Tài liệu Multi dimensional signal processing in broadband multiuser mobile communications

MINISTRY OF EDUCATION AND TRAINING THE UNIVERSITY OF DANANG NGUYEN DUY NHAT VIEN MULTI-DIMENSIONAL SIGNAL PROCESSING IN BROADBAND MULTIUSER MOBILE COMMUNICATIONS Specialty : Computer Science Code : 62.48.01.01 PHD. THESIS IN BRIEF DANANG - 2016 This thesis has been finished at: THE UNIVERSITY OF DANANG Supervisor: 1. Associate Prof., Dr. Tang Tan Chien, 2. Associate Prof., Dr. Nguyen Le Hung Examiner 1: ............................................................................... Examiner 2: ............................................................................... Examiner 3: ............................................................................... The thesis submitted for a defense in front of the Thesis Assessment Committee of The Danang University At Room No: .................... At ...................... 2016 The thesis is available at: 1. The National Library. 2. The Information Resources Center, The University of Danang. -1- Introduction In recent years, the next generation of wireless technologies are facing the long term challenge to properly address the resource system limitations with the growing demand on services, high data rate, fast mobility and wide coverage. There is a traceoff between data rate and movement speed of users. For high speed systems, the data-rate of users is limited due to the complicated error detection and correction schemes which are required to fight against the fast fading and the transmission impairments. Therefore, this thesis entitled Multi-dimensional signal processing in broadband multiuser mobile communications aims to improve the data rate and the movement speed of the users for high-bandwidth applications in the next generation wireless networks. Objectives of the thesis - Propose a channel estimation algorithm which efficiently works for high-speed movement users in full-duplex communication systems. - Propose algorithms for interference management to simultaneously improve the sum-rate and the coverage for multi-user wireless communication systems. Subjects of the thesis - Signal-to-interference ratio (SIR) analysis for orthogonal frequency-division multiplexing (OFDM) transmission in the presence of carrier frequency offset, phase noise and doubly selective fading. - Fast fading channel estimation in full-duplex MIMO-OFDM systems. - Pre- and post-coding matrix design for management interference and capacity optimization. Scopes of the thesis The effects of phase noise, carrier frequency, offset and fast fading; estimation techniques; pre/post-coding; power allocation techniques in the next generation of wireless communication systems. Methods of the thesis - Combined method between analysis and Monte-Carlo simulation based on computer. - Analytical method for modeling signals and systems, and resolving convex optimization problems under the constraints of realistic system conditions. - Monte-Carlo simulation method for analyzing the quality of the system using the proposed algorithms. Main system quality parameters include sum-rate, MSE, BER, SIR, and so on. Novelty of the thesis - The thesis has derived signal-to-interference ratio (SIR) formula for time-variant channels of OFDM transmission systems in the presence of carrier frequency offset and phase noise. - The thesis has developed channel estimation algorithms for MIMO-OFDM full- -2- duplex transmission systems. - The thesis has designed pre/post-coding matrices of multi-hop multi-user communications. - The dissertation has proposed algorithms for interference management for multicell broadcast system in the absence of perfect channel state information. - Structure of the thesis Chapter 1: Overview of wireless communication systems. In this chapter, the overview of wireless communication systems is presented, including important factors influencing the radio signal propagation. Motivation of the thesis is given after a comprehensive literature review on the fields. Chapter 2: Multi-dimensional signal processing in mobile communications. In this chapter, principles of multi-dimensional signal processing for mobile communications such as OFDM, MIMO, estimation techniques, full-duplex transmissions and so on are present. Theoretical SIR expressions for the time-variant channel are developed in the presence of phase noise and carrier frequency offset. An estimation algorithm which is useful for high mobility full-duplex communication systems is also proposed in this chapter. Chapter 3: Capacity improvement for the multi-user multi-hop mobile communication systems In this chapter, a method to