Wireless Future - Telenor

signals can be made on one side only, at the
receiver, where the channel can be easily measured.
If available, the transmitter weights could
be used in a joint transmit-receive optimisation
to maximise the wanted powers. The formulation
in equations 4 and 5 is of course equivalent
to the angular description above, but it leads to
the more normal situation in Figure 2 where
there is a multitude of rays, and there is no
chance with a few elements to put many nulls in
the radiation pattern. The key point is that it is
not necessary to do so. The description in equations
4 and 5 is still valid so it is still possible to
choose the weight factors appropriately to separate
the two data streams and increase the capacity.
Physically we can explain the situation as
putting the unwanted signal in a deep fade instead
of a null in a radiation pattern, the result is
the same. Note that the scattering from widely
separated scatterers is a necessity for the increased
capacity; a line-of-sight situation where
the two antenna arrays see each other directly
would only lead to one channel, although with a
larger gain. This follows directly from Shannon
where the capacity in bits/s/Hz for independent
parallel channels is given by
�
C = N log2 1+ (6)
where P is the power over noise, or SNR, divided
equally over the channels. The expression
grows with N, the more so the larger P is, but the
beauty of the array solution is that antenna gain
will also grow with N, so we end up with the
following
P
�
N
C = N log 2 (1 + P) (7)
Telektronikk 1.2001
90
120 60
2
150 1.5
1
0.5
210
240
270
300
30
Beam 1
0
330
Beam 2
Figure 1a A simple example with two scatterers widely
separated. The antennas are multibeam antennas with
two beams, the blue ones (beam 1) having a null in the
radiation pattern in the direction of beam 2, and vice
versa. The antennas only have two elements, so they cannot
also have a maximum in the wanted direction. The system has
doubled the capacity, since the transmissions take place at the
same frequency
Multibeam antenna
with complex
antenna weights
W 1
W 2
Thus parallelism is a very promising technique,
it can only be realised in scattering environments
with wide angular spreads, and multiple antennas
at both ends are needed.
Although we have seen that only the receiver
array has to know the channel, it is an advantage
to let the transmitter array know the channel as
well, which would increase the P in eq. (7). The
information must in all cases be spread over the
transmit elements, and considerable research has
gone into finding optimum ways to do this using
so-called space-time coding (Tarokh et al [8]).
Foschini [1] and Winters [2] realised that this
situation could also be created with closely
spaced elements in a scattering environment,
where the scatterers would act as angularly
widely spread parasitic elements of the array.
90
120 60
2
150
1.5
1
30
0.5
180
0
210
240
270
300
330
Figure 1b Two independent
data streams are sent out and
received over both antennas,
and the weights are chosen
such that there is isolation
between the two beams
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