mbol instant is obtained as (3.55) where the complex quantity Gin= = , between the uth user in the cell and the 1th antenna of the base station, represents the CFR at subcarrier m. The term gl,"[k] is the corresponding Lh-tap channel impulse response. The demodulated noise nm,n at the 1th BS antenna obeys CN(0,0,2). The quantity is the virtual symbol for the uth user. The interference Im.n is expressed by (3.24). For convenience, (3.55) can be expressed in vector form as (3.56) where ym,nyyT CLx1 comprises observed symbols across L antennas of the BS, while Nm,N E CLx1 is the noise vector such that Enn, = 0,21L. The vector bm,n symbol of the U users such = LUis CSI matrix between the U users in the cell and the base station. The matrix Gm is commonly modelled as [60] (3.57) where the diagonal matrix D = diag(8),, BU) RUxU with Bu being the large-scale fading coefficient for the uth user. The quantity Bu, which remains same for many coherence time intervals, can be assumed to be known at the base station. Also, it is assumed to be independent from BS antennas and subcarriers. The matrix Hm= hujeclau consists of small-scale fading factors from the U users in the cell to the base station. The entries of Hm are i.i.d. as CN(0, 1). P. Singh and E. Sharma 3.5.3 Uplink Sum Rate for Massive MIMO-FBMC with Imperfect CSI The combiner matrix Am for the ZF and MRC receivers, which are widely used due to their low complexity and linear nature, is Am = for MRC (3.58) OQAM symbols at output of the combiner Am are obtained as The CSI matrix Gm, in practice, is estimated at the BS using pilot symbols. Reference [49] derived the uplink achievable rate for FBMC-based multi-user multi- cell massive MIMO systems by considering the effect of pilot contamination. This chapter considers single-cell multi-user massive MIMO-FBMC systems, wherein users transmit orthogonal pilot symbols for channel estimation at the base station. Thus, there is no pilot contamination. Let each user in the cell transmit M pilot symbols on each subcarrier for