Two or more antennas for receiving first and second modulated signals and for providing signals to one or more demodulators for demodulating the first modulated signal and providing cross-correlated demodulated in-phase and quadrature-phase baseband signals and demodulating the second modulated signal and providing a demodulated baseband signal and a selector for selecting either the first or the second demodulated signal.In certain embodiments the demodulator demodulating the first or the second modulated signal is comprised of bit rate switchable filters and/or mis-matched filters which are mismatched to that of the filters of the modulator of the first or the second bit rate modulated signal. In some of the applications the first or the second modulated received signal is a TDM or TDMA or Orthogonal Frequency Division Multiplexed (OFDM) modulated signal and/or a CDMA or other spread spectrum modulated signal and/or Phase Shift Keying (PSK) modulation, or a Quadrature Modulation (QM), or a Frequency Modulation (FM) modulated signal. In certain implementations and applications the demodulator is used for demodulation of Gaussian Minimum Shift Keying (GMSK) modulated signals and spread spectrum modulated signals or burst operated signals.