"Complex Matched Filter" What does a complex matched filter mean? . A complex bandpass filter can be formed by multiplying a low pass filter by exp(jwt) getting an analytic filter (one sided in the frequency domain)  which is complex, the filter will have complex coefficients but it is implemented as two filters with real coefficients (coefficients multiplied by cosines for the real and the same coefficients multiplied bu sines for the imaginary) but how about the matched filter which is supposed to be a low pass filter centered around DC? how does that one look like?
A matched filter is matched to the received pulse shape. If the matched filter is implemented in the baseband, i.e., after down-conversion, the received pulse shape can be complex-valued, e.g., if the channel frequency response is not symmetric with respect to the carrier frequency. In that case the matched filter is a complex-valued low-pass filter matched to the received (complex low-pass) pulse shape. The frequency response of such a filter is centered around DC but it is not symmetric with respect to DC.