0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 10 -4 10 -3 10 -2 10 -1 10 0 e 2 Average Uncoded BER SW-THP, N=2 Robust SW-THP, N=2 SW-THP, N=3 Robust SW-THP, N=3 15 20 25 30 35 40 10 -3 10 -2 10 -1 10 0 SNR (dB) Average Uncoded BER Stat. Robust THP, Robust SW-THP, Robust SW-THP, =0.005 e 2 =0.01 e 2 =0.01 e 2 =0.005 e 2 Stat. Robust THP, σ σ   λ −  λ    λ  λ  ≥    λ  λ     λ  λ     λ  λ  −   λ −  λ   ≥ −    −  ≥  −  · − − − −  Π F T R  Π R F T t  Π F T R    Π F  T  R  F  T  Π R Π R  F T Π F T R Π R  Π R   Π F  T  R  R Π  Π  Π Π Π  Π Π  Π R    Π R   Π R   Π F T R  R  Π F T R    Π F T R   Π F T R    Π F T R   − − [...]... Transmit and Receive Weights for MIMO Systems Fig 15 SINR vs γ (K=4, SNRmax=10dB) Fig 16 SINR vs γ (K=8, SNRmax=10dB) 281 282 Fig 17 Bit Error Rate Performance (K=4) Fig 18 Bit Error Rate Performance (K=8, N=3) MIMO Systems, Theory and Applications Iterative Optimization Algorithms to Determine Transmit and Receive Weights for MIMO Systems 283 4 Conclusion We proposed optimization algorithms of transmit and. .. capacity performance (Nt×2) MIMO Systems, Theory and Applications Iterative Optimization Algorithms to Determine Transmit and Receive Weights for MIMO Systems 275 Fig 10 Channel capacity performance (2×Nr) 3 Iterative optimization of the transmitter weights under constraint of the maximum transmit power for an antenna element in MIMO systems 3.1 System model Figure 11 shows MU -MIMO system considered in... Bold upper and lower case letters are used to denote matrices and column vectors, respectively (·) T , and (·)∗ refer to transpose and conjugate transpose, respectively · and · F stand for vector 2-norm and matrix Frobenius norm, respectively I N refers to the N × N identity matrix CN (μ, σ2 ) stands for the circularly symmetric complex Gaussian distribution with mean μ and covariance σ2 Pr and denote... achieve almost the same BER performance Figures 9 and 10 show the MIMO channel capacity in case of two data streams In this paper, for simplicity, MIMO channel capacity is defined as the sum of each eigenpath channel capacity which is calculated based on Shannon channel capacity in AWGN channel [3]; C = log2 (1+SNR) [bit/s/Hz] (17) 272 MIMO Systems, Theory and Applications The transmit power allocation for... Spring'02, pp .107 4 -107 8, May 2002 [9] T Nishimura, T Ohgane, Y Ogawa, Y Doi, & J Kitakado Downlink Beamforming Performance for an SDMA Terminal with Joint Detection, Proceedings of the IEEE Vehicular Technology Conference Fall'01, pp.1538-1542, Oct 2001 [10] B S Krongold Optimal MIMO- OFDM Loading with Power-Constrained Antennas, Proceedings of the IEEE PIMRC'06, Sept 2006 284 MIMO Systems, Theory and Applications. .. ε if g( W ) > ε 278 MIMO Systems, Theory and Applications K Ψ( W ) = ∑ψ j ( W ) j =1 ⎧ − h (1W ) j ⎪ ψ j ( W ) = ⎨ 2ε − h ( W ) j ⎪− ε2 ⎩ if h j ( W ) ≤ ε if h j ( W ) > ε Here, ε(0) denote the design parameters for non-constrained problem In Eq.(24), Φ( W ) and Ψ( W ) increase rapidly as approaches to the boundary When g(W) = ε and hj(W)=ε, the continuity of Φ( W ) and Ψ( W ) is guaranteed... the number of antennas 280 MIMO Systems, Theory and Applications Figures 17 and 18 show BER performance as a function of SNRmax, where the number of users is set to 1∼3 for K=4 in Fig.17, and set to 3 for K=8 in Fig.18 In these figures, we can see that, when the maximum per-antenna transmit power is limited to 1/K, BER performances is degraded by about 0.7∼0.8 dB at BER =10- 2 as compared with case of... transmitted in random direction within the angle range of 12 degrees at the BS Each of the plane waves has constant amplitude and takes the random phase distributed from 0 to 2π All users are randomly distributed with a uniform distribution in a range of the coverage area of a BS Channel states and distribution of users Iterative Optimization Algorithms to Determine Transmit and Receive Weights for MIMO Systems. .. of K=4 and 8 These results mean that the proposed optimization algorithm enables to use a low cost power amplifier at base stations in MIMO systems 5 References [1] T Ohgane, T Nishimura, & Y Ogawa Applications of Space Division Multiplexing and Those Performance in a MIMO Channel, IEICE Transactions on Communications, vol.E88-B, no.5, pp.1843-1851, May 2005 [2] G Lebrun, J Gao, & M Faulkner MIMO Transmission... constrain the average transmit power per each antenna to be less than or equal to pth is given as 276 MIMO Systems, Theory and Applications N ∑ wij 2 i =1 ≤ pth ∀j (1 ≤ j ≤ K) (20) #1 User #1 ・ ・ ・ ・ Base Station ・ ・ ・ H #K User #N Maximum permissible transmit power per antenna: pth Fig 11 MU -MIMO Systems Modulated Signal Modulated Signal x1 ・ ・ ・ ・ xN #1 Root Nyquist Filter Wt Root Nyquist Filter . 0.06 0.07 0.08 0.09 0.1 10 -4 10 -3 10 -2 10 -1 10 0 e 2 Average Uncoded BER SW-THP, N=2 Robust SW-THP, N=2 SW-THP, N=3 Robust SW-THP, N=3 15 20 25 30 35 40 10 -3 10 -2 10 -1 10 0 SNR (dB) Average. [bit/s/Hz] (17) MIMO Systems, Theory and Applications 272 The transmit power allocation for each eigenpath is determined based on the water-filling theorem [3]. In Figs.9 and 10, it can be. Frame format MIMO Systems, Theory and Applications 268 The optimum weight matrices are obtained by minimizing the error signal attributable to inter-stream interference and noise at the