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: Associate Prof., Dr Tang Tan Chien, 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: The National Library 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 N −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]: L−1 yn = e j2πεn N jφn e 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 N −1 Gk,k Xk + Zk , Yk = Gk,k Xk + (2.2) k =0 k =k where k = 0, , N − 1, Zk is the noise sample in the frequency domain Gk,k can be calculated is Gk,k 2.3.2 = N hl,n e j2π(nk −nk−lk +nε) N ejφn (2.3) l=0 n=0 SIR formulation Based on E hl,n h∗l,n+m (fd = L−1 N −1 vfc c0 , = 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 − is the power-delay-profile -6- (PDP) of the considered channel L is the number of resolvable paths, E[ejφn e−jφn ] = e−πβTs |n−n |/N and (N − |r|) are both even functions, and J0 (2πfd rTs /N ) is a normalized L−1 σl2 = 1, we have: PDP l=0 = N +2 N E |Gk,k | N −1 (N − r)J0 r=1 2πfd rTs N × cos 2πr∆ N cos 2πrε − πβTs r e N N (2.4) As a result, we can obtain the SIR expression: N −1 N +2 SIR(fd Ts , ε, βTs ) = r=1 N −1 N −1 d Ts − ) cos( 2πrε (N − r)J0 ( 2πrf N N )e (N − r) cos N +2 r=1 ∆=1 2πr∆ N πrβTs N d Ts − ) cos( 2πrε J0 ( 2πrf N N )e πrβTs N (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 Simulated SIR, Theoretical SIR Simulated SIR, Theoretical SIR Simulated SIR, 26 24 20 a: b: c: d: e: 35 SIR (dB) SIR (dB) 22 (2.5), = 0.001 =0.001 (2.5), = 0.05 =0.05 (2.5), = 0.01 =0.01 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 under fd Ts = 0.03 (v = 100 km/h) 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 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 ˙ Nt L−1 Nt L−1 (r) yn,m (r,t) (t) (r) h˙ l,n,m x˙ n−l,m + zn,m , (r,t) (t) hl,n,m xn−l,m + = t=1 l=0 t=1 l=0 intended signal (2.6) AWGN self-interference signal (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, h˙ is the channel gain of a self-interference link at node A zn,m is an additive l,n,m white Gaussian noise (AWGN) sample with variance No L and L˙ 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 Q (r,t) hl,n,m (r,t) = bn+Ng +mNs ,q cq,l , l ∈ {0, , L − 1}, (2.7) (r,t) b˙ n+Ng +mNs ,q c˙q,l , l ∈ {0, , L˙ − 1}, (2.8) q=1 Q˙ (r,t) h˙ l,n,m = q=1 where Ns = N + Ng denotes the OFDM symbol length after CP insertion, m = 0, , M − 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) (r,t) are the BEM coefficients used for the desired and self-interference channels, respectively Q and Q˙ are the numbers the qth basis function values of the used BEM cq,l and c˙q,l 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) ˙ mp c˙ , h˙ l,mp = B l , (2.9) where hl,mp and h˙ l,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 ˙ L c˙ (r,t) , h(r,t) = BL c(r,t) , h˙ (r,t) = B where h(r,u) (r,u) h0 = BL = IL ⊗ B, B = T , , (r,u) hL−1 T T , (r,u) hl T BTm1 , , BTmp , , BTmP v T (r,u) hl,m1 = c(r,u) (2.10) , , T (r,u) c0 = (r,u) hl,mp , , T , , (r,u) cL−1 (r,u) hl,mP T T , T T With the BEM-based channel representation, the received signals (2.6) can be rewritten as ˙ Q˙ Nt L−1 Nt L−1 Q (r) yn,m (r,t) (t) bn+Ng +mNs ,q cq,l xn−l,m + = t=1 l=0 q=1 (r,t) (t) b˙ n+Ng +mNs ,q c˙q,l x˙ n−l,m t=1 l=0 q=1 intended signal + (r) zn,m self-interference signal (2.11) 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: c yP = S S˙ + z = Ta + z, (2.12) c˙ where yP T= T , , yT T , ym mp = ymp = S S˙ , S = STm1 , , STmP (t) (t) sl,mp = diag (1) ymp T (t) T , , (1) c˙ (r) = c(1) T x0−l,mp , xN −1−l,mp , , c(Nr ) c˙ (r,1) T T T , , c˙ (r,Nt ) , c(r) = T T T T (N ) T , S˙ = S˙ Tm1 , , S˙ TmP c(r,1) T (r) (r) (t) (t) , (t) , Smp = s0,mp Bmp , , sL−1,mp Bmp , T (t) , S˙ mp = () x˙ 0−l,mp , x˙ N −1−l,mp , , c(r,Nt ) T (r) , ymp = y0,mp , , yN −1,mp , Smp = Smp , , Smpt (t) (t) (t) (t) S˙ mp = s˙ 0,mp Bmp , , s˙ L−1,mp Bmp , s˙ l,mp = diag c= (N ) ympr T T , c˙ = c˙ (1) T (1) (N ) S˙ mp , , S˙ mpt , , a = cT , c˙ T T , , c˙ (Nr ) T , T T , - 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) K The total number of antennas at the BS and the K MSs is NN = 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 } is precoding matrix at BS and K MSs, s = [sT0 , sT1 , , sTK ]T information bearing symbols (1) (K) from BS and K MSs, s0 = sB sB , nr denotes AWGN vector having zero mean 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]: T = (HP)H (HP) −1 (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 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 Wk = ˜k = for all k = k and ≤ k, k ≤ Define G GT1 , · · · , GTk−1 , GTk+1 , · · · , GTK , GT0 where, k = 1, , K, The transmit precoder matrix will thus have the following form: W = BΨ, (3.5) ˜ k ) the last ˜ kn contains NR − rank(H ˜ 1n V ˘ 1s V ˜ Kn V ˘ Ks V ˜ 0n V ˘ 0s , V where B = V ˜ k, V ˘ ks contains singular vectors of Gk V ˜ kn non zero and Ψ = singular vectors of G 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 ˘ ∈ CLk ×Nk to eleminate MUI [50]: T ˘ = (Gk Wk )H (Gk Wk ) T −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 T , - 13 Mean Sum Rate vs SNR 100 100 a: DPC 5users b: BD+WF users c: BD users d: BD+WF users e: BD users f: ZF single antenna users [13] g: Channel Inversion users [72] Sum Rate (bps/Hz) 80 70 60 80 50 40 30 70 60 50 40 30 20 20 10 10 0 10 12 SNR (dB) a: DPC users × antennas b: ZF+WF users × antennas c: ZF users × antennas d: ZF+WF users × antennas e: ZF users × antennas f: ZF users × antennas [13] g: CI users × antennas [72] 90 Sum Rate (bps/Hz) 90 14 16 18 20 Figure 3.1: Sum-rate of MAC phase 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 × additive 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 ˜ r = UH ˜R , H r = ΣH ΣA s + n (3.8) where n ˜ R = 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 ˜k = G GT1 , · · · , GTk−1 , GTk+1 , · · · , GTK , GT0 T , (3.9) 1/2 ˜ Gkn hold ˜ G1n V ˘ G1s V ˜ GKn V ˘ GKs V ˜ G0n V ˘ G0s , V where Bk = WGk ΣBk , WGk = V ˜ k , VGks = VH V ˜ Gkn represents the the last NR − rank(Gk ) right singular vectors of G Gk ˜ Gkn with non-zero singular values, and Σ1/2 = diag{bk,1 , , bk,N } singular vectors of Gk V k Bk - 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 are recovered by y ˆ = UH ˜R + n ˆ , where n ˆ = UH G y = ΣG ΣB ΣH ΣA s + ΣG ΣB n G n Multiuser Power Allocation Considering an multiuser power allocation to maximize the network sum-rate: K Nk maximize 1+ log2 hk,i ak,i σk2 1+ k=0 i=1 gk,i dk,i σR , (3.10) dk,i ≤ PR , ak,i ≤ Pk , subject to : + gk,i dk,i σR Nk K Nk hk,i ak,i σk2 1+ (3.11) k=0 i=1 i=1 , P and P are the power constraints at the kth node where dk,i = bk,i hk,i ak,i + σR R k K Nk log2 + and the RS, respectively Let J0 (ak,i , bk,i ) = K Nk log2 + k=0 i=1 k=0 i=1 K Nk hk,i ak,i σk2 v J2 (ak,i , bk,i ) = log2 + k=0 i=1 hk,i ak,i σk2 + gk,i dk,i σR , J1 (ak,i ) = gk,i dk,i σR Suboptimal Solution by Using J0 (ak,i , bk,i ) and J1 (ak,i ) −J1 (ak,i ) + J0 (ak,i , bk,i ), minimize (3.12) Nk ak,i ≤ Pk , subject to : (3.13) i=1 With ak,i ≥ 0, we obtained the unique solution of the above equation are: ak,i σk2 = 2hk,i gk,i dk,i σR where [x]+ = max(0, x), µk = K Nk k=0 i=1 σk2 2hk,i λk gk,i dk,i σR gk,i dk,i hk,i gk,i dk,i +4 −2 µ − k 2 σR σk2 σR + , (3.14) = Pk (3.15) is decided by gk,i dk,i hk,i gk,i dk,i +4 µk − −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 ), K (3.16) Nk dk,i ≤ PR , subject to : (3.17) k=0 i=1 In the case γ = 0, we have the quadratic equation in the form: dk,i σR = 2gk,i hk,i ak,i σk2 hk,i ak,i gk,i hk,i ak,i +4 ν − −2 σk2 σR σk2 + , (3.18) - 15 - where [x]+ = max(0, x), ν = K Nk k=0 i=1 σR 2gk,i γ is decided by hk,i ak,i σk2 hk,i ak,i hk,i ak,i gk,i ν− −2 +4 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 Figure 3.3: nodes 10 12 SNR (dB) 14 16 18 20 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 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 Kc y ˆc,k = H Wc,k Hc,k vc,k sc,k H + Wc,k Hc,j vc,j sc,j j=1,j=k Kc H +Wc,k H nc , Hc ,k vc ,k sc ,k + Wc,k (4.1) c =c k =1 where sc,k is the signal transmitted from MSc,k to BSc , sc ,k is the desired signal at BSc from MSc ,k but interferes to BSc , Hc,k ∈ CNc,B ×Nc,k denotes the channel matrix from MSc,k to BSc and Hc ,k ∈ CNc,B ×Nc ,k is the channel matrix from MSc ,k to BSc , vc,k and vc,k are the precoding vector at MSc,k and MSc ,k , 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 , vc ,k , (k = 1, , Kc ), (k = 1, , Kc ), ZFbased postcoding design can be formulated as minimize Wc,k subject to E{||ˆ sc,k − sc,k ||2 }, (4.2) Wc,k Hc,i Hc,i = 0, i = k, i = 1, , Kc , Wc,k Hc ,j wc ,j = 0, c = c , j = , Kc , k = 1, , Kc , c, c = 1, , C, (4.3) sc,k : denotes where vc,k , vc ,k , (k = 1, , Kc ), (k = 1, , Kc ): the precoding matrices, ˆ 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 ˜ ˜ c,k (H ˜H H Mc,k = I − H c,k c,k ) Hc,k , (4.5) ˜ c,k = G1 , , Gc−1 , Hc,1 wc,1 , , Hc,k−1 wc,k−1 , Hc,k+1 wc,k+1 , , Hc,Kc wc,Kc , where: H Gc+1 , , GC , Gc = Hc,1 wc,1 , , Hc,Kc wc,Kc , c = 1, , C (4.2) can be rewritten H 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 Kc maximize k=1 subject to Hc,k Qc,k FH k log I + σc2 tr Qc,k ≤ Pc,k Qc,k 0, k = 1, , Kc , c = 1, , C, H , Q Nc,k ×Nc,k , k = 1, , K , c = 1, , C, where Qc,k = vc,k vc,k c c,k ∈ C (4.8) denotes positive semidefinite matrices Solve this problem, we have the solution: Qc,k = Υc,k diag 1 − γ c,k dc,k,1 + 1 , , − γ c,k dc,k,Nc,k + ΥH c,k (4.9) where [x]+ = max (0, x) The water-filling level µc,k = γc,k is determined by the power constraint Nc,k + = Pc,k (4.10) µc,k − dc,k,n n=1 Simulation Results Kc × Nc ,k ) is used to characterise the antenna Notation of (Nc,B : Kc × Nc,k : c =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, 