Interference-Free Transmission for X channels - Interference Cancellation Using Space-Time Processing and Precoding Design - page 74

where

y t 2 =[ y 2 ( n t 2 =[ n t 2 ( i , 1 ) ] M × 1 , i , 1 ) ] M × 1 (5.13)

Equations ( 5.10 ) and ( 5.12 ) are the channel equations on which we will base our
design in this chapter.

5.2 Precoder Design

In this chapter, we aim to design precoders to achieve the following two goals:

1. At each time slot, each receiver can obtain interference-free signals from each
user when all the users transmit at the same time.
2. Our system can provide full diversity for each user.

The first goal is easy to understand. The second goal needs explanation as different
users and different codewords may have different diversities. Full diversity for User
1 means at Receiver 1, the diversity for codeword C 1 is full and at Receiver 2,
the diversity for codeword C 2 is full. Similarly, by saying the diversity for User
2 is full, we mean that at Receiver 1, the diversity for codeword S 1 is full and at
Receiver 2, the diversity for codeword S 2 is full. In this section, we show our main
idea to achieve interference-free transmission. Later, we will show that based on
our proposed interference-free transmission scheme in this section, we can further
achieve full diversity.
Our main idea to achieve interference-free transmission is to adjust each signal in
the signal space of X channels by using precoders for each transmitter, such that at
the receiver each desired signal is orthogonal to all other signals. In this way, we can
achieve interference-free transmission. To make our scheme easier to understand,
we will start our design for the case with M 4 first and see the minimum number

of transmit antennas needed to achieve interference-free transmission. Later we will
generalize our scheme for any N and M .
In Eq. ( 5.10 ), we use

=

H t 11 = H 1 A t 1 , H t 12 = H 1 A t 2 , G t 11 = G 1 B t 1 , G t 12 = G 1 B t 2 (5.14)

to denote the equivalent channel matrices. Then Eq. ( 5.10 ) becomes

y t 1 = H t 11 C 1 ( H t 12 C 2 ( G t 11 S 1 ( G t 12 S 2 ( n t 1 t ) + t ) + t ) + t ) + (5.15)

Similarly, in Eq. ( 5.12 ), if we use

H t 21 = H 2 A t 1 , H t 22 = H 2 A t 2 , G t 21 = G 2 B t 1 , G t 22 = G 2 B t 2 (5.16)

to denote the equivalent channel matrices, we have