A communication system includes a set of microphones, a speaker, memory and a processor. The processor is configured to operate on input signals from the microphones to obtain a resultant signal representing the output of a virtual microphone which is highly directed in a target direction. The processor also is configured for self calibration. The processor may provide an output signal for transmission from the speaker. The output signal may be a noise signal, or, a portion of a live conversation. The processor captures one or more input signals in response to the output signal transmission uses the output signal and input signals to estimate parameters of the speaker and/or microphone.