Engineering, 2009, 2, 9198 doi:10.4236/eng.2009.12010 Published Online August 2009 (http://www.SciRP.org/journal/eng/). Copyright © 2009 SciRes. ENGINEERING Optimal Power Allocation Strategy for TBLAST Based 4G Systems Wu YIN1, Pei XIAO2 1ZTE corporation, Shenzhen, China 2The Institute of ECIT, Queen’s University, Belfast, UK Email: wu.yin@ncl.ac.uk Received May 21, 2009; revised July 13, 2009; accepted July 20, 2009 ABSTRACT There is a big demand for increasing number of subscribers in the fourth generation mobile communication systems. However, the system performance is limited by multipath propagations and lack of efficient power allocation algorithms in conventional wireless communication systems. Optimal resource allocation and in terference cancellation issues are critical for the improvement of system performance such as throughput and transmission reliability. In this paper, a turbo coded bell lab space time system (TBLAST) with optimal power allocation techniques based on eigen mode, Newton and convex optimization method and carrier interferenceandnoise ratio (CINR) are proposed to improve link reliability and to increase throughput with reasonable computational complexity. The proposed scheme is evaluated by MonteCarlo simulations and is shown to outperform the conventional power allocation scheme. Keywords: Carrier Interference and Noise Ratio (CINR), Convolutional Turbo Coded Bell Space Time (TBLAST), Eigen Mode (EM), Optimal Power Allocation (OPL), Automatic Differentiation (AD), Symbolic Derivative (SD) 1. Introduction This decade has witnessed incredible development in mobile wireless communications. Multipleinput and multipleoutput (MIMO) techniques and adaptive an tenna system (AAS) have been adopted in the 4th gen eration (4G) systems, e.g., worldwide interoperability microwave access (WiMAX) and long term evolution (LTE) systems. It is well known that wireless communi cation systems are interference limited, i.e. their through put and quality of service are largely affected by various impairments such as multiuser inference (MUI), inter symbol interference (ISI) and spatial correlation, etc.. MIMO and orthogonal frequency division multiplex ing (OFDM) techniques have been adopted in 4G sys tems. OFDM technique transforms a frequency selective fading channel into parallel flat fading channels which provides an efficient way to improve MIMO and AAS system performance. The singlecarrier frequency divi sion multiple access (SCFDMA) and orthogonal fre quency division multiple access (OFDMA) have been employed in the uplink of the WiMAX (IEEE802.16e) and LTE systems, respectively, to mitigate the effect of channel fading and interference. In 4G systems, the channel quality is measured by the carrierinterferer noiseratio (CINR), defined by the ratio between the power of useful subcarriers in the OFDM and the power of noise plus interference. The issues of allocating power among subcarriers in OFDM systems have been investigated extensively [1,2]. The power control of an OFDM system and its sub channels is an efficient way to improve system perform ance such as maximizing system capacity and reducing bit error ratio (BER). Thus, the power allocation schemes and their application in the MIMOOFDMA as well as AAS systems have attracted a lot of attention from both academia and industry. It has also been reported that in 4G systems, there ex
W. YIN ET AL. Copyright © 2009 SciRes. ENGINEERING 92 ists carrier frequency offset which destroys the orthogo nality between subcarriers, leading to intercarrier inter ference [3] which can deteriorate system performance significantly. In addition, spatial correlation has more impact on the uplink than on the downlink [4] of 4G systems. Interference cancellation (IC) techniques have been recommended as an efficient solution to tackle this problem. In 4G systems, optimal resource allocation (OPL) can be implemented by adaptive modulation and coding (AMC) as well as with channel state information at the transmitter (CSIT). Precoding (beamforming) with CSIT is a technique that can effectively utilize optimal resource to maximize throughput or improve transmis sion link quality. In 4G systems, CINR [5] gives an indication for the underlying channel condition, and has been used in Wi MAX and LTE systems as feedback information from mobile terminals to base station. Conventional optimal methodologies usually have prohibitive computation complexity which prevents them from practical imple mentation. Eigenvalue mode (EM) has been regarded as an efficient way to achieve desirable performance with reasonable complexity. For these reasons, we consider the use of CINR and develop an EM based