Sensing performance is typically evaluated by classical radar metrics, such as Cramér-Rao bound and signal-to-clutter-plus-noise ratio. The recent development of the integrated sensing and communication (ISAC) framework motivated the efforts to unify the performance metric for sensing and communication, where sensing mutual information (SMI) was proposed as a sensing performance metric withdeterministicsignals. However, the communication need in ISAC systems necessitates the transmission ofrandomsignals for sensing applications, whereas an explicit evaluation for the SMI with random signals is not yet available in the literature. This paper aims to fill the research gap and investigate the unification of sensing and communication performance metrics. For that purpose, we first derive the explicit expression for the SMI with random signals utilizing random matrix theory. On top of that, we further build up the connections between SMI and traditional sensing metrics, such as ergodic minimum mean square error (EMMSE), ergodic linear minimum mean square error (ELMMSE), and ergodic Bayesian Cram´er- Rao bound (EBCRB). Such connections open up the opportunity to unify sensing and communication performance metrics, which facilitates the analysis and design for ISAC systems. Finally, SMI is utilized to optimize the precoder for both sensing-only and ISAC applications. Simulation results validate the accuracy of the theoretical results and the effectiveness of the proposed precoding design.

Intensity modulation and direct detection (IM-DD) based optical wireless communication (OWC), requires the modulated signal to be real and non-negative. To satisfy the requirements, this paper proposes two types of mixed orthogonal frequency division multiplexing (X-OFDM) waveforms. The Hermitian symmetry (HS) characteristic of the sub-carriers in the frequency domain, guarantees the signal in the time domain to be real, which reduces the spectral efficiency to 1/2. For the odd sub-carriers in the frequency domain, the signal in the time domain after the inverse fast fourier transform (IFFT) is antisymmetric. For the even sub-carriers in the frequency domain, the signal in the time domain after the IFFT is symmetric. Based on the antisymmetric and symmetric characteristics, the two types of X-OFDM waveforms are designed to guarantee the signal in the time domain to be non-negative. With$M$sub-carriers in the frequency domain, the generated signal in the time domain has$3M/2$points, which further reduces the spectral efficiency to 1/3. The numerical simulations show that, the two types of X-OFDM waveforms greatly enhance the power efficiency considering the OWC channel with the signal-dependent noise and/or the signal-independent noise.