 uplink channel estimation, as shown in Fig. 3.3. As explained in [49], the pilot-aided MMSE estimate of channel at subcarrier m from the uth user to the BS is obtained as where yu is the L X 1 observed pilot vector at the subcarrier m of the uth user and Pp = 2PàM represents the pilot power. the channel estimation error vector for the uth user. One can show that (3.59) (3.60) 3.5.3.1 MRC Receiver Employing the expression in (3.56) can be expanded as The OQAM symbol estimate at subcarrier m and symbol index n for the uth user at the output of MRC receiver can be formulated as 3 FBMC: A Waveform Candidate for Beyond 5G Here the noise-plus-interference Um, is Upon employing (3.34), the QAM symbol estimate at the MRC receiver output is (3.61) where we have is and for even, As shown in [49], the uth user SINR at subcarrier m in the existence of imperfect knowledge of channel is determined as where the random variable obeys The uplink rate for the uth user is determined as Upon utilizing Jensen's inequality E[f(x)] f (f[E[x]) along with the convexity of log (1+1), as shown in [49], the uplink rate of the uth user is lower bounded as u,mrc Pp(L - 1)(p")2 (3.62) By setting 2Pd = Eu/VL for a fixed Eu, and L -> 8, one obtains ~u,mrc Rm,IP (3.63) P. Singh and E. Sharma 3.5.3.2 ZF Receiver The estimated OQAM symbol vector at the output of ZF receiver in the existence of imperfect channel knowledge is given as Here the noise plus interference etor It follows from [49] that the SINR for the uth user can be determined as The operation above extracts the uth diagonal element of the matrix (GHGm)-1 As given in [49], the uplink rate of the ZF receiver for the uth user is lower bound as Pp(L - U)(B")2 (3.64) Note that for 2Pd = Eu/VL and L ~ u , ff It is important to note that similar to OFDM-based massive MIMO systems, the uplink power scaling laws also hold for their FBMC counterparts in the existence of imperfect channel knowledge. 3.5.4 Uplink Sum Rate for Massive MIMO-FBMC with Perfect The uplink rate for the ZF and MRC recei