Precoder design for physical layer multicasting

1. A method for operating a transmit precoder for multicast communication over a downlink in a wireless network, comprising:

performing a channel estimate for each user in said wireless network;

updating for each said user a receive filter and a slack matrix;

updating said transmit precoder by solving a second order cone routine solvable in closed form as:

max



W



F

2

≤

P

⁢

⁢

β

s

.

to

⁢

⁢

c

k

-

β

≥



B

k

†

⁡

(

G

k

†

⁢

H

k

⁢

W

-

I

d

)



F

2

,

∀

k

 where the optimization is over W and β, the constant c k :=log |S k |+d−∥G k B k ∥ F 2 , S k =B k B k † denotes a Cholcsky factorization and P denotes the power budget in a power constraint, G k denotes said receive filter per user k, S k denotes said slack matrix per user k, β becomes equal to a minimum of achievable costs among all K users, and H k denotes the channel seen by user k:

determining if a predetermined convergence is met; and

outputting the transmit precoder responsive to a convergence criteria.

2. The method of claim 1 , wherein said predetermined convergence ensures a monotonically non-decreasing objective across iterations.

3. The method of claim 1 , wherein said receive filter comprises G k ←(H k WW 554 H k † +I N k ) −1 H k W where W denotes dimensions of the transmit precoder, H k denotes the channel seen by user k, I denotes interval, and N k denotes the number of receive antennas at user k and d denotes the upper bound on the number of symbols (in the rank constraint).

4. The method of claim 1 , wherein said slack matrix comprises S k ←W † H k † H k W+I d , where W denotes the transmit precoder, H k the channel seen by user k, I denotes and N k denotes the number of receive antennas at user k and d denotes the upper bound on the number of symbols in the rank constraint.