Adaptive Interference Nulling and Direction of Arrival Estimation in GPS Dual-Polarized Antenna Receiver - Adaptive Signal Processing in Wireless Communications - page 414

In minimizing E {| y ( k )| 2 }, the dual-polarized antenna array will attempt to reduce the
output power of the interference, which could be horizontally polarized, vertically polar-
ized, right-hand circularly polarized (RHCP), or LHCP. Each antenna may act alone, by
setting one of the two values of its corresponding complex weights to zero, or by forcing
the two polarization weight components into a complex conjugation relationship. This
would be clearly the case for cancelling any large number of horizontally polarized,
vertically polarized, or LHCP interferers. The antenna may also act in conjunction with
other receiver antennas, in which case the interference DOA plays a role in determining
the weight values.
Since GPS signals are RHCP, the number of RHCP interferers that can be suppressed
with N dual-polarized antennas is limited to N - D . The cancellation of a large or infinite
number of horizontally polarized interferers is achieved by setting the weights of the
horizontally polarized elements to zero. In this case, the total number of degrees of free-
dom is reduced to N , out of which N - D degrees can be used to cancel, through spatial
nulling, N - D types of jammers, such as RHCP, LHCP, or vertically polarized interfer-
ers. Similarly, an infinite number of vertically polarized interferers can be cancelled
along with a maximum of N - D RHCP, LHCP, or horizontally polarized interferers.
Further, an infinite number of LHCP interferers can be cancelled by the RHCP antenna
array, which can additionally cancel N - D RHCP, horizontally polarized, or vertically
polarized interferers through spatial nulling.
It is noted, however, that depending on the number of dual-polarized antennas and
the number of satellites in the field of view (FOV), D , one set of array weights may not be
sufficient to cancel all interferers in dense jamming environments, even with the use of
dual-polarized antenna array. This problem can be mitigated by using multiple MVDR
beamformers, each corresponding to one satellite. In this case, several sets of weight
vectors are applied; each weight vector is associated with one satellite and designed to
satisfy a single unit-gain constraint. As a result, up to N - 1 RHCP interferers can be
cancelled by the multiple beamformer approach, compared to only N - D interferers in
the case of the single beamformer approach. In addition to increasing the number of
degrees of freedom, another important advantage of the multiple MVDR beamform-
ers is in achieving regular array patterns. It is noted that in order to keep unit gain
at all GPS satellite directions, a single MVDR beamformer will encounter difficulty
suppressing the undesired signal, if it is close in angle to any one of the GPS satellites.
With close angular separation between one satellite and one jammer position, the array
response will be highly irregular, giving rise to several lobes in a random manner that
makes the receiver vulnerable to newly borne interferers or on-off interferers with a long
duty cycle. Insufficient interference cancellation compromises the receiver delay lock
loops and provides undesirable tracking and positioning errors. With multiple MVDR
beamformers, however, each of the D - 1 beamformer responses will null all interfer-
ers impinging on the GPS receiver, subject to the available degrees of freedom. Only
the one response associated with the satellite that is aligned or close to an interference
DOA will fail and provide an irregular pattern. In this respect, loss of acquisition, if it
occurs, will be confined to only one satellite. With typically more than four satellites in
the FOV, the loss of one satellite's information is not detrimental to the receiver pseudo-
range estimate calculations. The multiple MVDR beamformers approach is shown in