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 10 SNR (dB) 15 20 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: L Kl hl,l,k vlj slj + yl,k = hl,l,k vl,k sl,k + j=1,j=k hi,l,k Vi si + nl,k , (4.11) i=1,i=l T , , vT ]T ∈ CnTl ×Kl is the transmitter beamforming matrix at BS , and where Vi = [vi1 l iKl nRl,k ×1 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 L Kl E{||ˆ yl,k − sl,k ||2 } (4.12) H ) ≤ Pl , ∀l Tr(vl,k vl,k (4.13) (P 1) : vl,k ,wl,k l=1 k=1 Kl subject to k=1 Precoding matrices designs ˘H H ˘ lH ˘H Let define Cl = InTl − H l l ˘ l [22] H ˘l = the null space of H −1 ˘ l , represents orthogonal projection onto H HTl,1 , , HTl,(l−1) , HTl,(l+1) , , HTl,L T , and Hl,j = - 19 - hl,j,1 , hl,j,2 , , hl,j,Kl denotes the channel matrix from the BSl to all MSs in j cell The transmit precoding matrix at the lth BS will thus have the following form: Vl = Cl Pl , (4.14) where Pl ∈ CnTl ×Kl is any arbitrary matrix that satisfies the sum-power constraint The total received signal of the receivers in cell l affter receiver beamformer is ˆ l = Wl Hl Cl Pl sl + Wl nl , Y T ,y T , ,y T ˆl = y where Y ˆl,1 ˆl,2 ˆl,K l nTl,1 , nTl,2 , , nTl,Kl (4.15) T , Wl = blkdiag wl,1 , wl,2 , , wl,Kl , and nl = T This problem is formulated as follow Kl L (P 2) : H H H H H H H Tr PH l Cl hl,l,k wl,k wl,k hl,l,k Cl Pl − Tr Pl Cl hl,l,k wl,k pl,k ,wl,k l=1 k=1 H −Tr wl,k hl,l,k Cl Pl + Tr (I) + σl,k Tr wl,k wl,k (4.16) Solve this problem, we get the following solution −1 wl,k = H H PH l Cl hl,l,k H H hl,l,k Cl Pl PH l Cl hl,l,k + σl,k I , (4.17) The problem of minimizing the total MSE under the total transmit power constraint can be written as L (P 3) : subject to : Pl Tr E ||Pl sl + Bl Wl nl − Bl sl ||2 l=1 H PH l Cl Cl Pl ≤ Pl , ∀l, (4.18) (4.19) where Bl = (Wl Hl Cl )† We have the solution Pl = I + γl CH l Cl −1 Bl H Tr PH l C l C l P l = Pl (4.20) (4.21) The MSE minimization problem can be solved by using an iterative process as summarized in the Algorithm 4.1 Simulation Results To investigate the system condition of nTl > LKl nRl,k (different from Figs and 3), Fig 4.3 shows the sum-rate performance of the proposed scheme versus SNR As aforementioned in this paper, the ZF-based precoding scheme [37] outperforms the proposed MSE-based one in the condition where the number of transmit antennas (at each BS) is greater than that of receive antennas at all users (i.e., nTl = 30 > 24 = LKl nRl,k ) - 20 - Algorithm 4.1 MSE-based precoding design 1: Initialization: Choose an initial value Pl satisfying the power constraint while not converge 2: 4: For fixed Pl , calculate wl,k according to (4.17) For fixed wl,k , calculate γl according to (4.21) 5: Update Pl according to (4.20) with γl solved 3: end while 6: 100 45 Proposed Algorithm [37] 40 10−1 nTl = 30 < LKl nRl,k = 36 Tc tng (bits/s/Hz) 35 BER 10−2 10−3 nTl = 30 > LKl nRl,k = 24 25 20 15 nTl = 30 < LKl nRl,k = 36 10 10−4 [37] Proposed Algorithm 10−5 nTl = 30 > LKl nRl,k = 24 30 Figure 4.3: 10 15 SNR (dB) 20 25 30 0 10 15 SNR (dB) 20 25 30 BER performance when the Figure 4.4: Sum-rate performance when the number of transmit antennas is greater than number of transmit antennas is greater than that of receive antennas that of receive antennas As