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Description:
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In this work , first the Cramer -Rao lower bound (CRLB ) of the signal -to -noise
ratio (SNR ) estimate for binary phase shift keying (BPSK ) modulated signals in
additive white Gaussian noise (AWGN ) channels is derived . All the steps and results
of this CRLB derivation are shown in a detailed manner . Two major estimation
scenarios are considered herein : the non -data -aided (NDA ) and data -aided (DA )
frameworks , respectively . The non -data -aided scenario does not assume the periodic
transmission of known data symbols (pilots ) to limit the system throughput , while
the data -aided scenario assumes the transmission of known transmit data symbols
or training sequences to estimate the channel parameters . The Cramer -Rao lower
bounds for the non -data -aided and data -aided scenarios are derived . In addition , the
modified Cramer -Rao lower bound (MCRLB ) is also calculated and compared to the
true CRLBs . It is shown that in the low SNR regime the true CRLB is tighter than
the MCRLB in the non -data -aided estimation scenario .
Second , the Bayesian Cramer -Rao lower bound (BCRLB ) for SNR estimate is
considered for BPSK modulated signals in the presence of time -selective fading channels . Only the data -aided scenario is considered , and the time -selective fading channel
is modeled by means of a polynomial function . A BCRLB on the variance of the SNR estimate is found and the simulation results are presented . |