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In this paper, a general channel model including the correlation effect at the transceiver and the I-CSI is proposed. Performance of the existing HRSM detectors is investigated under this model. Besides, in order to obtain comprehensive understanding about the HRSM system, the system capacity under two cases: P-CSI and I-CSI is studied.
Research EFFECT OF IMPERFECT CHANNEL ESTIMATION ON HIGH- RATE SPATIAL MODULATION DETECTORS Nguyen Tien Dong*, Le Thi Thanh Huyen, Tran Xuan Nam Abstract:Recently, anew Spatial Modulation (SM) system, called high rate spatial modulation (HRSM), was proposed to achieve spectral efficiency linearly increased with the number of transmit antennas In this system, the HRSM receiver is assumed to exactly know the channel state information (CSI) However, in practice, this assumption is not realistic due to channel estimation error Furthermore, the spatial correlation between antennas at the transceiver affects on the CSI As a result, the HRSM performance deteriorates due to the imperfect CSI (I-CSI) and the correlation effect In this paper, a general channel model including the correlation effect at the transceiver and the I-CSI is proposed Performance of the existing HRSM detectors is investigated under this model Besides, in order to obtain comprehensive understanding about the HRSM system, the system capacity under two cases: P-CSI and I-CSI is studied Keywords: Spatial modulation, Detector, Channel state information, Correlation effect INTRODUCTION Recently, a promising multi-input multi-output (MIMO) scheme, called spatial modulation (SM) has been proposed [1] In this model, antenna indices are exploited as an additional source to convey information bits Since only one transmit antenna is activeat a time, the SM scheme totally avoids the Interchannel Interference (ICI) effect.The SM transmitter can also facilitate the antenna synchronization requirements as well as require less radio frequency (RF) chains compared with the conventional MIMO systems However, the SM spectral efficiency is limited to log nT where nT is the number of transmit antennas Therefore, many researchers have focused on methods to increase the SM spectral efficiency In [2], by activating more than one transmit antenna at a time, a generalized SM (GSM) was proposed The spectral efficiency of this model is higher than that of the SM However, this technique requires multiple RF chains Furthermore, by applying the Spatial Constellation (SC) concept and Almouti code matrix, Le et al proposed a Spatially Modulated Orthogonal Space Time Block Coding (SM-OSTBC) scheme [3] This scheme obtains the maximum spectral efficiency of nT log M bpcu when the number of transmit antennas is equal the number of active antennas, i.e nT nA where M is the signal constellation level Recently, the so-called High Rate Spatial Modulation (HRSM) scheme which has the spectral efficiency linearly increased with the number of transmit antennas, i.e, 2( nT 1) log M ,was proposed in [4] However, in this model the CSI was assumed exactly known or perfectly estimated at the receiver Related to the imperfect channel problem, in [5] Renzo et al studied the SM-MIMO system under generalized fading channels Furthermore, the SM scheme is surveyed in the presence of channel estimation error in [6] Mesleh et al studied the SM systemperformance under the Gaussian imperfect channel estimation [7] Besides, the SM system was analyzed over correlated fading channels in [8] Recently, the authors of [9] compared the performance of the SM detectors under channel impairments where only correlation effectwas considered between neighboring antennas at the receiver