what is Axial ratio bandwidth of antenna

It related to the polarization bandwidth and this number expresses the quality of the circular polarization of an antenna. In GPS antennas we are interested to know how well the antenna suppresses the unwanted left hand circular polarization. This is particularly important if you need multipath suppression: when a GPS signal reflects off a near by object, the first reflection will have its polarization inverted (from right hand circular to left hand circular). When the left hand circular suppression of the antenna is poor (and at low elevations it will at least degrade to some extent), the reflected signal will cause interference in the receiver. The ratio by which a polarization is suppressed vs. another polarization is referred to as cross polar suppression.