Variable modulus mechanism for performing equalization without a priori knowledge of modulation type or constellation order
View Patent ↗A system, method and memory medium for performing blind equalization. A block {u n } of the baseband samples is received. A function J of a vector f is minimized to determine a minimizer f MIN . The function J depends on vector f according to J(f)=Σ(|y n | 2 −γ) 2 . The summation Σ corresponds to a sequence {y n } of equalized samples. The sequence {y n } of equalized samples is related to the block {u n } according to a convolution relation {y n }={u n }*f. Parameter γ is a current modulus value. The current modulus value γ is updated to equal a ratio of a fourth moment of the sequence {y n } to a second moment of the sequence {y n }. The minimization and parameter update operations are repeated for a series of received blocks of baseband samples. The minimizer f MIN from a last of the repetitions is used to determine final equalized samples.
1. A method for performing blind equalization on received samples, the method comprising:
(a) receiving at a computer system a block {u n } of the received samples;
(b) minimizing a function J of a vector argument f to determine a minimizing vector f MIN , wherein said minimizing is performed by the computer system, wherein the function J depends on the vector argument f according to the expression J(f)=Σ(|y n | 2 −γ) 2 , wherein the summation Σ corresponds to a sequence {y n } of equalized samples, wherein the sequence {y n } of equalized samples is related to the block {u n } of received samples according to a convolution relation {y n }={u n }*f, wherein γ is a current modulus parameter value;
(c) computing a fourth moment of the sequence {y n } corresponding to the minimizing vector f MIN , wherein said computing the fourth moment is performed by the computer system;
(d) computing a second moment of the sequence {y n } corresponding to the minimizing vector f MIN , wherein said computing the second moment is performed by the computer system;
(e) updating the current modulus parameter value γ to be equal to a ratio of the fourth moment to the second moment, wherein said updating the current modulus parameter value γ is performed by the computer system;
repeating (a) through (e) until a termination condition is satisfied, wherein said repeating is performed by the computer system;
convolving the received samples with the minimizing vector f MIN from a last of said repetitions of (a) through (e) to determine final equalized samples, wherein said convolving is performed by the computer system.
2. The method of claim 1 , wherein the termination condition is the condition that a change in the current modulus parameter value y between successive repetitions of (a) through (e) is smaller than a predetermined threshold.
3. The method of claim 1 , further comprising:
displaying a constellation plot of the final equalized samples via a display device.
4. The method of claim 3 , further comprising:
receiving user input identifying a modulation type and constellation order after said displaying the constellation plot;
demodulating the final equalized samples based on the identified modulation type and identified constellation order in order to obtain a bit sequence.
5. The method of claim 1 , further comprising:
performing a cluster analysis on the final equalized samples to determine a constellation order implicit in the received samples; and
displaying an indication of the constellation order via the display device.
6. The method of claim 1 , wherein said minimizing the function J comprises performing a stochastic gradient descent algorithm.
7. The method of claim 1 , wherein said method operates without any a priori knowledge of the modulation type used to form the received samples.
8. The method of claim 1 , wherein a next repetition of said minimizing starts with the minimizing vector f MIN determined in a current repetition of said minimizing.
9. A non-transitory computer-readable memory medium having stored thereon program instructions executable by a computer system, wherein the program instructions, when executed by the computer system, cause the computer system to perform a method of blind equalization on received samples, the method comprising:
(a) receiving a block {u n } of the received samples;
(b) minimizing a function J of a vector argument f to determine a minimizing vector f MIN , wherein the function J depends on the vector argument f according to the expression
J ( f )=Σ(| y n | 2 −γ) 2 ,
wherein the summation Σ corresponds to a sequence {y n } of equalized samples, wherein the sequence {y n } of equalized samples is related to the block {u n } of received samples according to a convolution relation {y n }={u n }*f, wherein γ is a current modulus parameter value;
(c) computing a fourth moment of the sequence {y n } corresponding to the minimizing vector f MIN ;
(d) computing a second moment of the sequence {y n } corresponding to the minimizing vector f MIN ;
(e) updating the current modulus parameter value γ to be equal to a ratio of the fourth moment to the second moment;
repeating (a) through (e) until a termination condition is satisfied;
convolving the received samples with the minimizing vector f MIN from a last of said repetitions of (a) through (e) to determine final equalized samples.
10. The memory medium of claim 9 , wherein the termination condition is the condition that a change in the current modulus parameter value y between successive repetitions of (a) through (e) is smaller than a predetermined threshold.
11. The memory medium of claim 9 , wherein the method further comprises:
displaying a constellation plot of the final equalized samples via a display device.
12. The memory medium of claim 11 , wherein the method further comprises:
receiving user input identifying a modulation type and constellation order after said displaying the constellation plot;
demodulating the final equalized samples based on the identified modulation type and identified constellation order in order to obtain a bit sequence.
13. The memory medium of claim 9 , wherein said minimizing the function J comprises performing a stochastic gradient descent algorithm.
14. The memory medium of claim 9 , wherein a next repetition of said minimizing starts with the minimizing vector f MIN determined in a current repetition of said minimizing.
15. A computer system for performing blind equalization on received samples, the computer system comprising:
a processor; and
memory storing program instructions, wherein the program instructions, when executed by the processor, cause the processor to:
(a) receive a block {u n } of the received samples;
(b) minimize a function J of a vector argument f to determine a minimizing vector f MIN , wherein the function J depends on the vector argument f according to the expression
J ( f )=Σ(| y n | 2 −γ) 2 ,
wherein the summation Σ corresponds to a sequence {y n } of equalized samples, wherein the sequence {y n } of equalized samples is related to the block {u n } of received samples according to a convolution relation {y n }={u n }*f, wherein γ is a current modulus parameter value;
(c) compute a fourth moment of the sequence {y n } corresponding to the minimizing vector f MIN ;
(d) compute a second moment of the sequence {y n } corresponding to the minimizing vector f MIN ;
(e) update the current modulus parameter value γ to be equal to a ratio of the fourth moment to the second moment;
repeat (a) through (e) until a termination condition is satisfied;
convolve the received samples with the minimizing vector f MIN from a last of said repetitions of (a) through (e) to determine final equalized samples.
16. The computer system of claim 15 , wherein the termination condition is the condition that a change in the current modulus parameter value y between successive repetitions of (a) through (e) is smaller than a predetermined threshold.
17. The computer system of claim 15 , further comprising a display device, wherein the program instructions, when executed by the processor, further cause the processor to display a constellation plot of the final equalized samples via the display device.
18. The computer system of claim 15 , wherein the processor includes a programmable hardware element.
19. The computer system of claim 15 , wherein said minimize the function J comprises performing a stochastic gradient descent algorithm.
20. The computer system of claim 15 , wherein a next repetition of said minimize starts with the minimizing vector f MIN determined in a current repetition of said minimizing.