TY - JOUR
T1 - Carrier phase and amplitude estimation for phase shift keying using pilots and data
AU - McKilliam, Robby G.
AU - Pollok, André
AU - Cowley, William
AU - Clarkson, I. Vaughan L
AU - Quinn, Barry G.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is asymptotically biased and converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. This appears to be the first time that the statistical properties of a non-data-aided estimator for carrier amplitude have been analyzed theoretically. The results of Monte Carlo simulations are provided and these agree with the theoretical results.
AB - We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is asymptotically biased and converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. This appears to be the first time that the statistical properties of a non-data-aided estimator for carrier amplitude have been analyzed theoretically. The results of Monte Carlo simulations are provided and these agree with the theoretical results.
KW - Asymptotic statistics
KW - detection
KW - phase shift keying
UR - http://www.scopus.com/inward/record.url?scp=84904746023&partnerID=8YFLogxK
U2 - 10.1109/TSP.2014.2332976
DO - 10.1109/TSP.2014.2332976
M3 - Article
AN - SCOPUS:84904746023
SN - 1053-587X
VL - 62
SP - 3976
EP - 3989
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 15
M1 - 6843974
ER -