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a question about frequency offset estimation!

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enjoypercy

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I find that in some algorithm the received signal(atfer matched filter) is expressed as:

r(t)=∑Sk*exp{j*(Δωt+Θ)}*g(t-kT-τ)+n(t)

2 questions:

1, why is Sk a complex array? If so, it will impact the angle of correlation of r(n)(sampled) and the final offset not only contain the carrier frequency offset but also the phase of SK.
2, why is there Δω after matched filter?

thanks a lot if anyone could help me!
 

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