enhance the capacity of multi-user multi-hop wireless communication systems is proposed by designing pre/post-coding matrices. Chapter 4: Interference management for multi-cell wireless networks. Issues of pre- and post-coding designs for multi-cell wireless networks are studied to propose algorithms for managing both inter-user interference (IUI) and inter-cell interference (ICI). The interference management is investigated under mean square error (MSE) criterion, especially in the absence of perfect channel state information (CSI). The simulated results show a simultaneous improvement of the sum-rate and the coverage for multi-cell multi-user transmissions. Conclusions and Outlook. -3- Chapter 1: Overview of wireless communication systems 1.1 Introduction 1.2 Evolution of Mobile Communications 1.3 Mobile commnucation system 1.4 Wireless channel 1.5 Literature review Recently, orthogonal frequency division multiplexing (OFDM) has been recognized as a promising solution to facilitate the explosive growth in broadband data traffic of wireless multimedia services [74]. However, the superior advantages of OFDM only exist under the condition of perfect synchronization and quasi-static fading channel [73]. In particular, synchronization impairments (e.g., CFO and PHN) give rise to inter-carrier interference (ICI) that would significantly degrade the performance of OFDM transmissions [24], [87]. In addition, the presence of high-speed moving subscribers (in 4G mobile networks) causes time-selective channel response that also leads to ICI in OFDM systems [47]. In the literature, most of existing studies consider one or two of these channel impairments in system analysis. In particular, the CFO effect on OFDM systems has been extensively studied in [24] while the investigation of phase noise has been addressed in [87]. Besides imperfect synchronization conditions, the effect of time-selective channels has been considered in [47], [63]. Combined time-selective fading and phase noise effects on OFDM systems have been analyzed in [100]. In addition, the effect of CFO and time-selective channels in SIR analysis has been well documented in [7], [103] while the impacts of CFO and phase noise have been investigated in [58]. The problem of channel estimation has been intensively studied in OFDM systems [74], [20]. In particular, numerous blind or pilot-aided channel estimation techniques have been proposed for various OFDM transmission models ranging from single-cell, singleuser, single-hop, single-antenna systems to multicell, multiuser, multihop, multi-antenna networks ... [88]. However, most of the existing channel estimation studies have considered half-duplex wireless systems where signal transmission and reception occupy two different time or frequency slots [74], [88]. Recently, full-duplex transmission has appeared as a promising candidate for the next generation of wireless communications [101]. Using the full-duplex principle, both signal transmission and reception can simultaneously use the same frequency band and thus increasing the system spectral efficiency up to two times [35]. However, using the full-duplex principle produces strong self-interference signals at receive antennas [35]. In full-duplex systems, self-interference cancellation and coherent signal detection require the use of channel state information (CSI). So far, the problem of CSI acquisition in full-duplex -4- systems has not received much attention in the literature. More recently, [52] and [53] has develop ML-based channel estimation algorithms for self-interference cancellation in fullduplex MIMO-OFDM systems over quasi-static fading channels (i.e., under a block-fading channel assumption). Multiple-input multiple-output (MIMO) communication techniques have been an important area of focus for next-generation wireless systems because of their potential for high capacity, increased diversity, and interference suppression [18]. Recent information theoretic studies have proved that dirty paper coding (DPC) achieves the capacity region of the MIMO [85]. The power allocation technique to achieve optimal capacity is proposed in [31], [39]. Precoding is a generalization of beamforming to support multi-stream transmission in MIMO wireless communication systems. Block diagonalization (BD) precoding has proposed in [72] and singular value decomposition (SVD) precoding has proposed [50]. One-way relaying has been intensively studied in wireless communications to extend cell coverage area and to gain spatial diversity [42]. However, the benefits of using one-way relay transmission come at the cost of reduced spectrum efficiency. In