observed, the performance gap between [37] and the proposed one reduces as SNR increases To show BER performance comparison under the condition of nTl > LKl nRl,k , Fig 4.4 shows numerical results of BER performance of [37] and the proposed one as the number of transmit antennas (at each BS) is greater than that of receive antennas at all users As can be seen, the proposed MSE-based precoding technique and [37] have the same BER performance as nTl = 30 > 24 = LKl nRl,k 4.3 Interference management in multi-user multi-cell communication systems in the absence of perfect channel state information 4.3.1 Signal model Using postcoding matrices Wl,k ∈ Cd×Nl,k , the received signal rl,k at MS-k in cell-l can be obtained by L ˆ l,i,k − El,i,k Vl xl + Wi,k ni,k , H ri,k = Wi,k (4.22) l=1 ˆ l,i,k = Hl,i,k + El,i,k , H ˆ l,i,k the channel where Vi ∈ CMi ×dKi is precoding matrix at BS-i H response matrix from BS-l to MS-k in cell i and El,i,k denotes the channel model error due - 21 - to imperfect channel estimation El,i,k can be assumed to be Gaussian distributed with H zero mean E{El,i,k EH l,i,k } = σh I and variance E{El,i,k El ,i ,k } = with l = l , i = i or k=k 4.3.2 Pre/post-coding matrices Design The joint precoding and postcoding design for the considered multicell system (hav- ing L cells) can be formulated as the following optimization problem L (4.23) fl αl , Vl , Wl,k minimize αl ,Vl , Wl,k l=1 Tr Vl VlH ≤ Pl , l = 1, , L, subject to : where Pl denotes the per-base station power constraint of BS-l Kl k=1 E ||Wl,k αl−1 zl,k − Dk xl ||2 + L Ki i=1 k=1 i=l (4.24) fl αl , Vl , Wl,k = E ||Wi,k αl−1 cl,i,k ||2 , Proposition For fixed postcoding matrices Wl,k , the optimal solution of precoding matrices Vl can be obtained by Kl −1 ˆ H W H Dk , αl H l,l,k l,k Vl = (Tl ) (4.25) k=1 where Pl αl = Kl Tr k=1 (4.26) ˆ l,l,k T−2 H ˆ H WH Wl,k H l,l,k l,k l and L Ki Tl = i=1 k=1 Kl ˆ H WH Wi,k H ˆ l,i,k + σn H l,i,k i,k Pl L Tr H Wl,k Wl,k k=1 Ki I + σh2 H Tr Wi,k Wi,k I i=1 k=1 (4.27) Proof Proposition For fixed precoding matrices Vl , the optimal solution of postcoding matrices Wl,k can be determined by L Wl,k = ˆH αl Dk VlH H l,l,k Ki × i=1 k=1 −1 L ˆ i,l,k Vi ViH H ˆH H i,l,k + σn2 I + σh2 Tr Vi ViH I i=1 (4.28) Proof Using (4.25) and (4.28), the detailed steps of the iterative robust precoding and postcoding design in multicell multiuser transmissions are described in Algorithm 4.2 It is noted that the proposed precoding and postcoding algorithm requires the use of global CSIT/CSIR at all the BSs and MSs - 22 - Algorithm 4.2 Iterative Postcoding and Precoding Design 1: Initialization Choose initial values of postcoding matrices Wl,k with l = 1, , L 2: 3: 4: repeat For fixed Wl,k , obtain αl by (4.26) and obtain precoding matrices Vl by (4.25) For fixed Vl and fixed αl , update postcoding matrices Wl,k by (4.28) 5: 6: until Predetermined accurary of ε is met 4.3.3 Complexity Analysis (a) Lagrange multiplier (b) Precoding matrix (c) Postcoding matrix O LKl2 Nk dk O 2L2 Ml Kl2 Nk dk +L2 Kl3 Nk2 dk +LMl3 + LMl2 Kl2 Nk2 +LMl Kl2 Nk dk O L2 2Ml Kl3 Nk dk +L2 Ml2 Kl2 dk +LKl4 Nk3 + LMl Kl3 Nk2 +LMl Kl3 Nk dk Total complexity = (a)+(b)+(c) O L2 2Ml Kl3 Nk dk + L2 Ml2 Kl2 dk Algorithm 4.2 +LKl4 