The permissible dB level for the co and cross polarization is less than -20 dB as given in literature..Cross polarization quantifies that how much your antenna is radiated in undesired directions...so it should be as less as possible...i hope this will help u..

Thank you @ashish Gupta' for your response. Your answer very helpful

. Is there any books or research articles regading this,  I want concepts of radiation patterns detaily..

Basically, cross polarisation is a loss of a signal at the receiver end. Also it is a noise as far as detection is concern. Generally, 20 dB down is ok, unless and otherwise receiver has specific requirement. It could be negotiable term with reference to receiver. The unwanted signal can be made acceptable till it does not affect the detection. Special requirement arises in case of critical systems

Hi

I agree with the above but would like to add a smal note. When dealing with RF with long wavelength typically outdoor, or to the extrem, satellite communication, polarisation is extremely crucial as the signals are weak and have a clear polarization.

However, if you are dealing with GHz signals indoor and have small antennas, you do not have control over the polarisation. The polarisation in a room varies from place to place and it can completely flipp just by moving your measurement antenna a few centimeters. Also, having the measurement antenna at a fixed position will tell you that the polarisation also will change over time, just because a door opened in the other room or someone walked by. For those systems, e.g. wlan and bluetooth in mobile phones, it is better to simply describe the antenna with its antenna efficiency.

BR

Peter 

Thank you @Peter Sjöblom sir for your note. surely i will consider antenna efficiency.

Peter Sjöblom Sir,

If I measure my antenna in Anchoic Chamber, then there would not be such kind of disturbance. So in that case what should be the acceptable value of cross-polarization level? If I got -120 dB level of cross-polarization, then is it acceptable for an antenna designed with Roger RT 5880 substrate material for DBS application?