particular, one-way relaying needs four time slots for one round of information exchange between two source nodes in a multihop network [61], [55]. To avoid the spectrum efficiency loss of one-way relaying, two-way relay communications has been proposed for reducing the number of time slots from four to two in the information exchange round [45], [99]. To further enhance the, space division multiple access (SDMA) transmission has been leveraged in two-way relay network [32, 98]. As a result, the SDMA-based multiuser transmission can significantly boost the capacity of the two-way relay network. [59]. In mobile communications systems, universal frequency-reuse (multicell) transmission has been extensively employed to enhance system-wide spectral efficiency. However, the benefit of multicell transmissions comes at the price of inter-cell interference (ICI) in the system. Therefore, universal frequency-reuse transmission would be employed at cells with sufficiently large inter-cell distances (ICD). To facilitate frequency-reuse transmissions for neighboring cells (having short ICD), appropriate precoding techniques can be deployed at base stations (BS) to eliminate ICI [84], [70], [2], [95]. 1.6 Motivation The content of the thesis will focus on the following issues: - SIR analysis for OFDM transmission in the presence of CFO, phase noise and doubly selective fading. - Doubly selective channel estimation in full-duplex MIMO-OFDM transmission - Precoding design and power allocation in two-way relay networks - Inter-cell interference management in multiuser transmissions. 1.7 Conclution -5- Chapter 2: 2.1 Multi-dimensional signal processing in mobile communications Introduction In this chapter, we analyzed the effect of CFO, phase noise and time-selective chan- nel responses in deriving an exact expression of SIR and proposed the maximum-likelihood estimation in OFDM-MIMO full-duplex transmissions. 2.2 Wireless chanel model and multi-dimension signal processing techniques 2.2.1 Wireless chanel model 2.2.2 Orthogonal frequency-division multiplexing (OFDM) 2.2.3 Multiple-antenna technique 2.2.4 Estimation technique 2.2.5 Full-duplex tranmission 2.3 Formulate the SIR expression for OFMDM transmission in presend of in the presence of pCFO, PHN and Doppler shift 2.3.1 Signal model The transmitted baseband samples in an OFDM symbol can be written as xn = √1 N NP −1 k=0 Xk exp j 2πkn , n ∈ {0, ..., N − 1}. In the presence of doubly selective fading, N
carrier frequency offset and phase noise, the complex baseband received signal in an OFDM symbol can be written by [100], [7], [58]: yn = e j2πεn N jφn e L−1 X xn−l hl,n + zn , (2.1) l=0 where, ε is CFO, φn is PHN, and zn is AWGN. After performing FFT at OFDM receiver, the kth received subcarrier can be expressed by Yk = Gk,k Xk + N −1 X Gk,k0 Xk0 + Zk , (2.2) k0 =0 0 k 6=k where k = 0, .., N − 1, Zk is the noise sample in the frequency domain. Gk,k0 can be calculated is Gk,k0 L−1 N −1 j2π(nk0 −nk−lk0 +nε) 1 XX N = hl,n e ejφn . N (2.3) l=0 n=0 2.3.2 SIR formulation Based on E (fd = vfc c0 , h hl,n h∗l,n+m i = J0 (2πmfd Ts /N )σl2 , where, fd is Doppler frequency v is is the mobile speed, fc denotes the carrier frequency, c0 is the speed of   light), Ts is the OFDM symbol duration, σl2 ; l = 0, 1, ..., L − 1 is the power-delay-profile -60 (PDP) of the considered channel. L is the number of resolvable paths, E[ejφn e−jφn ] = 0 e−πβTs |n−n |/N and (N − |r|) are both even functions, and J0 (2πfd rTs /N ) is a normalized L−1 P PDP σl2 = 1, we have: l=0 2  E |Gk,k0 |  N −1  X 1 = 2 N +2 (N − r)J0 N r=1  2πfd rTs N   × cos 2πr∆ N  cos  2πrε  N sr − πβT N  e . (2.4) As a result, we can obtain the SIR expression:  N +2 SIR(fd Ts , ε, βTs ) = NP −1  N +2 NP −1 (N r=1 NP −1 s d Ts − πrβT N ) cos( 2πrε − r)J0 ( 2πrf N N )e (N − r) cos r=1 ∆=1
2πr∆ N  s d Ts − πrβT N ) cos( 2πrε J0 ( 2πrf N N )e  (2.5) 0.20 0.20 0.15 NDF C=7 0.10 C=7 0.05 C=9 0.00 0.20 0.15 0.10 C=12 PHN 0.05 C=16 0.00 -0.2 -0.1 0.0 CFO 0.10 0.20 Figure 2.1: SIR contour versus: Figure 2.2: SIR as a function of CFO, PHN for dif- PHN βTs , CFO ε and NDF fd Ts ferent speed values Fig. 2.1 illustrates the level surfaces of the SIR as a func- tion of CFO, PHN and NDF. one can find that PHN becomes the dominant factor in SIR values when CFO is smaller than 0.1 as shown in Fig. 2.1. Fig 2.2 show the two value surfaces of SIR versus CFO and PHN when NDF= 0.05 and NDF= 0.35. By using Fig. 2.2 and (2.5), one can determine allowable ranges of CFO, PHN level and mobile speeds to satisfy a target SIR. 2.3.3 Simulation and illustrative results To verify the validity of SIR analysis, numerical results of (2.5) versus PHN level