Nk3 + LMl Kl3 Nk2 +LMl Kl3 Nk dk +2L2 Ml Kl2 Nk dk + L2 Kl3 Nk2 dk +LMl3 + LMl2 Kl2 Nk2 +LMl Kl2 Nk dk + LKl2 Nk dk O 2L2 Ml Nk dk O niter 8LMl3 [67] +L2 Nk2 dk +LMl3 + LMl2 Nk2 +LMl Nk dk O 2L2 Ml Nk dk + L2 Ml2 dk O 2LMl2 Nk dk +LMl2 dk +Nk3 + Ml Nk2 + Ml Nk dk +LNk3 + LMl Nk2 + LMl Nk dk +2L2 Ml Nk dk + L2 Nk2 dk +LMl3 + LMl2 Nk2 + LMl Nk dk +LNk dk + niter 8LMl3 O L2 2Ml Kl3 Nk dk + L2 Ml2 Kl2 dk [38] [40, 69, 56] O 2L2 Ml Kl2 Nk dk O L2 2Ml Kl3 Nk dk O niter 2L(Ml3 +L2 Kl3 Nk2 dk +L2 Ml2 Kl2 dk +Ml2 Kl Nk ) +LMl3 + LMl2 Kl2 Nk2 +LKl4 Nk3 + LMl Kl3 Nk2 +LMl Kl2 Nk dk +LMl Kl3 Nk dk O 2L2 Ml Kl2 Nk dk O L2 2Ml Kl3 Nk dk +L2 Kl3 Nk2 dk +L2 Ml2 Kl2 dk O niter 8LMl3 +LMl3 + LMl2 Kl2 Nk2 +LMl Kl2 Nk dk +LKl4 Nk3 + LMl Kl3 Nk2 +LMl Kl3 Nk dk +LKl4 Nk3 + LMl Kl3 Nk2 +LMl Kl3 Nk dk +2L Ml Kl2 Nk dk + L2 Kl3 Nk2 dk +LMl3 + LMl2 Kl2 Nk2 +LMl Kl2 Nk dk +niter 2L(Ml3 + Ml2 Kl2 Nk ) O L2 2Ml Kl3 Nk dk + L2 Ml2 Kl2 dk +LKl4 Nk3 + LMl Kl3 Nk2 +LMl Kl3 Nk dk +2L2 Ml Kl2 Nk dk + L2 Kl3 Nk2 dk +LMl3 + LMl2 Kl2 Nk2 +LMl Kl2 Nk dk +niter 8LMl3 Table 4.1: Complexity of Precoding and Postcoding Design Algorithms Table 4.1 shows the complexity orders of computing (a) Lagrange multipliers, (b) precoding matrices and (c) postcoding matrices The total complexity of these considered algorithms for each outer iteration is shown in the last column of Table 4.1 As shown in Table 4.1, Algorithm 4.2 offers a lower complexity as compared to [38, 40, 69, 56] Similar to [67], the complexities of [38, 40, 69, 56] significantly increase as a large number of inner iterations for computing Lagrange multipliers are used (e.g., slow convergence happens at inner loops) 4.3.4 Numerical Results and Discussions To investigate the effect of imperfect CSI, Fig 4.5 shows the performance of the “robust” and “non-robust” transceiver designs of Algorithm 4.2 and [67] As a special version of Algorithm 4.2, the non-robust precoding and postcoding design can be simply - 23 - Sum-rate performance (bits/s/Hz) non-robust 12 l = 1, , Imperfect L, k = Kl CSI:1, σ , = 0.04 robust h 10 Robust design (using σh2 in Algorithm 1) Non-robust design (ignoring σh2 in Algorithm 1) 80 70 60 50 non-robust a: b: c: d: Imperfect CSI: 2σh2 = 0.04 robust 14 L = 3, Kl = 1, Ml = 6, Nl,k = 6, Sum-rate performance (bits/s/Hz) 90 L = 3, Kl = 1, Ml = 6, Nl,k = 6, l = 1, , L, k = 1, , Kl 16 [67] (robust design) Proposed Algorithm (robust design) [67] (non-robust design) Proposed Algorithm (non-robust design) 10 15 SNR (dB) 20 25 40 30 L = 3, Kl = 2, Ml = 8, Nl,k = 4, l = 1, , L, k = 1, , Kl 20 30 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 σ 2h Figure 4.5: Sum-rate performance of the Figure 4.6: Sum-rate performance of the considered single-user multicell system using considered multiuser multicell system versus imperfect CSI CSI imperfection level σh2 a: by [67]setting (robust design) obtained σh2 = in (4.25) and (4.28) at Steps and of Algorithm 4.2 As b: Proposed Algorithm (robust design) expected, using statistical information of imperfect CSI σh2 in the robust transceiver designs c: [67] (non-robust design) d: Proposed Algorithm (non-robust design) (curves a and b) offers better performance than ignoring the effect of CSI imperfection