Digital Signal Processing Reference
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independently varying channels, there is likely to be at least a single user whose channel
is near its peak at any time, if the number of users is sufficiently large. By allowing only
the user having the best channel to use the system resource at a given time, the total
throughput of the entire system can be maximized. In [7], Knopp and Humblet focused
on the uplink channel of a multiuser system. In order to maximize the total information-
theoretic capacity of the system, they showed that the optimum strategy was to trans-
mit the signals of the user with the best channel at any time. Similar results were also
obtained by studying the downlink channel from the base station to the mobile users [8].
In [9], the space-time coding was combined with multiuser diversity. In [10] and [11], the
interaction between multiple-antenna diversity and multiuser diversity was discussed in
detail. Furthermore, the multiuser diversity technique has been implemented in practi-
cal communication systems, such as the downlink of the IS-856 system [12].
In a multiuser system exploiting multiuser diversity, channel fading can be consid-
ered a source of randomization providing multiuser diversity, as opposed to an impair-
ment. Therefore, large multiuser diversity gain is achieved when the dynamic range of
the channel fluctuation is large or the variation rate of the channel is fast. In practice,
however, the channel fluctuation may not be large enough to provide satisfactory mul-
tiuser diversity. Furthermore, when the channel fading is slower than the delay con-
straint of a system or an application, the user cannot wait until its channel reaches the
peak, and thus, the multiuser diversity gain may get smaller. Addressing these problems,
in [13], Viswanath et al. proposed opportunistic beamforming , which artificially induced
channel fluctuation when the fluctuation of the underlying physical channel was small
or the fading was slow. They studied a system where the base station was equipped with
multiple antennas and the same signal was transmitted from the antennas after being
multiplied by pseudorandom weight coefficients. The phase and magnitude of each
weight coefficient were changing in a controlled but pseudorandom fashion. By using a
single pilot signal, the signal-to-noise ratio (SNR) of the overall equivalent channel was
measured at every user and was fed back to the base station. Based on the SNR feedback,
the base station picked the user with the best equivalent channel and the data only for
this user were transmitted.
Over the past few years, many works have been devoted to extend the opportunistic
beamforming technique. In [14], multiple weight coefficients were used at every time slot
and the one producing the highest SNR was chosen. By doing this, better performance
could be achieved at the expense of the increased feedback overhead. Opportunistic
beamforming was combined with the water-filling method and extended to multiple-
input multiple-output systems in [15]. Furthermore, several new opportunistic schemes,
including opportunistic cophasing and antenna selection, were proposed and their per-
formance was analyzed in [16].
Very recently, Kim et al. proposed an adaptive version of opportunistic beamforming
in Ricean fading channels [17]. This new scheme improved the performance substan-
tially over Ricean fading channels without introducing multiple weight coefficients or
increasing the feedback overhead. Unlike the opportunistic beamforming in [13], which
generated the weight coefficients in a pseudorandom fashion, the improved opportunis-
tic beamforming generated the weight coefficients more intelligently by estimating the
directions of arrival (DOAs) of the users.
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