βTs are shown in Fig. 2.3. SIR curves are provided under different CFO values. It is observed that the SIR decreases as synchronization impairments increases. In addition, Fig. 2.3 shows a good agreement between simulated and theoretical results (2.5). To illustrate the need of considering the joint effect of CFO, PHN and Doppler -740 28 Theoretical SIR (2.5),  = 0.001 Simulated SIR, =0.001 Theoretical SIR (2.5),  = 0.05 Simulated SIR, =0.05 Theoretical SIR (2.5),  = 0.01 Simulated SIR, =0.01 26 24 SIR (dB) SIR (dB) 22 a: b: c: d: e: 35 20 18 Theoretical SIR ignores PHN and CFO[63] Theoretical SIR ignores CFO[100] Theoretical SIR ignores PHN[7] Theoretical SIR (2.5) Simulated SIR 30 25 16 20 14 12 0.001 0.002 0.003 0.004 0.005 0.006 βTs (rad) 0.007 0.008 15 0.009 Figure 2.3: SIR versus PHN level βTs 0.01 0.02 0.03 0.04 0.05 fd Ts (rad) 0.06 0.07 0.08 0.09 Figure 2.4: SIR versus the NDF when ε = 0.05 and βTs = 0.005. under fd Ts = 0.03 (v = 100 km/h). spread in SIR analysis, Fig. 2.4 shows numerical results of the SIR expression (2.5) and other ones in the literature. In the considered system settings, one can find that ignoring only phase noise incurs the smallest gap between the theoretical and simulated SIR values. 2.4 2.4.1 Doubly selective channel estimation in full-duplex MIMO-OFDM transmission Signal model After CP removal, the nth received sample in the mth OFDM symbol at the rth receive antenna of node A can be given by (r) yn,m = Nt X L−1 X |t=1 (r,t) (t) hl,n,m xn−l,m + l=0 {z intended signal } Nt X L̇−1 X |t=1 (r,t) (t) (r) ḣl,n,m ẋn−l,m + zn,m , (2.6) |{z} l=0 {z self-interference signal } AWGN (r,t) where hl,n,m is the lth channel tap gains at the nth time instance in the mth OFDM symbol from the tth transmit antenna of node B to the rth receive antenna of node A. (r,t) Similarly, ḣl,n,m is the channel gain of a self-interference link at node A. zn,m is an additive white Gaussian noise (AWGN) sample with variance No . L and L̇ denote the numbers of resolvable paths of the desired channel (from node B to node A) and the self-interference channel (from node A to node A). Using BEMs, the channel impulse responses of desired and self-interference links can be approximately represented by (r,t) hl,n,m = Q X (r,t) (2.7) (r,t) (2.8) bn+Ng +mNs ,q cq,l , l ∈ {0, ..., L − 1}, q=1 (r,t) ḣl,n,m = Q̇ X ḃn+Ng +mNs ,q ċq,l , l ∈ {0, ..., L̇ − 1}, q=1 where Ns = N + Ng denotes the OFDM symbol length after CP insertion, m = 0, ..., M − 1 and M is the number of both data and pilot OFDM symbols in a burst. The node speed is assumed to be unchanged within a burst of M OFDM symbols. bn+Ng +mNs ,q stand for -8(r,t) the qth basis function values of the used BEM. cq,l (r,t) and ċq,l are the BEM coefficients used for the desired and self-interference channels, respectively. Q and Q̇ are the numbers of basis functions used for the desired and self-interference channels, respectively. The lth time-variant channel tap gains of desired and self-interference channels corresponding to the pilot OFDM symbol at the position mp in a burst can be expressed in a vector form as follows (r,t) (r,t) hl,mp = Bmp cl (r,t) (r,t) , ḣl,mp = Ḃmp ċl , (2.9) where hl,mp and ḣl,mp denote vectors of channel responses of desired and self-interference channels, respectively. For a group of P pilot OFDM symbols, a vector representation of all related timevariant channel tap gains can be expressed by h(r,t) = BL c(r,t) , ḣ(r,t) = ḂL ċ(r,t) , where h(r,u) = h (r,u) h0 iT , ..., h (r,u) hL−1 i T T ,  BL = IL ⊗ B, B = BTm1 , ..., BTmp , ..., BTmP (r,u) hl T h = (r,u) hl,m1 v c(r,u) = h iT (2.10) , ..., (r,u) c0 h iT (r,u) hl,mp , ..., h iT , ..., (r,u) cL−1 h (r,u) hl,mP i T T iT T , . With the BEM-based channel representation, the received signals (2.6) can be rewritten as (r) yn,m = Q Nt X L−1 X X (r,t) (t) bn+Ng +mNs ,q cq,l xn−l,m + Q̇ L̇−1 X Nt X X t=1 l=0 q=1 t=1 l=0 q=1 {z | (r,t) (t) ḃn+Ng +mNs ,q ċq,l ẋn−l,m | } intended signal {z } self-interference signal (r) + zn,m . (2.11) |{z} AWGN For the formulation of the Maximum Likelihood (ML) estimation approach, the received samples corresponding to P pilot OFDM symbols can be represented in a vector form as follows: " # h i c yP = S Ṡ + z = Ta + z, (2.12) ċ where yP T= h =  T , ..., yT ym mp 1 i , ymp =  S Ṡ , S = STm1 , ..., STmP (t) sl,mp = diag h (t) T h (t) T (t) h (t) (t) iT h , ..., h ċ(r) = c(1) h T  , ..., c(Nr ) ċ(r,1) T  T i T , ..., ċ(r,Nt ) , c(r) = T i T . (N ) ympr (1) i T T (N ) iT i , Ṡ = ṠTm1 , ..., ṠTmP (t) h  Ṡmp = ṡ0,mp Bmp , ..., ṡL−1,mp Bmp , ṡl,mp = diag c= h , Smp = Smp , ..., Smpt x0−l,mp , ...xN −1−l,mp i (1) ymp h c(r,1) T  (r) ymp , (t) = h (r) (r) y0,mp , ..., yN −1,mp h , i (t) , Smp = s0,mp Bmp , ..., sL−1,mp Bmp , T (t) , Ṡmp = () ẋ0−l,mp , ...