Evaluation of method using invariant transmit dimensions for a realistic mimo diagonal channel matrix

Currently, use of a virtual MIMO diagonal channel model (fixed spatial bins) that represents realistic environment is researched. The author has applied the invariant transmit dimensions, or on the other way, on the physical paths directing to the slow or fixed scatterers in centres of these bins.

Kỹ thuật điều khiển & Điện tử EVALUATION OF METHOD USING INVARIANT TRANSMIT DIMENSIONS FOR A REALISTIC MIMO DIAGONAL CHANNEL MATRIX Tran Hoai Trung* Abstract: Currently, use of a virtual MIMO diagonal channel model (fixed spatial bins) that represents realistic environment is researched The author has applied the invariant transmit dimensions, or on the other way, on the physical paths directing to the slow or fixed scatterers in centres of these bins The result is the invariant dimensions are better in increasing the channel capacity comparing with no CSI or the strongest beam at the transmitter as number of the dimensions is enough large Keywords: Wireless communication, MIMO diagonal channel matrix, Invariant transmit beams, Channel State Information (CSI) I PROBLEM The number of diagonals of the virtual channel matrix H v is an important factor in assessing the channel capacity [1] A solution to give a channel matrix for the simpler computation of the capacity could be the use of an equivalent diagonal channel matrix H k that represents the virtual channel matrix H v [1] Channel capacity using proposed invariant transmit is compared with a no CSI ([2], [3] and [4]) and the use of the strongest transmit beam ([5] and [6]) II THE INVARIANT DIMENSIONS IN THE REALISTIC ENVIRONMENT This discrete physical environment- a so called the virtual MIMO model has size of L  L as explained in [1] The fading from transmit antenna m to receive antenna can be rewritten as: 2 2 sin  T , l l1  L j cos  R, l l vt L j  hm,1   e  l l e  12 l1 1 l 1 (1) where T ,l l , R,l l  provide the transmit and receive directions ~ s s l ~ l  T , l l   T sin T , l l   ;  R, l l   R sin  R, l l    L  L normalised transmit and receive angles where l   that called ( L  1) ( L  1) v, t are velocity  2L 2L and time of moving of the receiver  l1l is the fading computed over physical paths l1,l2 that are reflected from the centres of the bins at the first and last columns of the channel matrix The determination of the invariant dimensions in the discrete physical environment is repeated so that the invariant dimensions are then obtained under the same topology of the virtual model that represents the realistic environment [2] In the situation where the virtual model has the parameters as below: 104 Tran Hoai Trung, “Evaluation of method using… MIMO diagonal channel matrix.” Nghiên cứu khoa học công nghệ Table Table of environmental parameters simulating the beams at the the transmitter using the virtual model Wavelength Velocity of the receiver The spacing between the transmit elements, receive elements The number of elements at transmit and receive antenna Magnitudes of paths Number of the bins at the transmitter and the receiver Transmit angles Receive angles  v sT , s R M N 11   22    LL L T ,1,T ,2 , ,T , L  R,1, R,2 , , R, L The number of observation K The proposed beamforming in this paper is based on dividing channel matrix into L  L spatial bins The directions of the transmit beams should focus on the centres of the bins on the first column of the bin matrix, illustrated in figure Example, the resulting transmit angles of 45 o ,315 o (using beams for transmitting) are known from the maximal power angles of the beams for the model in figure (using the first column of the channel matrix hm,1 in (1) for forming the beam vectors) The weight vectors w l that represent the invariant dimensions are included in matrix W :   2   j sin  T ,l l sT   e   W  w1 , w , , w L , w l      2  sin  T ,l l sT ( M 1)   j e   (2) Figure Dividing the transmission space into L  L bins Tạp chí Nghiên cứu KH&CN quân sự, Số 52, 12 - 2017 105 Kỹ thuật điều khiển & Điện tử Beam pattern 90 Beam pattern 120 90 60 120 1.5 60 1.5 150 30 150 0.5 array factor array factor 180 210 330 240 30 0.5 180 210 300 330 240 300 270 270 transmit angle transmit angle Figure Beams observed by the receiver using the virtual model III DIAGONAL MATRIX FOR COMPARISON OF CHANNEL CAPACITY The paper [7] describes some models for the MIMO