Journal of Military Science and Technology, Special Issue, No 48A, - 2017 31 Electronics and Automation In this paper, basing on the exponential correlation model [10], a comprehensive model including the correlation effect at the transceiver and the I-CSI is proposed We then use this model to investigate the performance of existing HRSM detectors including MVBLAST (Modified Vertical Bell Laboratories Space-Time), MSQRD (Modified Sorted QR Decomposition), ISQRD (Improved SQRD) [11] and Maximum likelihood (ML) detector [4] in flat Rayleigh fading channel under perfect CSI (P-CSI) Furthermore, the HRSM system capacity in I-CSI and P-CSI is studied HRSM System model l bits Data (l+m) bits SC codewords 1 2 S S/P n1 + n2 + X m bits x M-QAM/PSK nR nT Data ML detector nnR + Figure High rate spatial modulation scheme Fig illustrates a general model of the HRSM scheme with nR receive and nT transmit antennas At each transmission instant, a block ( l m ) of data bits is separated in two groups of l bits and m bits where the l bits are used to select an arbitrary SC matrix s from the spatial constellation set S and the latter is modulated to generate a modulated symbol x A set of SC matrices is designed by fixing the first entry of s by and randomly allocating the others from a set 1, j where j 1 Generally, with nT transmit antennas, the total number of the SC matrices in S is K nT 1 Therefore, the number of information bits carried by the SC matrices increase linearly with the number of transmit antennas, l log K nT 1 bit per channel use (bpcu) Finally, the HRSM codeword c is the product of the chosen SC matrix s and the modulated symbol x, i.e c sx At the receiver, the nR receive signal vector y is given by y nT Es Hc n nT Es Hsx n (1) where H is an nR nT channel matrix and nis noise vector H and nare assumed to have independent and identically distributed (i.i.d.) complex Gaussian random variables with zero mean and unit variance Es is the average symbol energy of x and is the average Signal-to-Noise Ratio (SNR) at each receive antenna HRSM DETECTORS An optimal detector [4] and suboptimal detectors [11] in the HRSM scheme are briefly introduced in this section A ML Detector 32 N.T.Dong, L.T.T.Huyen, Tr.X.Nam, “Effect of imperfect channel estimation ” Research Corresponding to SC codeword s k S , k 1, , K , an nR equivalent channel matrix h Hs is obtained Then, the pair signals sˆ, x is recovered as follows k k sˆ k , xˆk nT Es h k F 2 nT Es y H h k x (2) Detailed detection algorithm is summarized in Table I Table I:An optimal ML decoding algorithm of HR-SM scheme Compute the equivalent channel matrix h k Hs k s k S For each matrix h and for modulated symbol x compute the Euclidean x k distances based on (2), dkm dk xm m 1, , M Find d kmin among M values of d km and define xˆk Find index kˆ corresponding to the minimum distance d among K value of d kmin The estimated SC codeword and modulated symbol is given sˆ skˆ , x xkˆ Data bits are recovered from sˆ, xˆ B MVBLAST Detector Considering the HRSM as a MIMO system, the MMSE (Minimum Mean Square Error) filter matrix is given by G MMSE Where: H nT Es H HH H I H n Es R 1 (3) H TheMVBLAST algorithm is summarized in Table II Table II.MVBLAST detection algorithm 1 H Compute P H H I nT Es Find the strongest signal index based on k arg P j , j where P j , j is the j -th j diagonal entry of P , and reorder the entries of c so that the smallest diagonal entry is the first one Compute the MMSE filter matrix G MMSE and form the LMS estimate c k g MMSE, k y where g MMSE ,k is the kth row of G MMSE Obtain cˆ k by slicing c k by deleting its Cancel effect of cˆ k from y and re-organize the channel matrix H kth column Repeat Steps