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QPSK Baseband Demodulation

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EngrAdnan

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I have problem in demodulating a complex base band signal(QPSK) which is downconverted from IF to baseband (I and Q channels) with some phase and frequency offset (i.e LO at IF did not lock with the phase and frequency of the incoming signal, hence causing frequency and phase error in baseband signal and the QPSK constellation rotates due to this error).
Normal Phase lock loops (i.e costas loop) can track well at IF but at complex baseband level what are the options left for me?
I also needs to avoid upsampling and then upmixing technique due to system limitations.
please help.
 

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