Superimposed Pilot Transmission in Cell-Free Massive MIMO With Non-Ideal RF Responses

In this paper, the performance of cell-free massive multiple-input multiple-output (CF-mMIMO) systems under the transceiver non-ideal radio-frequency responses (NI-RF-RPs) that rely on the superimposed pilot (SP) and regular pilot (RP) transmission protocols is investigated. Specifically, the transceiver NI-RF-RPs encapsulate the non-ideal amplitude responses (NI-A-RPs) and non-ideal phase responses (NI-P-RPs) at both access points (APs) and users (UEs). By virtue of a generic RF-RP model, rigorous closed-form expressions of uplink (UL) and downlink (DL) achievable spectral efficiencies (SEs) with different NI-RF-RPs and pilot transmission protocols are respectively derived, which enable us to quantify the impact of the key system parameters, such as the transceiver amplitude (and phase) response variances and the transceiver reciprocity. Numerical results demonstrate that the SP protocol is superior to the RP protocol in terms of the UL and DL SEs, regardless of the presence of the NI-RF-RPs. Besides, the NI-A-RPs have negative effect on both UL and DL SEs, and the DL SE is immune to the transceiver amplitude non-reciprocity. Moreover, from the perspective of the NI-P-RPs, it is shown that the DL SE is only sensitive to the AP NI-P-RPs and whether the AP phase is reciprocal or not will significantly disturb the effect of the NI-P-RPs on the DL SE.