Carrier phase and amplitude estimation for phase shift keying using pilots and data
A least squares estimator of carrier phase and amplitude in a receiver in a communication system using a phase shift keying modulation scheme that uses both known pilot symbols and unknown data symbols is described. That is, the method exploits knowledge of pilot symbols in addition to the unknown data symbols to estimate carrier phase and amplitude. Further, an efficient recursion based estimation method is described that only requires O(L. log L) arithmetic operations where L is the number of received signals. This method uses the M-Ary rounded phase offsets to sort the data symbols and this sorted order is used to recursively calculate candidate values in an optimization process. Simulation results show that the estimation methods Using data and pilot symbols outperform estimation methods using only data symbols (ie non-coherent detection methods). Further, the system can be used for systems using multiple M-ary phase shift keying digital modulation schemes.
1. A method for estimating the carrier phase and amplitude in a received signal by a receiver including hardware components, comprising:
receiving, by the receiver, a signal comprising a plurality of symbols modulated using one or more M-ary phase shift keying digital modulation schemes, the plurality of symbols comprising a plurality of pilot symbols known to the receiver, and a plurality of data symbols unknown to the receiver;
calculating the M-ary rounded phase offset from the received signal for each one of the received plurality of data symbols;
obtaining a sorted order of the data symbols, wherein the sorted order is determined using the M-ary rounded phase offsets;
calculating a plurality of candidate values of an objective function, wherein the objective function is optimised with respect to estimation of the carrier phase and amplitude, and each candidate value after a first candidate estimate is calculated recursively from the previous candidate value, wherein the order of the calculation is determined according to the sorted order of the data symbols; and
determining an optimum candidate value from the plurality of candidate values, and determining the carrier phase and amplitude associated with the optimum candidate value.
2. The method as claimed in claim 1 , wherein the sorted order is an ascending order of the M-ary rounded phase offsets.
3. The method as claimed in claim 1 , wherein the objective function is a sum of squares function.
4. The method as claimed in claim 3 , wherein the sum of squares function is minimised with respect to estimation of the carrier phase and amplitude.
5. The method as claimed in claim 3 , wherein the number of modulation schemes is |G| and
H
=
∑
m
∈
G
m
D
m
=
O
(
L
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candidate sum or squares values are calculated, where |D m | is the number of data symbols in the received signal modulated according to the m th modulation scheme and D m is the set of indices describing the positions of symbols modulated with the m th modulation scheme.
6. The method as claimed in claim 5 , wherein the sum of squares value is a weighted sum of squares value.
7. The method as claimed in claim 6 , wherein the weighting is based upon a Signal to Noise Ratio (SNR) to give more importance to pilot symbols when the SNR is low.
8. The method as claimed in claim 1 , wherein the step of determining an optimum candidate value from the plurality of candidate values is performed as the plurality of candidate values are calculated.
9. The method as claimed in claim 8 , wherein as each candidate value is calculated it is compared with a current optimum candidate value, and if the calculated candidate value is optimal compared to the current optimum candidate value, the current optimum candidate value is updated with the calculated candidate value.
10. The method as claimed in claim 9 , wherein if the current optimum candidate value is updated, a corresponding carrier phase and an amplitude value is calculated.
11. The method as claimed in claim 1 , wherein the plurality of symbols are modulated using a single M-ary phase shift keying digital modulation scheme.
12. The method as claimed in claim 1 , wherein the plurality of symbols are modulated using a two or more M-ary phase shift keying digital modulation schemes.
13. A non-transitory processor readable medium, comprising instructions for causing a processor to carry out a method for estimating the carrier phase and amplitude in a received signal by a receiver including hardware components, comprising:
receiving, by the receiver, a signal comprising a plurality of symbols modulated using one or more M-ary phase shift keying digital modulation schemes, the plurality of symbols comprising a plurality of pilot symbols known to the receiver, and a plurality of data symbols unknown to the receiver;
calculating the M-ary rounded phase offset from the received signal for each one of the received plurality of data symbols;
obtaining a sorted order of the data symbols, wherein the sorted order is determined using the M-ary rounded phase offsets;
calculating a plurality of candidate values of an objective function, wherein the objective function is optimised with respect to estimation of the carrier phase and amplitude, and each candidate value after a first candidate estimate is calculated recursively from the previous candidate value, wherein the order of the calculation is determined according to the sorted order of the data symbols; and
determining an optimum candidate value from the plurality of candidate values, and determining the carrier phase and amplitude associated with the optimum candidate value.
14. A receiver comprising:
a receiver module for receiving a signal, the receiver module including receiver hardware components; and
a processing module including processing hardware components, the processing module comprising a memory and a processor operatively coupled to the memory and configured to carry out a method for estimating the carrier phase and amplitude in a received signal by the receiver, the method comprising:
receiving a signal comprising a plurality of symbols modulated using one or more M-ary phase shift keying digital modulation schemes, the plurality of symbols comprising a plurality of pilot symbols known to the receiver, and a plurality of data symbols unknown to the receiver;
calculating the M-ary rounded phase offset from the received signal for each one of the received plurality of data symbols;
obtaining a sorted order of the data symbols, wherein the sorted order is determined using the M-ary rounded phase offsets;
calculating a plurality of candidate values of an objective function, wherein the objective function is optimised with respect to estimation of the carrier phase and amplitude, and each candidate value after a first candidate estimate is calculated recursively from the previous candidate value, wherein the order of the calculation is determined according to the sorted order of the data symbols; and
determining an optimum candidate value from the plurality of candidate values, and determining the carrier phase and amplitude associated with the optimum candidate value.
15. A communication system comprising:
a transmitter including transmitter hardware components; and
a receiver including receiver hardware components, the receiver comprising:
a receiver module for receiving a signal;
a processing module comprising a memory and a processor operatively coupled to the memory and configured to carry out a method for estimating the carrier phase and amplitude in a received signal by the receiver comprising:
receiving a signal comprising a plurality of symbols modulated using one or more M-ary phase shift keying digital modulation schemes, the plurality of symbols comprising a plurality of pilot symbols known to the receiver, and a plurality of data symbols unknown to the receiver;
calculating the M-ary rounded phase offset from the received signal for each one of the received plurality of data symbols;
obtaining a sorted order of the data symbols, wherein the sorted order is determined using the M-ary rounded phase offsets;
calculating a plurality of candidate values of an objective function, wherein the objective function is optimised with respect to estimation of the carrier phase and amplitude, and each candidate value after a first candidate estimate is calculated recursively from the previous candidate value, wherein the order of the calculation is determined according to the sorted order of the data symbols; and
determining an optimum candidate value from the plurality of candidate values, and determining the carrier phase and amplitude associated with the optimum candidate value;
wherein the transmitter is configured to implement said one or more M-ary phase shift keying digital modulation schemes and transmits said plurality of symbols comprising the plurality of pilot symbols known to the receiver, and the plurality of data symbols unknown to the receiver.