Abstract: This paper investigates the PSK parameter estimation problem with multiple independent cooperative receivers, and derives the Cramer-Rao Lower Bounds（CRLBs） of BPSK/QPSK frequency and phase estimation based on either known or random data. Compared with the CRLBs in traditional single receiver, the results indicate that the CRLBs for Data-Aided（DA） carrier frequency and phase estimation of PSK signals in multi-antenna cooperative receivers are the same with the CRLBs in traditional single receiver, but the CRLBs for Non-Data-Aided（NDA） estimation for multi-antenna cooperative receivers are lower than the traditional ones.

Key words: multi-antenna, frequency estimation, Phase Shift Keying（PSK） signal, Cramer-Rao Lower Bound （CRLB）

摘要： 针对利用多个独立天线对同一信号进行协同接收的问题，推导了数据辅助（DA）和非数据辅助（NDA）方式BPSK/QPSK信号频率及相位估计的Cramer-Rao下界（CRLB），并与传统单个天线接收时的CRLB进行了比较。结果表明，在DA方式下，多天线协同接收PSK信号频率及相位估计的CRLB与传统单天线接收的CRLB相同；在NDA方式下，多天线协同接收的CRLB则要低于传统单天线接收的CRLB。

关键词: 多天线, 频率估计, 相移键控（PSK）信号, Cramer-Rao下界