Light-fidelity (LiFi) is an emerging technology for high-speed short-range mobile communications. Inter-cell interference (ICI) is an important issue that limits the system performance in an optical attocell network. Angle diversity receivers (ADRs) have been proposed to mitigate ICI. In this paper, the structure of pyramid receivers (PRs) and truncated pyramid receivers (TPRs) are studied. The coverage problems of PRs and TPRs are defined and investigated, and the lower bound of field of view (FOV) for each PD is given analytically. It is shown that the lower bound of FOV for TPR and PR are 20° and 30°, respectively. The impact of random device orientation and diffuse link signal propagation are taken into consideration. The performances of PRs and TPRs are compared, and optimised ADR structures are proposed by jointly considering the impact of tilt angle, FOV, and the number of PDs. For a transmitter-bandwidth limited system, the optimal PD values are 6 for PR and 9 for TPR, whereas, for a receiver-bandwidth limited system, the optimal PD value is 15. In addition, the double source (DS) cell system, where each LiFi AP consists of two sources transmitting the same information signals but with opposite polarity, is proved to outperform the single source cell (SS) system in interference limited or noise-plus-interference limited scenario. However, the SS cell system outperforms the DS cell system in a noise-limited scenario.