Patent ID: 7564916

Claim:
A method for encoding message with space-time trellis code (STTC) and transmitting the encoded message in a communication system employing at least two transmit antennas and at least one receive antenna, comprising steps of: generating a codeword X by encoding a message using STTC; and multiplying the codeword X by a weighting matrix W, and then transmitting it through the transmit antenna, wherein, the signal received at the receive antenna is given in equation 3: Y =√{square root over ( E S )} HWX+N [Equation 3] wherein, X is a 2×l matrix of a codeword, W is a 2×2 weighting matrix, H is an m×2 matrix of channel coefficients, N is an m×l matrix of additive noise, Es is energy per symbol, and Y is an m×l matrix of received signals at the receive antenna; wherein, the weighting matrix W is chosen as W 1 or W 2 depending on the feedback channel information from the receive antenna to the transmit antenna as given in equation 5: W 1 = [ ω 0 0 1 - ω 2 ] , if ⁢ ⁢  h 1  2 >  h 2  2 ⁢ ⁢ W 2 = [ 1 - ω 2 0 0 ω ] , otherwise [ Equation ⁢ ⁢ 5 ] wherein, ω is a positive real number such that 0.5≦ω 2 ≦1, and h i denotes the i-th column of H; wherein, conditional pairwise error probability (PEP) for the channel coefficient H is given in equation 6: p ( X→X′|H )≦exp(−ρ tr ( HW k A X,X′ W k † H † )) [Equation 6] wherein, ρ=Es/4N 0 , where N 0 is noise power spectrum density, A XX′ is defined as (X-X′)(X-X′) † , wherein † denotes the complex conjugate transpose, k is 1 for |h 1 | 2 >|h 2 | 2 , and 2 for |h 1 | 2 <|h 2 | 2 , since A X,X′ is Hermitian, there is a unitary matrix U such that A X,X′ =UΛU † and there is a real diagonal matrix Λ=diag(λ 1 , λ 2 ), and the unitary matrix U=unit(r,θ1, θ2, θ3) is given as following equation 7: U = [ rⅇ jθ 1 1 - r 2 ⁢ ⅇ jθ 2 1 - r 2 ⁢ ⅇ jθ 3 rⅇ j ⁢ ⁢ ( θ 2 - θ 1 + θ 3 + π ) ] [ Equation ⁢ ⁢ 7 ] wherein, r is a real number such that 0≦r≦1, and −π≦θ1, θ2, θ3≦π; and wherein, from the following equation 8 regarding conditional PEP for {|h j,max |, |h j,min |}, r value is chosen such that |r 2 −0.5| is minimized, and ω=1 is chosen so that the absolute value of ξ is minimized: p ⁢ ( ⁢ X → X ′ ⁢  {  h j , max  ,  h j , min  } ) = 1 2 ⁢ ∏ j = 1 m ⁢ ⁢ I 0 ⁡ ( ρ ⁢ ⁢ ξ ⁢  h j , max  ⁢  h j , min  ) × ⁢ ( ⁢ exp ⁢ ( - ρ ⁢ ( ⁢ w 2 ⁢ γ 1 ⁢ ∑ j = 1 m ⁢  h j , max  2 + ( 1 - ω ⁢ 2 ) ⁢ γ ⁢ 2 ⁢ ∑ j ⁢ = ⁢ 1 ⁢ m ⁢  ⁢ h ⁢ j , ⁢ min  2 ⁢ ) ⁢ ) + ( ⁢ exp ⁢ ( - ρ ⁢ ( ⁢ w 2 ⁢ γ 2 ⁢ ∑ j = 1 m ⁢  h j , max  2 + ( 1 - ω ⁢ 2 ) ⁢ γ ⁢ 1 ⁢ ∑ j ⁢ = ⁢ 1 ⁢ m ⁢  ⁢ h ⁢ j , ⁢ min  2 ⁢ ))) [ Equation ⁢ ⁢ 8 ] wherein, γ 1 =λ 1 r 2 +λ 2 (1 −r 2 ), γ 2 =λ 1 (1 −r ) 2 +λ 2 r 2 , ξ=2(λ 1 −λ 2 )ω r √{square root over (1−ω 2 )}√{square root over (1− r 2 )}, and I 0 (x) is zero-order modified Bessel function of the first kind.