Is it necessary that all element's pattern of an adaptive array antenna (null-steering) have exact similar pattern? If it is, What is the consequence of different element pattern in an adaptive array?
It makes it much easier if the antennas all have the same pattern. If they do, then you can predict the nulls mathematically and just use a mathematical expression when combining the antenna signals to get a null where you want it. If the antennas have different patterns than you will either have to know them and include them in the mathematical expression, or use adaptive nulling with feedback to adjust the null. I think this requires that there is a signal there to null out so the feedback loop has something to work with.
To add to the above excellent contribution, and assuming you are talking about an adaptive array with automatic null steeriing using closed or open loop approaches, factors you might consider investigating are e.g. the effect on electronic beam steering capability it you wish to have that, the effect on the number of interference sources you can simultaneously steer nulls at (degrees of freedom), the angles over which you can achieve this, and perhaps the bandwidth over which the null is sustained at a low level. Sounds complex to me. So, It would be interesting to know whether you have something in mind, where answers could be fuller, or whether its a general question.
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