to until all element of vector c are detected Re-arrange the vector c following the transmitted order cˆ Recover the pair signals xˆ cˆ1 and sˆ xˆ C MSQRD Detector Journal of Military Science and Technology, Special Issue, No 48A, - 2017 33 Electronics and Automation To overcome the matrix inversion step in the MVBLAST, we apply MMSE-SQRD [12] to recover the received signal An nT nR nT extended channel matrix D and a received vector z is defined as H y (4) D ,z I nT 0 Es Table III.MSQRD detection algorithm Decompose D by MMSE-SQRD [12]toget Q,R and the permutation vector p Compute v Q H z Detection and cancellation: for nT : 1:1 if k nT obtain cˆk by slicing vk , k rk , k elsefor l k 1: nT vk vk rk ,l cˆk end Obtain cˆk by slicing vk , k rk , k end end Re-arrange the recovered vector cˆ by the permutation vector p cˆ The pair of signals is given xˆ cˆ1 , sˆ xˆ D ISQRD Detector The equivalent of the system is rewritten as where t y h x , nR nT 1 H h t Hc n (5) h h with h , k 1, , n being the k3 nT k T and c is the n 1 1 new transmitted thcolumn of the equivalent channel matrix H T codeword consisting the last nT 1 entries of c The remaining vector c is applied in MSQRD The ISQRD algorithm is summarized in Table IV Table IV.ISQRD detection algorithm Decompose H by MMSE-SQRD [12] to getQ, R andthe permutation vector p Detection and cancellation: for m 1: M t m Compute t m y h xm and v Q H 0 for k nT 1: 1:1 if k n obtain cˆ by slicing v r m,k T k ,k k ,k else for l k 1: nT v v r cˆ k k k ,l m ,l end 34 N.T.Dong, L.T.T.Huyen, Tr.X.Nam, “Effect of imperfect channel estimation ” Research obtain cˆm , k by slicing vk , k rk , k end end Compute d m t m Hcˆm ,p End Find mˆ : mˆ arg d m m Find index kˆ corresponding to the minimum distance d among K values of d kmin The estimated SC codeword and modulated symbol are given by: sˆ skˆ , x xkˆ The pair of signals is given xˆ xmˆ , sˆ xˆ xˆ T cˆmˆ ,p IMPERFECT CHANNEL MODEL In this section, we introduce a general imperfect channel model including the correlation effect (CE) and the channel estimation error (CEE) A Channel estimation error In [9], a measurement metric is proposed to denote the estimation error value, and P-CSI is i.e., The HRSM channel matrix is given by H H 1 (6) Where: is a complex Gaussian variable B Correlation effect Based onexponential correlation model [10] and Kronecker model [13], a comprehensive correlation model is proposed as H R T H R TR (7) j i r , i j ri , j * , r 1 rji , i j (8) Each element of R is given by: where r is the complex correlation coefficient of the neighboring branches Generally, a comprehensive HRSM channel matrix for both effects are given by (9) H R T H R TR 1 SIMULATION RESULTS In this section, the performance of the four HRSM detectors is compapred in I-CSI case where the HRSM is equipped with transmit and receive antennas, 4-QAM is used for modulation technique The channel is assumed to be Rayleigh fading and varies after each transmit data block Journal of Military Science and Technology, Special Issue, No 48A, - 2017 35 Electronics and Automation 10 -1 10 -2 BER 10 -3 10 -4 10 MSQRD,=0.7 MSQRD,=0.85 MVBLAST,=0.7 MVBLAST,=0.85 ISQRD,=0.7 ISQRD,=0.85 ML,=0.7 ML,=0.85 12 SNR (dB) 15 18 21 24 Figure Performance comparison of the HRSM detectors under I-CSI Figure compares the performance of various HRSM detectors under the I-CSI with two estimation error rates: 0.85 and 0.7 Simulation results show that all algorithms robust with the channel estimation error (CEE) In these outcomes, the MSQRD detector is affected by estimation error more heavily than the others Although the ISQRD detector achieves lower performance than the ML at the high SNR region, the ISQRD detector is