Method of estimating transmit symbol vectors in an overloaded communication channel
A computer-implemented method of estimating transmit symbol vectors transmitted in an overloaded communication channel includes receiving a signal represented by a received signal vector, the received signal vector corresponding to a superposition of signals representing transmitted symbols selected from a constellation of symbols and transmitted from one or more transmitters. Continuous first and second functions in a search space in a convex domain are defined. The first function and the second function are combined into a third function, and a fractional programming algorithm is applied to the third function, targeted to finding an input vector that minimizes the third function. A mapping rule translates the found input vector into an estimated transmit symbol vector, and the estimated transmit symbol vector is output to a decoder for decoding into an estimated transmit symbol from the constellation.
1. A computer-implemented method of estimating transmit symbol vectors transmitted in an overloaded communication channel that is characterized by a channel matrix of complex coefficients, the method including:
receiving, in a receiver, a signal represented by a received signal vector, the received signal vector corresponding to a superposition of signals representing transmitted symbols selected from at least one constellation of symbols and transmitted from one or more transmitters,
defining a search space in a convex domain including at least the components of the received signal vector and of transmit symbol vectors for all symbols of the at least one constellation,
defining a continuous first function, which is a function of the received signal vector and the channel characteristics, the first function having a global minimum where the product of an input vector from the search space and the channel matrix equals the received signal vector,
defining a continuous second function in the search space, which is a function of input vectors from the search space, the second function having a significant low value for each of the transmit symbol vectors of the symbols of the at least one constellation,
combining the first function and the second function into a third function by weighted adding,
applying a fractional programming algorithm to the third function, targeted to finding an input vector that minimizes the third function,
applying a mapping rule that translates the input vector that minimizes the third function into an estimated transmit symbol vector, in which every single component has a value from a list of possible values of corresponding components of transmit symbol vectors of the symbols of the at least one constellation, and
outputting the estimated transmit symbol vector to a decoder for decoding into an estimated transmitted symbol from the at least one constellation.
2. The method of claim 1 , wherein the second function has a tuneable factor that determines the gradient of the second function in a vicinity of the significant low value at each of the transmit symbol vectors of the symbols of the at least one constellation.
3. The method of claim 2 , wherein the tuneable factor is different for different symbols of the at least one constellation.
4. The method of claim 3 , wherein applying the fractional programming algorithm includes:
providing an initial estimated transmit symbol vector that is at least farther away from the received signal vector than a minimum distance between vectors of neighbouring symbols from the at least one constellation, or
providing a null vector as an initial transmit symbol vector.
5. The method of claim 1 , wherein the first function is monotonously increasing from the global minimum.
6. The method of claim 1 , wherein the fractional programming algorithm is targeted to find a value of the third function that is lower than the global minimum of the first function.
7. The method of claim 1 , wherein the first function is a Euclidian distance function centered around the received signal vector.
8. The method of claim 1 , wherein the second function is a function based on or tightly approximating the l 0 -norm.
9. A non-transitory computer-readable medium storing a computer program product comprising computer executable instructions, which, when executed on a computer, cause the computer to estimate transmit symbol vectors transmitted in an overloaded communication channel, which is characterized by a channel matrix of complex coefficients, by performing operations comprising:
receiving, in a receiver, a signal represented by a received signal vector, the received signal vector corresponding to a superposition of signals representing transmitted symbols selected from at least one constellation of symbols and transmitted from one or more transmitters,
defining a search space in a convex domain including at least the components of the received signal vector and of transmit symbol vectors for all symbols of the at least one constellation,
defining a continuous first function, which is a function of the received signal vector and the channel characteristics, the first function having a global minimum where the product of an input vector from the search space and the channel matrix equals the received signal vector,
defining a continuous second function in the search space, which is a function of input vectors from the search space, the second function having a significant low value for each of the transmit symbol vectors of the symbols of the at least one constellation,
combining the first function and the second function into a third function by weighted adding,
applying a fractional programming algorithm to the third function, targeted to finding an input vector that minimizes the third function,
applying a mapping rule that translates the input vector that minimizes the third function into an estimated transmit symbol vector, in which every single component has a value from a list of possible values of corresponding components of transmit symbol vectors of the symbols of the at least one constellation, and
outputting the estimated transmit symbol vector to a decoder for decoding into an estimated transmitted symbol from the at least one constellation.
10. The non-transitory computer-readable medium of claim 9 , wherein the second function has a tuneable factor that determines the gradient of the second function in a vicinity of the significant low value at each of the transmit symbol vectors of the symbols of the at least one constellation.
11. The non-transitory computer-readable medium of claim 10 , wherein the tuneable factor is different for different symbols of the at least one constellation.
12. The non-transitory computer-readable medium of claim 11 , wherein applying the fractional programming algorithm includes:
providing an initial estimated transmit symbol vector that is at least farther away from the received signal vector than a minimum distance between vectors of neighbouring symbols from the at least one constellation, or
providing a null vector as an initial transmit symbol vector.
13. The non-transitory computer-readable medium of claim 9 , wherein the first function is monotonously increasing from the global minimum.
14. The non-transitory computer-readable medium of claim 9 , wherein the fractional programming algorithm is targeted to find a value of the third function that is lower than the global minimum of the first function.
15. The non-transitory computer-readable medium of claim 9 , wherein the first function is a Euclidian distance function centered around the received signal vector.
16. The non-transitory computer-readable medium of claim 9 , wherein the second function is a function based on or tightly approximating the l 0 -norm.