电子科技大学：《贝叶斯学习与随机矩阵及在无线通信中的应用 BI-RM-AWC》课程教学资源（课件讲稿）04 Asymptotic Spectrum Theorems（3/4）

4.Asymptotic Spectrum Theorems 1

1 4. Asymptotic Spectrum Theorems

Overview Apply central limiting theorem into multi-user and multi-cell MIMO system ·MF detector in uplink MF and ZF precoding in downlink MF and ZF precoding with imprefect CSI ·Multi--cell system 2

2 Overview • MF detector in uplink • MF and ZF precoding in downlink • MF and ZF precoding with imprefect CSI • Multi-cell system Apply central limiting theorem into multi-user and multi-cell MIMO system

4.4 Central Limiting Theorem User User User Base station User Consider a MU-MIMO system with a single cell,where has K single-antenna users and one BS with N antennas. 3

3 4.4 Central Limiting Theorem Consider a MU-MIMO system with a single cell, where has K single-antenna users and one BS with N antennas

4.4 Central Limiting Theorem Denote the channel coefficient i from the k-th user to the n-th antenna of the BS as hk.n,v which is s equal to a complex small-scale fading factor times an amplitude factor that accounts for geometric attenuation and large-scale fading: hn =gknYdk where gkm and d represent complex small-scale fading and large-scale fading coefficients,respectively. 4

4 4.4 Central Limiting Theorem Denote the channel coefficient from the k-th user to the n-th antenna of the BS as hk,n , which is equal to a complex small-scale fading factor times an amplitude factor that accounts for geometric attenuation and large-scale fading: where gk,n and dk represent complex small-scale fading and large-scale fading coefficients, respectively. k n k n k , , h g d 

4.4 Central Limiting Theorem The small-scale fading coefficients are assumed to be different for different users or for different antennas at each BS while the large-scale fading coefficients are the same for different antennas at the same BS,but are user-dependent.Then,the channel matrix from all K users s in the to the BS can be expressed as H= h.N where hi.N g1,1 8K,1 G and D 81,N 8K.N

5 4.4 Central Limiting Theorem The small-scale fading coefficients are assumed to be different for different users or for different antennas at each BS while the large-scale fading coefficients are the same for different antennas at the same BS, but are user-dependent. Then, the channel matrix from all K users in the to the BS can be expressed as where and 1,1 ,1 1/2 1, , ... ... ... ... ... K N K N h h h h             H GD 1,1 ,1 1, , ... ... ... ... ... K N K N g g g g            G 1 ... K d d            D