transmission space, however, it can not state fully geometric characteristics of the real transmission channel The channel matrix H k defined in [1] can be used in the computation of the channel capacity in the validation of the use of the invariant dimensions From [1], this matrix, containing the k diagonals of the virtual channel matrix H v , given by a division of the transmission space into Q  P bins, is expressed as: Hk  ~ P ~   P, p  k        ~  ~  hv (q, p )a R  R, q aTH  T , p            (3) ~  ~ p   P q  max  P, p  k     where, hv q, p  is the fading factor for the transmit and receive bins, positioned beams at point p at the transmitter and point q at the receiver ~  ~  aT   T , p  and a R   R ,q  represent the array responses of the transmit and receive     antennas: ~  ~   j   T,p  aT  T , p   e    M    ~  ~    j 2  R, q   a R  R, q  e    N    ~   j 2  T , p ( M 1)  e   T   j 2  R,q ( N 1)  e   T (4) ~ ~ ~     and  R, q  q / Q ,  T , p  p / P where  Q  q  Q, P  p  P 106 Tran Hoai Trung, “Evaluation of method using… MIMO diagonal channel matrix.” Nghiên cứu khoa học công nghệ  P 1 where P is the number of columns in the virtual matrix H v P  Q 1 where Q is the number of rows of channel matrix H v Q  k  P  is the number of diagonals above and below the main diagonal of H v H v can be computed from the realistic channel matrix and is represented as: ~H ~ H v  Α R H AT (5) where ~  ~ ~ ~    ~      A R  a R  R, Q , a R  R, Q 1 , , a R  R,Q 1 , a R  R,Q                  ~  ~ ~ ~    ~      AT  aT  T , P , aT  T , P 1 , , aT  R, P 1 , aT  R, P                  (6) For clarity in comparison, the paper uses P  Q  L that is considered for the QxP virtual channel matrix H v since the transmit and the receive angles in the realistic environment are divided into the L equal ranges IV COMPARISON WITH THE CASE OF THE STRONGEST BEAM TRANSMITTER OR NO CSI The increase in channel capacity is a general issue of concern for MIMO model The transmit beam directions are got easier by the receiver because they are fixed for a enough long period, even the receiver may move causing the multipath phenomenon These beams are called invariant dimensions The advantage of using invariant dimensions is that its spatial characteristics that will be not changed when other parameter change so quickly in a short term fading channel as the signal phases, delays, etc The receiver can get the information of these transmit dimensions without instantaneous update in a short time The update for a short time is difficult for current receiving algorithms The update of these invariant transmit dimensions happens when the receiver moves in an enough long distance At this time, the transmitter decides to choose what L is The solution to increase this capacity could be using invariant productive dimensions can be rewritten from (2) as:   2   j sin  T ,l l sT   e    W  w1 , w , , w L , w l     2  sin  T ,l l sT ( M 1)   j e   Tạp chí Nghiên cứu KH&CN quân sự, Số 52, 12 - 2017 (7) 107 Kỹ thuật điều khiển & Điện tử ~ s ( L  1) ( L  1) where  T , p l   T sin T , l l  with l     2L 2L Therefore, when discovering the invariant dimensions, it is also important to consider the validity of the use of these dimensions with respect to the maximum capacity in case no CSI (Channel State Information) or the strongest beam For clarity in the reading of this validity, the channel capacity using the diagonal channel matrix H k for the use of the invariant dimensions is presented here only, while the channel capacity for the optimum beam method in no CSI or the strongest beam is presented later The channel capacity for the use of the invariant dimensions, according the extended Shannon channel capacity formula for MIMO, is expressed as: Cin  log det(Ι   W H H H H k W  (8) k   where H k is presented in equation (3) where k is chosen to be L  for the maximal scattering environment [1]; Wn  W / norm( W ) ;   PT / PN where PT is the transmit power and PN is the noise power; Ι is the M x M identity matrix For no CSI, the channel capacity can be expressed as [2]:    2 H C no  log det I  H H k   M k      (9) For the strongest beam, the channel capacity can be expressed as [5]: Cs  log det1   2w sH H kH H k ws     (10) L  L  where w s   w l / norm  w l  in which w l is expressed in (7)   l 1  l 1  Figure The channel capacity in the optimum beam method in the case of no CSI, the strongest beam for L = 21 and