Data Transmission with Terahertz Communication Systems
135
take up that the signal at the receiver side is Z(t), and at the first receive antenna (l
= 1), we have
Z 1 = h 11
s 1
−s
∗
2
+ h 12
s 2
s
∗
1
+
ℵ 11
ℵ 12
(14)
We obtain
Z 1 =
h 11 s 1 + h 12 s 2
h 12 s
∗
1 − h 11 s
∗
2
+
R 11
R 12
= Gh 1 + R 1 ; G =
s 1 s 2
−s
∗
2 s
∗
1
(15)
where h 1 = (h 11 h 12 )
t .
Likewise, for the second antenna, we can write
Z 2 = h 21
s 1
−s
∗
2
+ h 22
s 2
s
∗
1
+
ℵ 21
ℵ 22
(16)
We obtain
Z 1 =
h 21 s 1 + h 22 s 2
h 22 s
∗
1 − h 21 s
∗
2
+
R 21
R 22
= Gh 2 + R 2 ; G =
s 1 s 2
−s
∗
2 s
∗
1
(17)
where h 2 = (h 21 h 22 )
t .
Z l might be mapped into r l = M l s + N l by altering the second vector Z l2 of
Z l = (Z l1 Z l2 )
t with its complex conjugate vector. So, considering s = (s 1 s 2 )
t , we
can write
r l = M l s + N l =
Z l1
Z
∗
l2
, l = 1, 2
(18)
Thus,
r l =
h 11 h 12
h
∗
12 −h
∗
11
s 1
s 2
+
ℵ 11
ℵ 12
(19)
Or
r 1 = M 1 s + N 1 , M 1 =
h 11 h 12
h
∗
12 −h
∗
11
, M
∗
1 M 1 = =h 1
2
(20)
Similarly,
r 2 = M 2 s + N 2 , M 2 =
h 21 h 22
h
∗
22 −h
∗
21
, M
∗
2 M 2 = =h 2
2 I 2
(21)