still a potential candidate to substitute the ML in practice 10 -1 10 -2 BER 10 -3 10 -4 10 -5 10 MSQRD,r=0.3,=0.8 MBLAST,r=0.3,=0.8 ISQRD,r=0.3,=0.8 ML,r=0.3,=0.8 12 SNR (dB) 15 18 21 24 Figure HRSM detector preformances under proposed model Figure shows the HRSM detectors’ performance under the proposed model with correlation factor r 0.3 and channel error factor 0.8 It is seen that all detectors perform relatively well under correlation effect (CE) and CEE Specifially, the ISQRD surpasses the ML It can be explained by the fact that due to CE and CEE the ML 36 N.T.Dong, L.T.T.Huyen, Tr.X.Nam, “Effect of imperfect channel estimation ” Research incorrectly indentifies the transmited SC codeword while the ISQRD first chooses the best symbol to detect As a result, the ISQRD removes the chain detection error effect In [14], the SM system capacity is given by CSM m 1 pe log pe 1 pe log 1 pe (10) Where: m is the number of transmit bits in a transmission period and pe is the HRSM system probability error, pe 1 pS 1 px where pS and px are the SC codeword probability error and the modulated signal probability error, respectively Normalized Capacity (bits/s/Hz) 0 12 SNRdB HRSM(4,4,4),4QAM SM-OSTBC(4,4,4),64QAM STBC-SM(4,4,2),64QAM SM(4,4,1),64QAM 15 18 21 24 Figure Capacity comparison of HRSM, SM-OSTBC, STBC-SM, and SM at bpcu under P-CSI Normalized Capacity (bits/s/Hz) 0 12 SNRdB HRSM(4,4,4),=0.7 SM-OSTBC(4,4,4),=0.7 STBC-SM(4,4,2),=0.7 SM(4,4,1),=0.7 15 18 21 24 Figure Capacity comparison of HRSM, SM-OSTBC, STBC-SM, and SM at bpcu under I-CSI, 0.7 Journal of Military Science and Technology, Special Issue, No 48A, - 2017 37 Electronics and Automation The HRSM capacity is compared with the SM [1], the STBC-SM [14], and the SMOSTBC [3] ones under two cases: P-CSI and I-CSI Each system is equipped with transmit, receive antennas, and suitable active antennas and chooses an appropriate modulation technique at the same spectral efficiency bits per channel use (bpcu) Figure shows that at the low range of capacity, the HR-SM is less than the STBC-SM, but it is better than the others.At the high range of capacity, the HR-SM surpasses the others Particularly, at bits per second per Hz (bits/s/Hz), the HR-SM obtains at approximately 11 dB Signal-to-Noise (SNR) gain while the STBC-SM and the SM-OSTBC works at 13 dB and the SM is 17 dB Figure compares the capacity of the HR-SM, the STBC-SM, SM-OSTBC, and the SM under I-CSI with the estimation error rate 0.7 All systems’ performances moves SNRdB gain in the left compared with these systems performance under P-CSI CONCLUSION In this paper, a general channel model includingboth channel estimation error and correlation effect is proposed Performance of variousexisting HRSM detectors was investigated under the proposed model Simulation results show that all HRSM detectors are robust in this case Specifically, the ISQRD detector can be a potential candidate in the HRSM system Finally, it is also shown that the HRSM system outperforms the existing SM based MIMO ones in two cases: P-CSI and I-CSI REFERENCES [1] R Mesleh, H Haas, A C Wook, and Y Sangboh, "Spatial Modulation - A New Low Complexity Spectral Efficiency Enhancing Technique,"in First International Conference on Communications and Networking, China, (2006), pp 1-5 [2] A Younis, N Serafimovski, R Mesleh, and H Haas, " Generalised spatial modulation,"in Forty Fourth ASILOMAR Conference on Signals, Systems and Computers (ASILOMAR), (2010), pp 1498-1502 [3] M T Le, V D Ngo, H A Mai, X N Tran, and M Di Renzo, " Spatially Modulated Orthogonal Space-Time Block Codes with Non-Vanishing Determinants,"IEEE Transactions on Communications,Vol 62, (2014), pp 85-99 [4] T P Nguyen, M T Le, V D