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.