ẋN −1−l,mp , ..., c(r,Nt ) (t) iT T iT , ċ = h h i ċ(1) (1) (N ) Ṡmp , ..., Ṡmpt iT  T  T i T , a = cT , ċT T , , ..., ċ(Nr ) , , -9- 2.4.2 ML-Based Channel Estimation In particular, the ML-based estimates of BEM coefficients can be determined as follows: â = (TH T)−1 yP . (2.13) As a result, the ML estimates of BEM coefficients can be determined by (r,t) ḃ b(r,t) = BLb h c(r,t) , h (r,t) = ḂLḃ c , (2.14)  (r,t) T h iT h iT h iT T (r,t)   (r,t) T (r,t) (r,t) (r,t) (r,t) ḃ ḃ ḃ b b b b , hl = hl,m1 , ..., h , where hl = hl,m1 , ..., hl,mp , ..., hl,mP l,mp h  (r,t) T T h iT i T T   T (r,t) (r,t) ḃ , ..., b c ,b c(r,t) = b c ..., h , B = I ⊗B, B = BT , ..., BT , ..., BT L l,mP L m1 mP mp 0 L−1 h i h (r,t) iT T (r,t) T (r,t) c0 , ..., ḃ cL−1 . and ḃ c = ḃ 2.4.3 Cramér Rao Lower Bound Derivation The Cramér Rao Lower Bound of the estimated parameter ω can be obtained by  CRLB(ω) = diag  2.4.4 " 2 Re No −jSH S SH S #!−1  . (2.15) 102 a: b: c: d: 101 MSE ca p ng knh 100 MSE ca p ng knh jSH S Simulation Results 101 10−1 10−2 a: b: c: d: 10−3 10−4 SH S Block-fading CE-BEM GCE-BEM DPS-BEM 100 10−1 10−2 10−3 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 SNR (dB) Block-fading CE-BEM GCE-BEM DPS-BEM 0 50 100 150 200 300 Tc (km/h) 400 500 Figure 2.5: MSE of estimated time-variant Figure 2.6: MSE of estimated BEM coefficients versus mobile speed (km/h). CIR versus SNR. Fig. 2.5 shows the MSE results of ML-based time-variant CIR estimates versus SNR. As observed, the DPS-BEM offer the best MSE performance as compared to GCEBEM and CE-BEM. In addition, curve a illustrates a very poor MSE performance of using block-fading assumption under the condition of time-varying channels. Fig. 2.6 shows the MSE performance of CIR estimation under the use of various BEMs. As can be seen, the performance degradation under the use of the block-fading - 10 - assumption becomes worse as moving node speeds increase. Over time-variant channels, the problem of outdated CIR estimates incurs the poor estimation performance when using block-fading assumption. This figure also shows that the DPS basis function can provide stable MSE performance with high robustness against fast-fading channels. 2.5 Conclusion In this chapter, the author has formulated a SIR expression for OFDM transmissions in the presence of phase noise, carrier frequency offset, and time-selective channels. The analytical results using (2.5) showed an exact agreement with the simulation results over wide ranges of mobile speeds, CFO, and PHN. In addition, the author has formulated a BEM-based channel estimation algorithm for full-duplex MIM-OFDM systems over doubly selective channels. The proposed BEMbased full-duplex doubly selective channel estimation algorithm offered a stable performance with high robustness against fast time-variation of fading channels. - 11 - Chapter 3: 3.1 Capacity improvement for the multi-user multi-hop mobile communication systems Introduction In this chapter, a method to enhance the capacity of multi-user multi-hop wireless communication systems is proposed by designing pre/post-coding matrices. 3.2 Transmission techniques in multi-user multi-hop mobile communication systems 3.2.1 Multi-user chanel 3.2.2 Space division multiple access (SDMA) 3.2.3 Multi-hop transmission 3.2.4 Linear precoding Zero-forcing precoding MMSE precoding 3.2.5 Multi-user MIMO system model 3.2.6 Block diagonal (BD) precoding for multi-user downlink wireless communication systems 3.3 3.3.1 Propose pre/post-coding techniques in MIMO two-way relay transmission Signal model Consider a wireless two-way relaying system that consists of a single base station (BS) having N0 antennas, a single amplify-and-forward (AF) relay with NR antennas and K mobile stations (MS) where the kth MS is equipped with Nk antennas (k = 1, . . . , K). The total number of antennas at the BS and the K MSs is NN = K P Nk . In this paper, k=0 wireless channels are assumed to be block-fading and frequency-flat. It is assumed that there is no direct link between the BS and MSs. 3.3.2 Independent two phase design Multiple Access Phase The received signal at the relay can be expressed by r = HPs + nr , (3.1) where, H = [H0 , H1 , . . . , HK ] matrix of channel response, P = diag{P0 , P1 , . . . , PK } T T T T is precoding matrix at BS and h K MSs, s = i [s0 , s1 , . . . , sK ] information bearing symbols (1) (K) from BS and K MSs, s0 = sB . . . sB , nr denotes AWGN vector having zero mean 2 and covariance matrix of E[nr nH r ] = σr INR . Multiple access interference (MAI) can be eliminated by choosing