in the “non-robust” designs (curves c and d) As a result, the robust design (using a more model) the non-robust accurate channel 10 15 has larger 20gain than 25 30 one (using a less accurate channel model) does SNR (dB) Addressing a multiuser multicell system (L = 3, K1 = K2 = K3 = 2) using imperfect CSI, Fig 4.6 shows the sum-rate performance of Algorithm 4.2 versus σh2 under two different cases: (i) using statistical information of channel estimation error (robust design) and (ii) ignoring the imperfect CSI effect (i.e., the non-robust design obtained by setting σh2 = in (4.25) and (4.28) at Steps and of Algorithm 4.2) As a result, the performance gap between the robust and non-robust designs increases as the CSI imperfection level increases 4.4 Conclusion In this chapter, the author has developed a MSE-based pre-coding and post-coding scheme for multi-user transmissions under the impact of inter-cell interferences As a result, the proposed multi-user pre-coding/post-coding technique can be employed for multi-cell transmissions with a limited number of BS antennas in a large user pool The author has also derived a closed-form solution of Lagrangian multipliers which helped to avoid the users of inner iterative computation of Lagrangian multipliers Therefore, the proposed algorithm offered a robust transceiver design with a low computational complexity without sacrificing performance in comparison with previous algorithms in the literature The analytical and related simulated results showed that the convergence of the proposed iterative transceiver design algorithm is guaranteed - 24 - Conclusions and Outlook Conclusionsons The thesis has systemized and clarified some theoretical issues about signal processing in the next generations of mobile communications The thesis has showed that multi-dimensional signal processing is one of the key techniques to increase capacity and improve quality of mobile radio communications, supporting the continuous demand for high-bandwidth applications Based on studied signal processing techniques, the main contributions of the thesis can be summarized as follow: Firstly, the dissertation has derived signal-to-interference ratio (SIR) formula for OFDM transmission systems over time variant channels in the presence of carrier frequency offset and phase noise This results are associated with the author’s publications 2, 3, and Secondly, the dissertation has developed channel estimation algorithms for MIMOOFDM full-duplex transmission systems 10 and 12 Then, the dissertation has 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 schemes outperformed other existing techniques 4, and Finally, the dissertation has proposed algorithms for interference management for multi-cell broadcast system in the absence of perfect channel state information This algorithms have been we proposed in 7, and 11 From theoretical and practical studies, the proposed techniques in this dissertation can be considered to be employed in the next generations of wireless communications networks Outlook - Further research to propose time-variant channel estimation algorithms for multiuser full-duplex systems - Further research to propose interference management techniques in multi-cell networks with generation power constraints per antenna using the imperfect information status channels List of works published N.