Beamforming Techniques for OFDM
The objective of
beamforming is to separate the desired signal from interfering signals given
that all the signals share the same frequency band but have unique spatial
signatures associated with them. In addition to interference rejection and
multipath fading mitigation, beamforming increases the antenna gain in the
direction of the desired user. A beamformer essentially weights and sums the
signals from the different antenna elements to optimize the quality of the
Minimum Mean Squared
Maximum Signal to Interference and Noise Ratio (MSINR)
Maximum Signal to Noise Ratio (MSNR)
Adaptive weight update algorithms
x is the received
signal vector from each antenna element, and d is the desired signal vector.
Usually, matrix inversion operation leads to high complexity and should to be
avoided. However, if 2 or 4 receive antennas are employed, then the size of
the covariance matrix is small and calculating the inverse does not pose a
Square (LMS): Recursively computes and updates the weights to minimize the
cost function E[|e|^2]
In time domain
beamforming, the beamformer weights are calculated in the time domain, i.e.
before the FFT block. The FFT is performed after the signal is combined. Figure
1 shows a typical M-element time domain beamformer.
Figure 1: Time domain narrowband beamformer
The main challenge
of an OFDM beamformer is to correctly estimate the transmitted data symbols on
each of the OFDM sub-carriers. The most intuitive way is to combine the signals
in frequency domain, (that is, after the FFT operation at the receiver), since
pilot symbols and training sequence are usually inserted in the frequency domain
at the transmitter (before the IFFT block). Figure 2 shows a typical Frequency
Domain M-element beamformer.
Figure 2: Frequency domain beamformer
domain beamformer’s task is to minimize the effect of the multiplicative
distortion induced by fading channels. Note that the multiplicative distortion
can be eliminated by using a one-tap channel equalizer. However, equalization
removes the AOA information needed by the beamformer. Therefore, equalization is
not performed, and the multiplicative factor is passed to the beamformer which
steers the antenna array towards the desired direction.
Although a channel
may appear relatively flat from the view point of an individual sub-carrier, it
can be highly frequency selective when considering the whole OFDM bandwidth.
Hence, multiplicative distortion may be fairly distinctive across the spectrum.
In that case, a single set of beamforming weights is not sufficient for all
sub-carriers. A more efficient approach is to have multiple beamformers across
the sub-carriers. The optimal solution is to have one beamformer per
sub-carrier. However, if the channel does not vary significantly over a specific
set of sub-carriers, then a single beamformer can be assigned to these
Figure 3: Sub-band beamformer
Performance of beamforming for OFDM
OFDM beamformer for flat channel
provides substantial gains over the single antenna case (about 5 dB for a target
BER of 10^-2).
However, sub-band beamforming is not beneficial, since the channel is flat over
all sub-carriers i.e., the multiplicative distortion is constant for all
sub-carriers (See figures below).
Figure 4: DMI Beamforming in Flat Rayleigh Fading
Figure 5: LMS Beamforming in Flat Rayleigh Fading
Performance of OFDM beamformer
for frequency selective channel
frequency-domain beamforming fail and exhibit flat BER curves for frequency
selective channel. The reason for this is that a single beamformer is not
sufficient to keep track of fast channel variations on all sub-carriers.
However, using a sub-band beamformer with 4 sub-bands, performance is improved
drastically and a BER of
is obtained at Eb/No
= 10 dB (See below figures).
Furthermore, increasing the number of sub-bands may further improve the
performance, since the channel becomes flatter from the perspective of each
group of sub-carriers.
Figure 6: DMI Sub-band Beamforming in Frequency
Figure 7: LMS Sub-band Beamforming in Frequency