to [50]: P = VΦ, (3.2) - 12 - where, V = [V0 , V1 , . . . , VK ], columns of Vk ∈ CNk ×Nk , k = 0, . . . , K are right singular vectors of Hk . Φ = diag {Φ0 , Φ1 , . . . , ΦK }, Φk ∈ CNk ×Nk can be choosen arbitrary provided that satisfy the transmit power constraint. MAI can be eliminated by choosing to T [50]:  −1 H T = (HP) (HP) (HP)H . (3.3) Broadcast Phase Denote W as the precoding matrix used at the relay. As a result, the received signals at the BS and the MSk can be expressed as y = GW(s + Tnr ) + n (3.4) T , yT ]T , G = [G , . . . , G , G ], W = [W , . . . , W , W ] and where, y = [y1T , . . . , yK 1 0 1 0 K K BS n = [nT1 , . . . , nTK , nTBS ]T . Precoding at two-way relay The precoding matrix is used to mitigate the interference components. As a result, the precoding matrices W should satisfy the following zero-forcing condition: Gk Wk0 = 0 for all k 6= k0 and 1 ≤ k, k 0 ≤ 0. Define G̃k = h GT1 , GTk−1 , GTk+1 , , GTK , GT0 ··· , ··· where, k = 1, ..., K, 0. The transmit precoder matrix will thus have the following form: W = BΨ, h (3.5) i where B = Ṽ1n V̆1s . . . ṼKn V̆Ks Ṽ0n V̆0s , Ṽkn contains NR − rank(H̃k ) the last singular vectors of G̃k , V̆ks contains singular vectors of Gk Ṽkn non zero and Ψ = diag {Ψ1 , . . . , ΨK , Ψ0 } can be choosen arbitrary provided that satisfy the transmit power constraint. The Design of Precoding Matrices at the BS and the MSs In BC phase, desire signal can be recovered at BS anf K MSs by multiplexed with T̆ ∈ CLk ×Nk to eleminate MUI [50]: T̆ = (Gk Wk )H (Gk Wk )
−1 (Gk Wk )H . (3.6) Simulation Results Fig. 3.1 shows the sum-rate of the considered network under different scenarios. In this figure, the term WF is the abbreviation of water-filling. As observed, the BD-based precoding technique can increase the capacity of the network by allowing SDMA transmission for multiple multi-antenna terminals. For instance, the sum-rate of the network serving three multi-antenna users (by using the BD-based precoding designs) is greater than the network serving five single-antenna users (by using the conventional zero-forcing precoding as shown by curve e [13]). For reference, the paper also provides the sum-rate performance of dirty paper coding (DPC) technique to serve as upper bound of the network sum-rate. The sum-rate performance of the well-known channel inversion method is iT , - 13 Mean Sum Rate vs SNR 100 100 a: DPC 5users b: BD+WF 5 users c: BD 5 users d: BD+WF 3 users e: BD 3 users f: ZF 5 single antenna users [13] g: Channel Inversion 5 users [72] Sum Rate (bps/Hz) 80 70 60 80 50 40 30 70 60 50 40 30 20 20 10 10 0 0 2 4 6 8 10 12 SNR (dB) a: DPC 5 users × 2 antennas b: ZF+WF 5 users × 2 antennas c: ZF 5 users × 2 antennas d: ZF+WF 3 users × 2 antennas e: ZF 3 users × 2 antennas f: ZF 5 users × 1 antennas [13] g: CI 5 users × 2 antennas [72] 90 Sum Rate (bps/Hz) 90 14 16 18 0 20 Figure 3.1: Sum-rate of MAC phase 0 2 4 6 8 10 12 SNR (dB) 14 16 18 20 Figure 3.2: Sum-rate of BC phase plotted by curve f [72]. Similar to Fig. 3.1, Fig. 3.2 shows the sum-rate of the BD-based precoding technique in the network. As can be seen, the use of the BD-based precoding algorithm can help to increase the BC sum-rate as the number of multi-antenna users increases. 3.3.3 End-to-end design Multiple Access Phase Taking Singular Value Decomposition (SVD) for uplink channel matrix and choose 1/2 Ak = VHk ΣAk , ΣAk = diag{ak,1 , . . . , ak,Nk }, the received signal at the relay can be expressed by 1/2 1/2 r = UH ΣH ΣA s + nR , (3.7) where Ak is the precoding matrix at the BS or kth MS, nR denotes the NR × 1 additive 2 white Gaussian noise vector having zero mean and covariance matrix of E[nR nH R ] = σR INR , 1/2 1/2 1/2 1/2 1/2 1/2 UH = [UTH0 , . . . , UTHK ]T , ΣH = diag{ΣH0 , . . . , ΣHK }, and ΣA = diag{ΣA0 , . . . , ΣAK }. The postcoding will be implemented at RS before precoding and transmitting 1/2 1/2 r̃ = UH H r = ΣH ΣA s + ñR , (3.8) where ñR = UH H nR . Broadcast Phase 1/2 H, Let the SVD decompositions of the downlink channel matrix G be G = UG ΣG VG 1/2 where UG = [UTG0 , . . . , UTGK ]T , ΣG = diag {ΣG0 , . . . , ΣGK } , ΣGk = diag{gk,1 , . . . , gk,Nk }, T , . . . , VT ]T . We define: k = 0, . . . , K and VG = [VG GK 0 G̃k = where Bk = h 1/2 WGk ΣBk , GT1 , · · · , GTk−1 , GTk+1 , · · · , GTK , GT0 iT , (3.9) h i WGk = ṼG1n V̆G1s . . . ṼGKn V̆GKs ṼG0n V̆G0s , ṼGkn hold
