Tham khảo tài liệu 'recent advances in wireless communications and networks part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 110 Recent Advances in Wireless Communications and Networks It is assumed that the group size to be determined is chosen from a finite set of possible values Q Q1 . Qmax whose maximum Qmax is limited by the maximum detection complexity the receiver can support. Suppose that at block symbol k the receiver acquires knowledge of the channel to form the frequency response hlỉ k over all Nc subcarriers. Now using the maximum group size available Qmax it is possible to form the frequency responses for all Nmin Nc Qmax groups I h 1 k . hNmin k j . Taking into account the WSS property it should hold that E ị hij kìỉiL k ì E lh ừ k ỉhj k . E g q gv w i E m q m v w J 54 for all pairs of transmit and receive antennas i j and i1 j and any q v 6 1 . Qmax as the correlation among any two subcarriers should only depend on their separation not their absolute position or the transmit receive antenna pair. A group channel correlation matrix estimate from a single frequency response can now be formed averaging across transmit and receive antennas and groups min RU hg NTNRNr . . . rrt hii k hii k H. NTNRNgmin it tA1 g 55 1 Using basic properties regarding the rank of a matrix it is easy to prove that rank Rrn min Ngmin omax therefore Ngmin omax maximises the range of possible group sizes using a single CSI shot. Let us denote the non-increasingly ordered positive eigenvalues of R. n . .C g by Ăhg 1 hg q I where owing to the deterministic character of R-hm n they can all be assumed to be different and with order one and consequently Q represents the true rank of fc . For the purpose of adaptation and based on the CSE criterion a more flexible definition of rank is given as Qe min n Y n q 1 hg q 1 e I 1 K q 56 where n 6 1 . Q and e is a small non-negative value used to set a threshold on the normalised CSE. Notice that Qe Q as e 0. Since the group size Q represents the dimensions of an orthonormal spreading matrix C restrictions apply on the range of values it can take. For instance in