An analytical framework for the incorporation of non-orthogonal pilots in massive MIMO systems

Training-based cellular communication systems use orthogonal pilot sequences to limit pilot contamination. However, the orthogonality constraint imposes a certain pilot length, and therefore, in communication systems with a large number of users, time-frequency resources are wasted significantly in the training phase. In cellular massive MIMO systems, the time-frequency resources can be used more efficiently by replacing the orthogonal pilots with shorter non-orthogonal pilot sequences in such a way that more space is available for the transmission of additional data symbols, and thus achieving higher data rates. Of course, the use of non-orthogonal pilots introduces additional pilot contamination, so the performance improvement could be achieved under certain system conditions, which are thoroughly investigated in this paper. We first provide a performance analysis framework for the uplink of cellular massive MIMO systems in which the effect of user pilot non-orthogonality has been analytically modelled. In this framework, we derive analytical expressions for the channel estimation, user Signal-to-Interference-plus-Noise-Ratio (SINR), and the average channel capacity per cell. We then use the proposed framework to evaluate the achievable spectral efficiency gain obtained by replacing orthogonal pilots with non-orthogonal counterparts. In particular, the existing trade-off between pilot lengths and the additional data symbols that can be transmitted by reducing the number of pilot symbols, is numerically quantified over a wide range of system parameters.