Time-reversal with limited signature precision: Tradeoff between complexity and performance

The success of time-reversal (TR) technique relies on the design of TR signature from the multi-path profile. In practice, the signature is of limited precision instead of being infinite due to the finite resolution in hardware. Such limited signature precision will degrade the TR focusing effect and thus the system performance. Although several works have been proposed to study the performance of TR system with one-bit signature, a general relation between the resolution of signature and the system performance has not been established to answer the question: how many bits are needed for TR systems to achieve desirable system performance? In the paper, we address the question by studying the TR system with limited signature precision. We derive theoretically the relationship between the received signal-to-interference-plus-noise ratio (SINR) and the quantization step. Through simulations, we find that for a typical TR system, 4-bit resolution for the signature is good enough to achieve good system performance.