The capacity of a discrete-time multiple-input-multiple-output channel with correlated phase noises is investigated. In particular, the electro-optic frequency comb system is considered, where the phase noise of each channel is a combination of two independent Wiener phase-noise sources. Capacity upper and lower bounds are derived for this channel and are compared with lower bounds obtained by numerically evaluating the achievable information rates using quadrature amplitude modulation constellations. Capacity upper and lower bounds are provided for the high signal-to-noise ratio (SNR) regime. The multiplexing gain (pre-log) is shown to be $M-1$, where $M$ represents the number of channels. A constant gap between the asymptotic upper and lower bounds is observed, which depends on the number of channels $M$. For the specific case of $M=2$, capacity is characterized up to a term that vanishes as the SNR grows large.

翻译：研究了离散时间多输入多输出信道在相位噪声相关情况下的容量。特别地，考虑了电光频率梳系统，其中每个信道的相位噪声由两个独立的维纳相位噪声源组合而成。推导了该信道的容量上界和下界，并与通过正交幅度调制星座数值评估可达信息率所得的下界进行了比较。针对高信噪比区域，给出了容量的上界和下界。结果表明，复用增益（前置对数因子）为$M-1$，其中$M$代表信道数量。渐进上界与下界之间存在恒定间隙，该间隙取决于信道数量$M$。对于$M=2$的特例，容量被表征至一个随信噪比增大而消失的项。