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（4/4）

4.6 Continuing Mapping Theorem Here,we can use this result to derive the deterministic equivalence for SINR of MMSE detector. Example:For a single cell consisting of K single-antenna users and a base station equipped with N antennas.The uplink channel matrix H=[hh]eC where h,ECN,the receive signal is y=Hs+n=∑h,+n i=l where s=[sKC Ess=Ig and n is additive Gaussian noise vector with entries of zero mean and variance 82 6

6 4.6 Continuing Mapping Theorem Here, we can use this result to derive the deterministic equivalence for SINR of MMSE detector. Example: For a single cell consisting of K single-antenna users and a base station equipped with N antennas. The uplink channel matrix   where , the receive signal is 1 N K K C  H h h   N hi C 1 K i i i s  y Hs n h n      where , and n is additive Gaussian noise vector with entries of zero mean and variance  1  T K K s   s s C H E K      ss I 2 

4.6 Continuing Mapping Theorem For user k,the signal by multiplying MMSE decoder matrix is yMe=h(HH”+8Lw)厂y -空a+j2n The sienal part:h. The inerfarnce part[2hA+丁交g The nise prt(2②Au+,” 7

7 4.6 Continuing Mapping Theorem For user k, the signal by multiplying MMSE decoder matrix is   1 2 1 2 1 1 MMSE H H k k N K K H H k i i N i i i i y s                          h HH I y h h h I h n The signal part: 1 2 1 K H H k i i N k k i s           h h h I h  The interference part: 1 2 1 1 K K H H k i i N i i i i i k s             h h h I h   1 2 1 K H H k i i N i           The noise part: h h h I n 

4.6 Continuing Mapping Theorem The signal power wenj小s川 “[+,62A1小'H [2A+n八j】 where (a)is due toxx,x is a row vector and is the 2-norm of vector 8

8 4.6 Continuing Mapping Theorem The signal power : 2 1 2 1 1 1 (a) 2 2 1 1 2 1 2 1 | | K H H k i i N k k i K K H H H H H k i i N k k k k i i N k i i K H H k i i N k i E s E s s                                                                   h h h I h H h h h I h h h h I h H h h h I h where (a) is due to , x is a row vector and | | is the 2-norm 2 H x xx  of vector

4.6 Continuing Mapping Theorem Hence,the signal power is: (. The interference power: -.w小m However,we haveE 9

9 4.6 Continuing Mapping Theorem Hence, the signal power is: 2 1 2 1 K H H k i i N k i                   h h h I h  The interference power: 1 1 2 2 1 1 1 1 | K K K K H H H H k i i N i i i i i i N k i i i i i k i k E s s                                   h h h I h h h h I h H     However, we have 1 0 i j i j E s s i j          

4.6 Continuing Mapping Theorem Hence,the interference power can be written as 含a+s,)2u2+, Here,we know that 立a=[乞+，1，-a The interference power can be rewritten as -空j-[+mj八

10 4.6 Continuing Mapping Theorem Hence, the interference power can be written as   1 1 2 2 1 1 K K K H H H H k i i N i i i i N k i i k i                      h h h I h h h h I h    Here, we know that 2 2 1 K K H H H i i i i N N k k i k i                 h h h h I I h h The interference power can be rewritten as 2 1 2 1 2 2 2 2 1 1 1 K K K H H H H H H k i i N k k i i N k k i i N k i i i                                          h h h I h h h h I h h h h I h   