this type of mismatch on the performance of practical high-speed OFDM systems. The accuracy and efficiency of the proposed technique are demonstrated by comparing analytical results with brute-force Monte-Carlo simulations.