International Scholarly Research Notices

Research Article

Combined Transceiver Optimization for Uplink Multiuser MIMO with Limited CSI

Table 1

The QR-EPD noniterative algorithm.
(1) First, the QR factorization is employed to perform the decomposition of the matrix 𝐇 H 𝐇 as follows: 𝐇 H 𝐇 𝐑 𝐇 𝐇 = 𝐐 .
(2) A simple QR-based scheme [8] is utilized to find approximations of eigenvalues of 𝐇 H 𝐇 , that is, Λ 𝐇 = 𝐐 H 𝐇 𝐇 H 𝐇 𝐇 𝐐 . The diagonal elements of Λ 𝐇 are rearranged in a decreasing order.
(3) The matrix 𝐅 o p t is attained by 𝐅 o p t 𝐇 𝚺 = 𝐐 𝑓 𝐐 H 𝐇 , where [ 𝚺 𝑓 ] 𝑖 , 𝑖 = ⎛ ⎜ ⎜ ⎝ 𝜌 𝐇 ] 𝜇 [ Λ 𝑖 , 𝑖 − 𝜌 𝐇 ] [ Λ 𝑖 , 𝑖 ⎞ ⎟ ⎟ ⎠ + .
(4) As the matrix 𝐅 o p t is derived, the 𝑖 th block diagonal elements of 𝐅 o p t , for 𝑖 = 1 , 2 , … , 𝐾 , need to be acquired, that is, 𝐅 𝑖 𝐅 H 𝑖 𝐅 = [ o p t ] ( 𝑖 − 1 ) 𝑁 + 1 ∶ 𝑖 𝑁 , ( 𝑖 − 1 ) 𝑁 + 1 ∶ 𝑖 𝑁 .
(5) Finally, the EPD scheme is utilized to perform factorization of 𝐅 𝑖 𝐅 H 𝑖 to obtain suboptimal precoders 𝐅 𝑖 , 𝑖 = 1 , 2 , … , 𝐾 , 𝐅 𝑖 ̂ 𝐟 = [ 1 , ̂ 𝐟 2 ̂ 𝐟 , … , 𝑁 ] , where the column vector of 𝐅 𝑖 is given by ̂ 𝐟 𝑚 = ∑ 𝛾 𝑘 = 1 𝜆 𝑘 𝑁 ⋅ 𝑒 𝑗 ( 2 𝜋 𝑚 𝑘 / 𝑁 ) ⋅ 𝐮 𝑘 .