the use of invariant dimensions with size of the virtual channel matrix is L = 13, 15, 17, 19, 21 108 Tran Hoai Trung, “Evaluation of method using… MIMO diagonal channel matrix.” Nghiên cứu khoa học công nghệ Figure illustrates the channel capacity in the optimum beam method with no CSI or the strongest beam where H has a size of M x N (determined by H v ) and the use of the invariant dimensions where L  13,15,17,19, 21 , M  N  21 and H v is a L x L virtual channel matrix where all entries are It is found that the channel capacity in the case of the optimum beam method with no CSI or the strongest beam is smaller than the case of the use of the invariant dimensions In other case of larger L, the channel capacity is better than using the strongest beam or optimum solution in no CSI However, in case of L smaller, the channel capacity is not better than case of strongest beam, example L = 7,9 but better than optimum solution with no CSI The channel capacity is even lower than the case with no CSI when L = The figure shows this case Figure The channel capacity in the optimum beam method in the case of no CSI, the strongest beam for L = 21 and the use of invariant dimensions with size of the virtual channel matrix is L = 3, 7, Conclusion, choosing number of bins L is very important in order to make the capacity better than using the strongest beam or optimum solution with no CSI V CONCLUSION The author uses the invariant dimensions of beam based on the virtual channel matrix H , H k , that is described in [1] These dimensions are still good when it helps to increase the capacity of channel comparing with no CSI or the strongest beam at the transmitter with an enough large L REFERENCES [1] A M Sayeed, "Deconstructing Multiantenna Fading Channels," IEEE Transactions on Signal Processing , vol 10, no 50, 2002 [2] A Goldsmith, S.A Jafar, N Jindal and S Vishwanath, "Capacity limits of MIMO channels," IEEE Journal on Selected Areas in Communications, vol 21, issue.5, pp.684 - 702, 2003 [3] I E Telatar, "Capacity of multi-antenna Gaussian channels," European Transactions on Telecommunications, vol 10, no 6, pp 585–596, 1999 [4] G J Foschini and M J Gans, " On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Communications: Kluwer Academic Press, no 6, pp.311- 335, 1998 Tạp chí Nghiên cứu KH&CN quân sự, Số 52, 12 - 2017 109 Kỹ thuật điều khiển & Điện tử [5] S A Jafar, A Goldsmith, "On optimality of beamforming for Multiple Antenna Systems with Imperfect Feedback," IEEE International Symposium, 2001 [6] G Jongren, M Skoglund and B Ottersten, "Combining beamforming and orthogonal space-time block coding," IEEE Transactions on Information Theory, vol.48, issue 3, pp.611-627, 2002 [7] Kan Zheng, Suling Ou, and Xuefeng Yin, "Massive MIMO Channel Models: A Survey", International Journal of Antennas and Propagation, Hindawi Publishing Corporation, 2014 TÓM TẮT ĐÁNH GIÁ VIỆC SỬ DỤNG CÁC HƯỚNG BỨC XẠ THAY ĐỔI CHẬM HỮU ÍCH TRONG MƠI TRƯỜNG MA TRẬN KÊNH ĐƯỜNG CHÉO MIMO THỰC TẾ Hiện nay, việc sử dụng mơ hình kênh ảo (chia khơng gian thành kích thước cố định) đặc trưng cho môi trường truyền thực tế nghiên cứu Tác giả áp dụng hướng phát hữu ích thay đổi chậm, hay đường vật lý đến chướng ngại vật không đổi hay di chuyển chậm trung tâm khơng gian với mơ hình kênh ảo Kết thu hướng phát hữu ích làm tăng dung lượng kênh truyền so với trường hợp sử dụng xạ lớn khơng có CSI máy phát với số hướng đủ lớn Từ khóa: Thơng tin vơ tuyến, Ma trận kênh đường chéo MIMO, Hướng phát thay đổi chậm, Thông tin trạng thái kênh (CSI) Nhận ngày 21 tháng năm 2017 Hoàn thiện ngày 30 tháng 11 năm 2017 Chấp nhận đăng ngày 20 tháng 12 năm 2017 Author affiliation: University of Transport and Communications * Email: hoaitrunggt@yahoo.com 110 Tran Hoai Trung, “Evaluation of method using… MIMO diagonal channel matrix.” ... receiver may move causing the multipath phenomenon These beams are called invariant dimensions The advantage of using invariant dimensions is that its spatial characteristics that will be not changed... number of rows of channel matrix H v Q  k  P  is the number of diagonals above and below the main diagonal of H v H v can be computed from the realistic channel matrix and is represented as:... (Channel State Information) or the strongest beam For clarity in the reading of this validity, the channel capacity using the diagonal channel matrix H k for the use of the invariant dimensions is