-D.-N Vien, N.-L Hung and T.-T Chien (2012), Statistical Properties of Rayleigh Fading Models in Wireless Communications, The University of Danang Journal of Science and Technology, vol 3, no 8(57), pp 262–269 N.-D.-N Vien, N.-L Hung and T.-T Chien (2012), Interference Analysis for OFDM Transmissions in the Presence of Time-Varying Channel Impairments, REV Journal on Electronics and Communications, vol 2, no 3-4, pp 140–147 N.-D.-N Vien, N.-L Hung and T.-T Chien (2012), On the effect of phase noise and time-selective channel on OFDM transmission: SINR analysis, Proc of The International Conference on Advanced Technologies for Communications (ATC) pp 98–102 N.-D.-N Vien, N.-L Hung and T.-T Chien (2013), Multiuser Scheduling in Two-Way Relay Networks, Proc of The International Conference on Advanced Technologies for Communications (ATC) pp 147-151 N.-D.-N Vien, N.-L Hung, T.-T Chien and L.-N Tho (2013), SIR Analysis for OFDM Transmission in the Presence of CFO, Phase Noise and Doubly Selective Fading, IEEE Communications Letters, ISSN: 1089-7798 no (17) pp 1810 1813 (ISI index, SCI Journal List) N.-D.-N Vien, N.-L Hung, T.-T Chien and L.-T.-P Mai (2013), Multiuser Precoding in MIMO Two-Way Relay Transmission, Proc of The Fifth International Conference on Ubiquitous and Future Networks (ICUFN 2013), pp 139–143 N.-D.-N Vien, N.-L Hung, T.-T Chien and L Quang (2014), Multicell Transmission over Multiple Access Channel: Precoding and Postcoding, Proc of The International Conference on Communications and Electronics (ICCE) pp 599-602 N.-D.-N Vien, N.-L Hung and T.-T Chien, T.-T.- Huong, B.-T.-M Tu and N.-H Giang (2014), Two-Way Relay Networks with SDMA: Precoding Design and Power Allocation, Proc of The first NAFOSTED Conference on Information and Computer Science (NICS’14) pp 127–135 N.-D.-N Vien, N.-L Hung and T.-T Chien (2014), Interference Management over Multicell Broadcast Channels, Proc of The International Conference on Advanced Technologies for Communications (ATC) pp 512–516 10 N.-D.-N Vien, N.-L Hung, T.-T Chien and B.-T.-M Tu (2015), “Doubly Selective Channel Estimation in Full-Duplex MIMO-OFDM Systems,” Proc of The International Conference on Advanced Technologies for Communications (ATC) pp 578– 582 11 N.-L Hung, N.-D.-N Vien, T.-T Chien and V.N.Q Bao (2016), “Precoding and Postcoding for Multicell Multiuser Transmission Using Imperfect CSI,” Journal of Communications and Networks, vol 18, no 5, pp 762–772 (ISI index, SCIE Journal List) 12 N.-D.-N Vien, B.-T.-M Tu, T.-T Chien, V.N.Q Bao and N.-L Hung (2016), Joint Phase Noise and Doubly Selective Channel Estimation in Full-Duplex MIMO-OFDM Systems,” Proc of The International Conference on Advanced Technologies for Communications (ATC) pp 413–418 ... 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... theoretical issues about signal processing in the next generations of mobile communications The thesis has showed that multi-dimensional signal processing is one of the key techniques to increase capacity... 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