Interference-Free Transmission for X channels - Interference Cancellation Using Space-Time Processing and Precoding Design - page 89

J r

A t k t i ||

2

1 ||

F =

1 (5.63)

i =

×

Let H k t k r N channel matrix between Transmitter k t and Receiver

k r . Then at Receiver k r and time slot t , the received signal is

denote the M

J t J r

y t k r H jk r A t ji C ji (

= t ) (5.64)

j = 1 i = 1

First, we let each symbol of C ji ( transmit along the same direction as we did in

Sect. 5.2 . So we only need to determine one column of each precoder since each
column differs from other columns by certain coefficients. In other words, we have
N unknown parameters. At the signal vector space of each receiver, there are J t J r
signal vectors including J t useful signal vectors and J t (

t )

interference signal
vectors. From the previous discussion, we know that we only need to consider the
precoder A t J t J r

J r − 1 )

for C J t J r assuming that we have finished the design of precoders for

C k t k r , k t = 1 ,..., J t , k r = 1 ,..., J r − 1.

1, the signal vector of C J t J r is interference to
the receiver. Therefore, its direction should be aligned with the existing interference.
Since the interference signal vector is M

At Receiver k r , k r = 1 ,..., J r −

1 receivers, in
order to align the signal vector of C J t J r along the interference direction, we need M
equations. So, we will need to satisfy M

× 1, at each of the J r −

· ( J r − 1 ) equations to achieve our alignment

goal in all receivers.
At Receiver J r , the signal vector of C J t J r is useful signal to the receiver. Based
on our design strategy, its direction should be orthogonal to all other signal vectors.
Since all interference signals are aligned along the same direction and there are
already J t − 1 useful signals in the space, we need to satisfy J t equations.

Therefore, in order to solve all the above M

· (

J r −

) + ·

1 J t equations, we need M

(

J r −

) + · (

J r −

) +

1 J t transmit antennas which lead to M 1 J t unknown parameters,

i.e., N ≥ M · ( J r − 1 ) + J t .

5.6.2 M ≥ J t · J r

In this situation, we can use either Scheme II or Scheme I. We will show that
Scheme II requires more transmit antennas compared to Scheme I. So we will choose
Scheme I.
First, we consider Scheme I. Similar to previous cases, we only need to consider
the precoder A t J t J r for C J t J r assuming that we have finished the design of precoders

for C k t k r , k t = 1 ,..., J t , k r = 1 ,..., J r − 1.

1, the signal vector of C J t J r is interference to the
receiver. Therefore, its direction should be orthogonal to the useful signal vectors.

At Receiver k r , k r = 1 ,..., J r −