On the SER Performance of ZF and MMSE Receivers in Pilot-Aided Simultaneous Communication and Localization

Abstract: In this paper, a symbol error rate (SER) analysis is provided to evaluate the impact of localization inaccuracy on the communication performance under Zero-Forcing (ZF) and Minimum Mean-Square Error (MMSE) equalizers. Specifically, we adopt a pilot-aided simultaneous communication and localization (PASCAL) system, in which multiple drones actively transmit signals towards the base station (BS). Upon receiving the signal, the BS estimates the drones' location parameters to reconstruct the channel matrix, which is then utilized for ZF and MMSE equalization. As the channel matrix is characterized by the estimated parameters associated with the target's location and the matrix inversion involved in ZF and MMSE further complicates the analysis, obtaining a closed-form SER expression becomes intractable. Thus, a tightly approximated SER expression is respectively derived for ZF and MMSE by using a hybrid approximation method incorporating Neumann approximation and Taylor approximation. Our analysis reveals several important design insights: first, the average SER of drone $k$ for both ZF and MMSE can be affected by the localization errors from all drones including drone $k$; second, the average SER of ZF is unaffected by the estimation inaccuracy of range, whereas the average SER of MMSE is influenced by it; third, ZF and MMSE is the most susceptible to the influence of angle estimation errors compared to the other localization errors; fourth, ZF is highly sensitive to localization errors and may be even worse than maximal ratio combining (MRC) under some conditions of significant estimation errors. Numerical simulation results verify our findings and also validate the accuracy of the analysis across a wide range of system parameters.