Interference-Free Transmission for X channels - Interference Cancellation Using Space-Time Processing and Precoding Design - page 88

When there are J t transmitters each with N transmit antennas and J r receivers
each with M receive antennas, we can achieve interference-free transmission and full
diversity simultaneously for each user if N and M satisfy the following conditions:

1. When J t + J t , we can achieve our

goal using Scheme II, i.e., by aligning all interference along the same direction
which is orthogonal to the useful signal vectors.
2. When M

1 ≤ M < J t · J r , as long as N ≥ M · ( J r − 1 ) +

, we can achieve our goal using
Scheme I, i.e., by putting all interference in a subspace which is orthogonal to
the useful signal vectors.
3. Otherwise, the proposed scheme cannot achieve our goal.

≥ J t · J r , as long as N ≥ J t · ( 2 · J r − 1 )

In what follows, we explain how we derive these conditions and give the complete
design procedures to achieve interference-free transmission and full diversity for a
general case.

5.6.1 J t + 1 ≤ M < J t · J r

When J t + J r , the only way to achieve interference-free transmission is

to use Scheme II, i.e., align all the interference along the same direction. The reason
is that, in the M -dimensional signal space of each receiver, there are J t ·

1 ≤ M < J t ·

J r signal

vectors including J t useful signal vectors and J t · ( interference signal vectors.

If we do not use Scheme II, then each signal vector will occupy one dimension. But
the total dimension of the receiver space M is smaller than the total number of
signal vectors J t ·

J r − 1 )

J r . So without aligning the interference, we do not have enough
dimensions to achieve interference-free transmission for each useful signal vector.
On the other hand, we need M ≥ J t + 1. The reason is that, when M < J t + 1,

even if we align all the J t · ( J r − 1 ) interference signal vectors along one direction,

we still have J t + 1 signal vectors including J t useful signal vectors in each receiver

space. Therefore, we do not have enough dimensions to achieve interference-free
transmission for each useful signal vector if M

< J t + 1.

Now we analyze the requirement for N when J t + 1 ≤ M < J t · J r . We assume

that Transmitter k t , k t = 1 ,..., J t , transmits C k t k r ,a J t J r × J t J r rate-one space

time code at J t J r time slots to Receiver k r , k r = 1 ,..., J r . In other words, at

t th time slot, t J t J r , Transmitter k t sends the t th column of the space-

time code C k t k r to Receiver k r . We apply the N

= 1 ,...,

J t J r precoder matrix A t k t k r × on

C k t k r . Then at time slot t , Transmitter k t sends

J r

C t k t A t k t i C k t i ( = t ) (5.62)

i = 1

To satisfy the power constraint, we need