Ngo, X N Tran, and H W Choi, " Spatial Modulation for High-Rate Transmission Systems,"in Vehicular Technology Conference, (2014), pp 1-5 [5] M Di Renzo and H Haas, "Bit Error Probability of SM-MIMO Over Generalized Fading Channels,"IEEE Transactions on Vehicular Technology,vol 61, (2012), pp 1124-1144 [6] E Basar, U Aygolu, E Panayirci, and H V Poor, “Performance of Spatial Modulation in the Presence of Channel Estimation Errors,”IEEE Communication Letters, Vol 16, (2012), pp 176-179 [7] R Mesleh and S S Ikki, “On the Effect of Gaussian Imperfect Channel Estimations on the Performance of Space Modulation Techniques,”in Vehicular Technology Conference, (2012), pp 1-5 [8] M Koca and H Sari, "Performance Analysis of Spatial Modulation over Correlated Fading Channels," in Vehicular Technology Conference, (2012), pp 1-5 [9] E Soujeri and G Kaddoum, "Performance Comparison of Spatial Modulation Detectors under Channel Impairments," in IEEE International Conference on Ubiquitous Wireless Broadband (ICUWB), (2015), pp 1-5 38 N.T.Dong, L.T.T.Huyen, Tr.X.Nam, “Effect of imperfect channel estimation ” Research [10].S L Loyka, "Channel capacity of MIMO architecture using the exponential correlation matrix," IEEE Communication Letters, vol 5, 2001, pp 369-371 [11].T D Nguyen, X N Tran, T M Do, V D Ngo, and M T Le, "Low-complexity detectors for High-rate Spatial Modulation," in International Conference on Advanced Technologies for Communications (ATC),(2014), pp 652-656 [12].D Wubben, R Bohnke, V.Kuhn, D Kammeyer, "MMSE extension of VBLAST based on sorted QR decomposition," in Proceeding Vehicular Technology Conference, (2003), pp 508-512 [13].A M Tulino, A Lozano, and S Verdu, "Impact of antenna correlation on the capacity of multiantenna channels," IEEE Transaction on Information Theory, Vol 51, (2005), pp 2491-2509 [14].F Prisecaru, Mutual information and capacity of spatial modulation systems, Jacobs University, Bremen, (2007) [15].E Basar, U Aygolu, E Panayirci, and H V Poor, "Space-time block coding for spatial modulation," in 21st International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), (2010), pp 803-808 TĨM TẮT PHẨM CHẤT CÁC BỘ TÁCH TÍN HIỆU ĐIỀU CHẾ KHÔNG GIAN TỐC ĐỘ CAO TRONG ĐIỀU KHIỂN KÊNH TRUYỀN KHƠNG HỒN HẢO Hệ thống điều chế không gian tốc độ cao (HRSM) đề xuất với ưu điểm trội hiệu suất sử dụng phổ tần Tuy nhiên, việc đánh giá phẩm chất HRSM thực điều kiện kênh truyền ước lượng hoàn hảo Trong báo chúng tơi đề xuất mơ hình kênh truyền khơng hoàn hảo tổng quát bao gồm lỗi ước lượng kênh truyền hiệu ứng tương quan ăng-ten Các tách sóng đề xuất hệ thống HRSM khảo sát đánh giá sử dụng mơ hình Ngồi ra, dung lượng hệ thống HRSM phân tích trường hợp kênh truyền hồn hảo (P-ISI) kênh truyền khơng hồn hảo (I-ISI) Từ khóa: Điều chế khơng gian, Bộ tách sóng, Thơng tin trạng thái kênh truyền, Hiệu ứng tương quan Received date, 24thFebruary 2017 Revised manuscript, 4th April 2017 Published on 26th April 2017 Author affiliations: Military Technical Academy; *Corresponding author: qttdong@gmail.com Journal of Military Science and Technology, Special Issue, No 48A, - 2017 39 ... Modulation in the Presence of Channel Estimation Errors,”IEEE Communication Letters, Vol 16, (2012), pp 176-179 [7] R Mesleh and S S Ikki, On the Effect of Gaussian Imperfect Channel Estimations on. .. IMPERFECT CHANNEL MODEL In this section, we introduce a general imperfect channel model including the correlation effect (CE) and the channel estimation error (CEE) A Channel estimation error... Technology Conference, (2012), pp 1-5 [9] E Soujeri and G Kaddoum, "Performance Comparison of Spatial Modulation Detectors under Channel Impairments," in IEEE International Conference on Ubiquitous