H Ṽ the last NR − rank(Gk ) right singular vectors of G̃k , VGks = VG Gkn represents the k 1/2 singular vectors of Gk ṼGkn with non-zero singular values, and ΣBk = diag{bk,1 , . . . , bk,Nk } - 14 - can be any arbitrary matrix that satisfies the sum-power constraints. The received data 1/2 1/2 1/2 1/2 1/2 1/2 H are recovered by ŷ = UH G y = ΣG ΣB ΣH ΣA s + ΣG ΣB ñR + n̂, where n̂ = UG n. Multiuser Power Allocation Considering an multiuser power allocation to maximize the network sum-rate: K X Nk X maximize  1+ log2  k=0 i=1 Nk X subject to : ak,i ≤ Pk , hk,i ak,i σk2 1+  1+ hk,i ak,i σk2 Nk K X X + gk,i dk,i 2 σR gk,i dk,i 2 σR   , (3.10) dk,i ≤ PR , (3.11) k=0 i=1 i=1
2 , P and P are the power constraints at the kth node where dk,i = bk,i hk,i ak,i + σR R k and the RS, respectively. Let J0 (ak,i , bk,i ) = K P Nk P  log2 1 + k=0 i=1 hk,i ak,i σk2  v J2 (ak,i , bk,i ) = K P Nk P k=0 i=1 K P Nk P  log2 1 +  log2 1 + k=0 i=1 hk,i ak,i σk2 gk,i dk,i 2 σR + gk,i dk,i 2 σR  , J1 (ak,i ) =  Suboptimal Solution by Using J0 (ak,i , bk,i ) and J1 (ak,i ) −J1 (ak,i ) + J0 (ak,i , bk,i ), minimize Nk X subject to : (3.12) ak,i ≤ Pk , (3.13) i=1 With ak,i ≥ 0, we obtained the unique solution of the above equation are: ak,i σk2 = 2hk,i s where [x]+ = max(0, x), µk = gk,i dk,i 2 σR 1 λk k=0 i=1 2 σR + gk,i dk,i hk,i gk,i dk,i +4 −2 µ − k 2 2 σR σk2 σR , (3.14) = Pk . (3.15) is decided by s 2 Nk K X X σk2 gk,i dk,i 2hk,i 2 + gk,i dk,i hk,i gk,i dk,i +4 µk − −2 2 2 2 σR σk σR Suboptimal Solution by Using J0 (ak,i , bk,i ) and J2 (ak,i , bk,i ) minimize − J2 (ak,i , bk,i ) + J0 (ak,i , bk,i ), subject to : K X Nk X (3.16) dk,i ≤ PR , (3.17) k=0 i=1 In the case γ 6= 0, we have the quadratic equation in the form: dk,i 2 σR = 2gk,i s hk,i ak,i σk2 2 + hk,i ak,i gk,i hk,i ak,i +4 ν − −2 2 σk2 σR σk2 , (3.18) - 15 - where [x]+ = max(0, x), ν = 1 γ is decided by s 2 K X Nk 2 X σR hk,i ak,i k=0 i=1 σk2 2gk,i + hk,i ak,i hk,i ak,i gk,i ν− −2 +4 2 2 σk σR σk2 = PR . (3.19) Simulation Results 35 180 (4:16:32:4) ZF+PA proposed (4:16:32:4) ZF proposed (4:8:16:2) ZF+PA proposed (4:16:32:4) ZF proposed (4:4:8:1) ZF+PA proposed (4:16:32:4) ZF proposed Sum Rate (bits/s/Hz) 140 Proposed [91] [?] [6] [13] 30 Sum Rate (bits/s/Hz) 160 120 100 80 60 40 25 20 15 10 20 0 5 0 2 Figure 3.3: nodes 4 6 8 10 12 SNR (dB) 14 16 18 20 5 6 7 8 9 10 11 SNR (dB) 12 13 14 15 Sum-rate versus SNR at all Figure 3.4: The sum-rate performance under the system setting of (4:4:8:1) Fig. 3.3 shows the performance of the proposed precoding and power allocation technique under various system settings. In this figure, ”ZF” denotes that the precoding is only designed based on Zero-Forcing beamforming, while ”ZF+PA” indicates that the precoding is enhanced by power allocation after beamforming. As observed, the network sum-rate increases as adding more antennas at nodes. To show the performance comaprison between the proposed scheme and other related ones in the literature, Fig. 3.4 provides the network sum-rate values under the system configuration of (4:4:8:1). For a fair comparison, it is assumed the transmission powers at all MSs and RS are identical, i.e., PR = P0 = Pk , k = 1, . . . , K. In this figure, we can find that the precoding and power allocation algorithm proposed can obtain more performance gain over [6], [91], [13]. 3.4 Conclusions In this chapter, the author has presented a BD-based pre-coding technique to fa- cilitate a SDMA transmission in a two-way relay network with heterogeneous terminals. The numerical results showed that the BD pre-coding and greedy user scheduling designs could help to increase the capacity of two-way relay networks. The author has also developed a suboptimal power allocation scheme for a SDMA transmission in MIMO two-relay networks. By maximizing the network sum-rate of both uplink and downlink under power constraints at nodes, the proposed pre-coding and power allocation scheme outperformed other existing techniques. - 16 - Chapter 4: 4.1 Interference management for multi-cell wireless networks Introduction In this chapter, we focus signal processing techniques for multicell networks to improve sum rate under transmit power contrain with perfect/imperfect chanel status information (CSI). 4.2 Interference management over multicell networks considering perfect channel state information 4.2.1 Uplink interference management Consider a C-cell network where each cell c has one base station (BSc ) and Kc mobile stations (MSc,k ) as shown in Fig. 1. In each cell, the BS equipped with Nc,B antennas and each MS is equipped with Nc,k antennas. The received signal at the base station in the cth cell after poscoding can be presented as ŷc,k = H Wc,k Hc,k vc,k sc,k H + Wc,k Kc X Hc,j vc,j sc,j j=1,j6=k H +Wc,k Kc0 XX c0 6=c H nc , Hc0 ,k0 vc0 ,k0 sc0 ,k0 + Wc,k (4.1) k0 =1 where sc,k is the signal transmitted from MSc,k to BSc , sc0 ,k0 is the desired signal at BSc0 from MSc0 ,k0 but interferes to BSc , Hc,k ∈ CNc,B ×Nc,k denotes the channel matrix from MSc,k to BSc and Hc0 ,k0 ∈ CNc,B ×Nc0 ,k0 is the channel matrix from MSc0 ,k0 to BSc , vc,k and vc,k are the precoding vector at MSc,k and MSc0 ,k0 , respectively, and nc ∈ CNc,B ×1 is additive white complex Gaussian (AWGN) noise vector with zero mean and a covariance matrix σc2 INc,B . Wc,k is the postcoding matrix for user MSc,k . Postcoding matrices design Under the assumption of having perfect CSI, the postcoding matrix can be determined so that the received signal from different users are orthogonal to each other. Based on (4.1) and given precoding matrices vc,k , vc0 ,k0 , (k = 1, . . . , Kc ), (k 0 = 1, . . . , Kc0 ), ZFbased postcoding design can be formulated as minimize Wc,k subject to E{||ŝc,k − sc,k ||2 }, (4.2) Wc,k Hc,i Hc,i = 0, i 6= k, i = 1, . . . , Kc , Wc,k Hc0 ,j wc0 ,j = 0, c 6= c0 , j = 1 . . . , Kc0 , k = 1, . . . , Kc , c, c0 = 1, . . . , C, (4.3) where vc,k , vc0 ,k0 , (k = 1, . . . , Kc ), (k 0 = 1, . . . , Kc0 ): the precoding matrices, ŝc,k : denotes detected symbols at the kth user. Based on the zero-forcing principle, postcoding matrix - 17 - of the kth user can be obtained by Wc,k = Mc,k wc,k , (4.4) where alignment matrix Mc,k is a orthogonal complement subspace of Hc,k . Based on [22], Mc,k can be determined by −1 H Mc,k = I − H̃c,k (H̃H c,k H̃c,k ) H̃c,k , (4.5)  where: H̃c,k = G1 , . . . , Gc−1 , Hc,1 wc,1 , . . . , Hc,k−1 wc,k−1 , Hc,k+1 wc,k+1 , . . . , Hc,Kc wc,Kc ,    Gc+1 , . . . , GC , Gc = Hc,1 wc,1 , . . . , Hc,Kc wc,Kc , c = 1, . . . , C. (4.2) can be rewritten H 2 minimize E{||wc,k MH c,k Hc,k vc,k sc,k − sc,k || }. (4.6) wc,k H and setting to Taking the derivative the Lagrange objective function with respect to wc,k zero, we can obtained the optimal solution of wc,k as follow wc,k = MH c,k Hc,k vc,k  † , (4.7) where [.]† denotes the Moore-Penrose pseudo-inverse [22]. Precoding matrices design at users The precoding matrices can be determined by considering the following optimization problem maximize subject to Kc X   H  H Q F c,k c,k k  log I +  σc2 k=1
tr Qc,k ≤ Pc,k Qc,k  0, k = 1, . . . , Kc , c = 1, . . . , C, (4.8) H , Q Nc,k ×Nc,k , k = 1, . . . , K , c = 1, . . . , C,  denotes positive where Qc,k = vc,k vc,k c c,k ∈ C semidefinite matrices. Solve this problem, we have the solution:  Qc,k = Υc,k diag 1 1 − γ c,k dc,k,1 +  1 1 ,..., − γ c,k dc,k,Nc,k +  ΥH c,k (4.9) 1 where [x]+ = max (0, x). The water-filling level µc,k = γc,k is determined by the power constraint + Nc,k  X 1 = Pc,k . (4.10) µc,k − dc,k,n n=1 Simulation Results Notation of (Nc,B : Kc × Nc,k : P Kc0 × Nc0 ,k ) is used to characterise the antenna c0 6=c configurations. Fig. 4.1 shows the bit-error-rate (BER) versus SNR in a two-cell MIMO - 18 - system . The P-SVD scheme [97], [43] is not applicable to this MIMO configuration due to the lack of receive antennas. It is shown that the proposed precoding and postcoding scheme outperforms the P-SVD scheme in all SNR regions. Fig. 4.2 depicts the average capacity per cell vs. the signal-to-noise ratio (SNR) in a three-cell MIMO system with Nc,k = 2, c = 1, 2, 3 for two case (10:7x2:2x2) and (6:3x2:2x2). As expected, the proposed scheme provides higher capacity than the the PSVD scheme [97], [43] for all SNR regions, and the performance difference becomes larger with increasing of the number antennas. (10:7x2:2x2) Proposed (6:3x2:2x2) Proposed (6:3x2:2x2) P−SVD (10:7x2:2x2) P−SVD 120 100 Capacity (bits/s/Hz) 10 BER (ral) 140 (10:7x2:2x2) P−SVD (10:4x2:2x2) P−SVD (10:3x2:2x2) P−SVD (10:7x2:2x2) Proposed (10:4x2:2x2) Proposed (10:3x2:2x2) Proposed −1 −2 10 −3 10 80 60 40 20 −4 10 0 5 10 SNR (dB) 15 0 20 0 2 4 6 8 10 12 SNR (dB) 14 16 18 20 Figure 4.1: Average BER versus SNR for Figure 4.2: Average capacity versus SNR for MAC with 16-QAM modulation MAC transmission 4.2.2 Interference Management over Multicell Broadcast Channels Signal model The received signal at MSk in lth cell is then given by: Kl X yl,k = hl,l,k vl,k sl,k + hl,l,k vlj slj + j=1,j6=k L X hi,l,k Vi si + nl,k , (4.11) i=1,i6=l T , . . . , vT ]T ∈ CnTl ×Kl is the transmitter beamforming matrix at BS , and where Vi = [vi1 l iKl nRl,k ×1 2 nl,k ∈ C is AWGN nl,k ∼ CN (0, σl,k I)∀l, k. The problem of minimizing the total MSE under the total transmit power constraint at each BSl Pl can be formulated as (P 1) : min vl,k ,wl,k subject to Kl L X X E{||ŷl,k − sl,k ||2 } (4.12) H ) ≤ Pl , ∀l. Tr(vl,k vl,k (4.13) l=1 k=1 Kl X k=1 Precoding matrices designs Let define Cl = InTl − H̆H H̆l H̆H l l the null space of H̆l [22]. H̆l = h
−1 H̆l , represents orthogonal projection onto HTl,1 , . . . , HTl,(l−1) , HTl,(l+1) , . . . , HTl,L iT , and Hl,j =