Communication system and method using unitary braid divisional multiplexing (ubdm) with physical layer security

Abstract

A system includes first and second sets of communication devices. A processor coupled to the first set of communication devices produces a first encoded vector and transmits the first encoded vector to the second set of communication devices via a communication channel that applies a channel transformation to the first encoded vector during transmission. A processor coupled to the second set of communication devices receives the transformed signal, detects an effective channel thereof, and identifies left and right singular vectors of the effective channel. A precoding matrix is selected from a codebook of unitary matrices based on a message, and a second encoded vector is produced based on a second known vector, the precoding matrix, a complex conjugate of the left singular vectors, and the right singular vectors. The second encoded vector is sent to the first set of communication devices for identification of the message.

1 . A method, comprising:
 generating, at a first processor of a first communication device, a first encoded vector using a first known vector and a unitary matrix;   transmitting, to a second communication device and through a communication channel, a first signal representing the first encoded vector, the communication channel applying a channel transformation to the first signal during transmission;   receiving, from the second communication device and at the first processor, a second signal representing a second encoded vector and the channel transformation;   detecting, via the first processor, a representation of an effective channel based on the second signal;   performing, via the first processor, a singular value decomposition of the representation of the effective channel to identify right singular vectors of the representation of the effective channel; and   querying a codebook of unitary matrices to identify a message associated with the second signal based on the right singular vectors of the representation of the effective channel and the unitary matrix.   
     
     
         2 . The method of  claim 1 , wherein at least one of the first communication device or the second communication device includes a plurality of antennas, the first communication device and the second communication device configured to perform Multiple Input Multiple Output (MIMO) operations. 
     
     
         3 . The method of  claim 1 , wherein the codebook of unitary matrices is publicly-accessible. 
     
     
         4 . The method of  claim 1 , further comprising receiving, from the second communication device and at the first processor, a plurality of additional signals representing a plurality of additional encoded vectors via the communication channel from the second communication device until a predetermined number of messages have been received. 
     
     
         5 . The method of  claim 1 , further comprising:
 detecting, via the first processor, a precoding matrix associated with an index for the message,   the querying of the codebook of unitary matrices being based on the precoding matrix.   
     
     
         6 . The method of  claim 1 , wherein the unitary matrix is a random unitary matrix. 
     
     
         7 . The method of  claim 1 , wherein the unitary matrix is an arbitrary unitary matrix. 
     
     
         8 . The method of  claim 1 , wherein at least one of the generating the first signal or the detecting the representation of the effective channel includes performing one of an inverse Fast Fourier Transform (iFFT) or a Fast Fourier Transform (FFT). 
     
     
         9 . A method, comprising:
 applying an arbitrary transformation to a plurality of vectors to produce a plurality of transformed vectors, the arbitrary transformation including one of a unitary transformation, an equiangular tight frame (ETF) transformation, or a nearly equiangular tight frame (NETF) transformation;   producing, using the arbitrary transformation, a transformed signal based on at least one transformed vector from the plurality of transformed vectors;   transmitting the transformed signal, via a communications channel, to a signal receiver that is configured to detect the transformed signal; and   providing a signal representing the arbitrary transformation to the signal receiver, for recovery of the plurality of vectors at the signal receiver based on the arbitrary transformation and one of a location-specific physical characteristic of the communications channel or a device-specific physical characteristic of the communications channel.   
     
     
         10 . The method of  claim 9 , wherein the transmitting the transformed signal is performed using multiple access communication. 
     
     
         11 . The method of  claim 9 , wherein the signal receiver includes a plurality of antennas and is configured to perform Multiple Input Multiple Output (MIMO) operations. 
     
     
         12 . The method of  claim 9 , wherein the recovery of the plurality of vectors at the signal receiver includes performing one of an inverse Fast Fourier Transform (iFFT) or a Fast Fourier Transform (FFT). 
     
     
         13 . The method of  claim 9 , wherein the communications channel is part of a public network. 
     
     
         14 . The method of  claim 9 , wherein the communications channel is part of a private network. 
     
     
         15 . The method of  claim 9 , wherein the arbitrary transformation does not include an identity matrix and is not a discrete Fourier matrix. 
     
     
         16 . A non-transitory, processor-readable medium storing instructions to cause a processor to:
 produce a plurality of transformed vectors based on a plurality of vectors and using an arbitrary transformation that does not include a direct sum of Fourier matrices;   produce, using the arbitrary transformation, a transformed signal based on at least one transformed vector from the plurality of transformed vectors;   send the transformed signal, via a communications channel, to a signal receiver that is configured to detect the transformed signal; and   send a signal representing the arbitrary transformation to the signal receiver, for recovery of the plurality of vectors at the signal receiver based on the arbitrary transformation and one of a location-specific physical characteristic of the communications channel or a device-specific physical characteristic of the communications channel.   
     
     
         17 . The non-transitory, processor-readable medium of  claim 16 , wherein the instructions to send the transformed signal include instructions to send the transformed signal is performed using multiple access communication. 
     
     
         18 . The non-transitory, processor-readable medium of  claim 16 , wherein the signal receiver includes a plurality of antennas and is configured to perform Multiple Input Multiple Output (MIMO) operations. 
     
     
         19 . The non-transitory, processor-readable medium of  claim 16 , wherein the recovery of the plurality of vectors at the signal receiver includes performing one of an inverse Fast Fourier Transform (iFFT) or a Fast Fourier Transform (FFT). 
     
     
         20 . The non-transitory, processor-readable medium of  claim 16 , wherein the communications channel is part of a private network.