Device and method for precoding vectors in a communication system
A device and method for precoding vectors in a communication system is provided. A transmitter may precode a data vector using information regarding a communication channel prior to transmitting the data vector. The transmitter may precode the data vector in a manner that reduces an energy value of a resulting transmit data vector so as to minimize interference in a received signal at a receiver. The transmitter may perturb entries of the data vector one-by-one in an iterative fashion until a minimum in an energy value of the transmit data vector is obtained.
1. A method of precoding vectors in a communication system, the method comprising:
receiving an information symbol vector u and a channel matrix H;
calculating a transmit vector x using the information symbol vector u and the channel matrix H;
perturbing an entry of the information symbol vector u;
determining an energy value of the transmit vector, wherein if the energy value of the transmit vector x decreased, perturbing another entry of the information symbol vector u, and if the energy value of the transmit vector x did not decrease, transmitting the transmit vector x,
wherein the method comprises perturbing one entry of the information symbol vector u at a time.
2. The method of claim 1 , further comprising calculating a precoder matrix G from the channel matrix H using the following equation, G=H T (HH T ) −1 , and wherein the transmit vector x is calculated according to the equation, x=Gu, where G is an (N t ×N u ) precoding matrix, and where N t is a number of transmit antennas, and N u is a number of users.
3. The method of claim 2 , wherein perturbing an entry of the information symbol vector u comprises perturbing the entry so as to minimize an energy value of Gu.
4. The method of claim 1 , wherein perturbing an entry of the information symbol vector u comprises adding to the information symbol vector u a vector τp, in which τ is a positive real number determined based on a modulation scheme and the vector p has only one non-zero entry that corresponds to an entry of the information symbol vector u that is being perturbed.
5. The method of claim 1 , wherein perturbing an entry of the information symbol vector u comprises perturbing the information symbol vector u in such a way that a transformed vector ũ is another point in a lattice of a constellation of symbols used by the information symbol vector u such that:
ũ=u+τp
where p is a perturbation vector and τ is a positive real number.
6. The method of claim 5 , wherein τ is a constellation constant value and is given by:
τ=2| c max |+δ
where |c max | is a maximum value of either a real or imaginary component of constellation symbols used by the information symbol vector u, and δ is a spacing between the constellation symbols.
7. The method of claim 5 , wherein perturbing an entry of the information symbol vector u comprises changing a value of the entry of the information symbol vector u by an amount between −τ and +τ.
8. The method of claim 1 , wherein perturbing an entry of the information symbol vector u results in a perturbed vector ũ, and the determining step further comprises:
determining a first energy value of a transmit vector x using the information symbol vector u and the channel matrix H;
determining a second energy value of a transmit vector x using the perturbed vector and the channel matrix H; and
comparing the first energy value and the second energy value.
9. The method of claim 1 , wherein the energy value of the transmit vector x is a squared magnitude of a precoder matrix multiplied by the information symbol vector u.
10. The method of claim 9 , wherein the precoder matrix is given by G=H T (HH T ) −1 .
11. The method of claim 1 , wherein the method iteratively sequentially perturbs entries of the information symbol vector u until the energy value of the transmit vector x is at a minimum.
12. The method of claim 1 , wherein the method iteratively sequentially perturbs entries of the information symbol vector u until no decrease in the energy value of the transmit vector x occurs.
13. The method of claim 1 , wherein a bit-error rate (BER) of a received signal decreases for an increase in a number of base station antennas (N t ) and users (N u ).
14. The method of claim 1 , wherein a received signal-to-noise ratio (SNR) increases with an increase in a number of base station antennas (N t ) and users (N u ).
15. The method of claim 1 , further comprising perturbing more than one entry of the information symbol vector u.
16. A non-transitory computer-readable medium containing a set of instructions for causing a computing device to perform the functions of:
receiving an information symbol vector u and a channel matrix H;
calculating a transmit vector x using the information symbol vector u and the channel matrix H;
perturbing an entry of the information symbol vector u;
if an energy value of the transmit vector x decreased, perturbing another entry of the information symbol vector u; and
if the energy value of the transmit vector x did not decrease, transmitting the transmit vector x,
wherein the functions comprise perturbing one entry of the information symbol vector u at a time.
17. The non-transitory computer-readable medium of claim 16 , wherein perturbing an entry of the information symbol vector u results in a perturbed vector ũ, and the instructions further cause the computing device to perform the functions of:
determining a first energy value of a transmit vector x using the information symbol vector u and the channel matrix H;
determining a second energy value of a transmit vector x using the perturbed vector ũ and the channel matrix H; and
comparing the first energy value and the second energy value.
18. The non-transitory computer-readable medium of claim 16 , wherein perturbing an entry of the information symbol vector u comprises perturbing the entry so as to minimize an energy value of the transmit vector x.
19. The non-transitory computer-readable medium of claim 16 , wherein the instructions cause the computing device to iteratively perturb entries of the information symbol vector u until the energy value of the transmit vector x is at a minimum.
20. A precoder comprising:
a vector perturbation unit for receiving an information symbol vector u and perturbing an entry of the information symbol vector u to generate a perturbed information symbol vector ũ; and
a processing unit for receiving a channel matrix H and calculating a transmit vector x using the information symbol vector u and the channel matrix H, and if an energy value of the transmit vector x is smaller when using the perturbed information symbol vector ũ as compared to when using the information symbol vector u, instructing the vector perturbation unit to perturb another entry of the information symbol vector u.
21. The precoder of claim 20 , wherein if the energy value of the transmit vector x is not smaller when using the perturbed information symbol vector ũ as compared to when using the information symbol vector u, the processing unit transmits the transmit vector x as calculated using the information symbol vector u.
22. The precoder of claim 20 , wherein the vector perturbation unit perturbs the information symbol u so as to minimize the energy value of the transmit vector x.
23. The precoder of claim 20 , wherein the vector perturbation unit iteratively perturbs entries of the information symbol vector u until the energy value of the transmit vector x is at a minimum.