METHOD FOR WIRELESS X2X ACCESS AND RECEIVERS FOR LARGE MULTIDIMENSIONAL WIRELESS SYSTEMS
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.
1 . A computer-implemented receiver 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 a differentiable and convex function in a closed form of the received signal vector and of transmit symbol vectors for all symbols of the at least one constellation,
obtaining the differentiable and convex function in a closed form by changing the first optimization formulation given by a first function into a second optimization formulation given as a second function by applying a quadratic approximation of l o -Norm given as third function and after obtaining the second function a fourth function is calculated, and
applying an iterative procedure to find the optimal solution for the estimation of transmitting symbols is performed.
2 . The method of claim 1 , wherein differentiable and convex function in a closed form of the received signal vector and of transmit symbol vectors is obtained by applying the setting of the Wingerts derivative of the fourth function.
3 . The method of claim 1 , wherein the optimal solution calculated via a matrix multiplication for the fixed elements of the second function.
4 . A computer-implemented receiver 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 closed-form solution providing s and penalty parameter λ fifth function of the received signal vector and of transmit symbol vectors for all symbols of the at least one constellation,
obtaining a closed-form fifth function providing s and penalty parameter λ by changing the first optimization formulation given as a sixth function, which is a real-valued quadratically constrained quadratic program version of a seventh function, which is recalculated into a generalized eigenvalue formulation and the Möbus transformed function,
applying an iterative procedure to find the optimal solution for the estimation of transmitting symbols is performed.
5 . The method of claim 1 , wherein within the iterative procedure the coefficients β's, which are given in terms on the estimate solution s, the constellation alphabet, and the tightening parameter α are determined.
6 . The method of claim 1 , wherein an incrementation of the iteration number i of the iterative procedure is proceeded.
7 . The method of claim 1 , wherein the calculation of solution variation d using the Euclidian distance between the solution of the current and previous iteration is proceeded.
8 . The method of claim 1 , wherein the convergence criteria is controlled in a way, if d<e or the maximum number of iterations has been reached, the iteration is terminated and the solution of the solution of the estimated transmitted vector s is determined and created.
9 . A receiver of a communication system having a processor, volatile and/or non-volatile memory, at least one interface adapted to receive a signal in a communication channel, wherein the non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure the receiver to estimate transmit symbol vectors transmitted in an overloaded communication channel that is characterized by a channel matrix of complex coefficients operations 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 a differentiable and convex function in a closed form of the received signal vector and of transmit symbol vectors for all symbols of the at least one constellation,
obtaining the differentiable and convex function in a closed form by changing the first optimization formulation given by a first function into a second optimization formulation given as a second function by applying a quadratic approximation of l o -Norm given as third function and after obtaining the second function a fourth function is calculated; and
applying an iterative procedure to fin the optimal solution for the estimation of transmitting symbols is performed.
10 . (canceled)
11 . (canceled)
12 . The receiver of claim 9 , wherein differentiable and convex function in a closed form of the received signal vector and of transmit symbol vectors is obtained by applying the setting of the Wingerts derivative of the fourth function.
13 . The receiver of claim 9 , wherein the optimal solution calculated via a matrix multiplication for the fixed elements of the second function.
14 . The receiver of claim 9 , wherein an Incrementation of the iteration number i of the iterative procedure is proceeded.
15 . The receiver of claim 9 , wherein the calculation of solution variation d using the Euclidian distance between the solution of the current and previous iteration is proceeded.
16 . The receiver of claim 9 , wherein the convergence criteria is controlled in a way, if d<e or the maximum number of iterations has been reached, the iteration is terminated and the solution of the solution of the estimated transmitted vector s is determined and created.
17 . A receiver configured for estimating transmit symbol vectors transmitted in an overloaded communication channel that is characterized by a channel matrix of complex coefficients, by performing operations 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 closed-form solution providing s and penalty parameter λ fifth function of the received signal vector and of transmit symbol vectors for all symbols of the at least one constellation,
obtaining a closed-form fifth function providing s and penalty parameter λ by changing the first optimization formulation given as a sixth function, which is a real-valued quadratically constrained quadratic program version of a seventh function, which is recalculated into a generalized eigenvalue formulation and the Möbus transformed eighth function, and
applying an iterative procedure to find the optimal solution for the estimation of transmitting symbols is performed.
18 . The receiver of claim 17 , wherein within the iterative procedure the coefficients β's, which are given in terms on the estimate solution s, the constellation alphabet, and the tightening parameter α are determined.
19 . The receiver of claim 17 , wherein the optimal solution calculated via a matrix multiplication for the fixed elements of the second function.
20 . The receiver of claim 17 , wherein a Incrementation of the iteration number i of the iterative procedure is proceeded.
21 . The receiver of claim 17 , wherein the calculation of solution variation d using the Euclidian distance between the solution of the current and previous iteration is proceeded.
22 . The receiver of claim 17 , wherein the convergence criteria is controlled in a way, if d<e or the maximum number of iterations has been reached, the iteration is terminated and the solution of the solution of the estimated transmitted vector s is determined and created.