algorithm in this paper. Space time coding (STC) and spatial multiplexing (SM) also called the BLAST have been considered in the 4G standards [6]. In this paper, we investigate BLAST techniques, which can achieve good performance with low computational complexity by successive interference cancellation (SIC) algorithm [7]. The disadvantage of Vertical BLAST is the lack of diversity for transmission link. To tackle this problem, parallel convolutional cod ing (PCCC) coded BLAST can be employed to compen sate the diversity loss in the conventional VBLAST. Turbo BLAST (TBLAST) was proposed in [6] to reduce the complexity of such systems. The principle is to re peat the process of passing soft information instead of hard decision between the MIMO detector and the chan nel decoder. As such, the system performance can be improved in an iterative manner. However, the OPL and interference cancellation tech niques as well as TBLAST have not been considered in the current WiMAX and LTE standards. This paper pro vides a feasibility study of utilizing the OPL and TBLAST techniques on the transmitter and receiver side, respectively. It is reasonable to believe that the results obtained from this study are of direct relevance to the future development of 4G standards. 2. Literature Review 2.1. Review of CINR Utilization Channel estimation and resource optimisation are the two key issues that can determine the physical layer sys tem performance in both LTE and WiMAX systems. Recently, major equipment vendors issued a proposal that involved Physical CINR and power allocation to improve the WiMAX system performance [8,9] in Wi MAX Forum. Channel estimation is performed based on CINR. CSIT or PCINR information can be in the form of precoding matrix index (PMI) in both WiMAX and LTE systems. The eigen mode relies on the analysis of CINR, which is equivalent to one form of Shannon capacity [9]. In [10, 11], compensationbooting assisted OPL and AMC have been used to improve wireless system performance. However, there is lack of specific methodologies and application in 4G systems. In WiMAX beamforming or LTE precoding techniques, eigen mode based techniques can be considered for weight calculation or code book selection in the precoding mode of transmission in base station. OPL can be achieved by feedback of fast feed back (FFB) channel and CSIT from customer premise equipment (CPE) in a closedloop system. 2.2. Review of WaterFilling (WF) and SVD in Wireless Communication Power allocation schemes for the wireless communica tion systems mainly fall into three categories, i.e. equal power allocation, water filling power allocation that based on singular value decomposition SVD and Newton and convex optimization method based power allocation. The principle of SVD can be described briefly with the following equations: *()*()diag diag Hλvλ (1) 12n 1 2n ], where H is a normalised channel complex matrix, each element of which represents the complex channel gain with zero mean and unit variance; are eigen values of H corresponding to the power of each sub channel, and the relevant eigenvectors that can be re garded as weights in the beamforming or choice of PMI are as follows: mn i v = [v1 , v2···vn] (2) which can be utilized to form precoding matrix in MIMO systems. Waterfilling (WF) or water pouring schemes
W. YIN ET AL. Copyright © 2009 SciRes. ENGINEERING 93 Figure 1. Block diagram of the proposed transmit system. [12] have been proposed as iterative power allocation for transmit antennas after acquiring eigenvectors following channel estimation, covariance matrix calculation and SVD operation. In the waterfilling scheme, the iterative power allocation is implemented for each user and can be expressed as miλPp m i ici 2,1 1 1 (3) H ctrP QQ (4) where m is the number of transmit antennas; is the transmit power constraint; Q denotes the ith signal se quence in the transmit system; are the power allo cated to individual substreams in the transmitter and the c P i p 1 i are the waterfilling levels. However, the WF scheme is suboptimal for multiuser MIMO systems since it only considers separated power allocation for each user rather than joint power allocation for all the users [13,14]. More details can be seen in the following section of the proposed optimal method in the third part of the system model. In addition, the previous publications and research on the optimal power alloca tion of the VBLAST systems [14,15] have heavy compu tational complexity that prevents their application in practice. Furthermore, these researches only focus on uncoded VBLAST systems. In this paper, coded VBLAST systems with high efficiency have been inves tigated and the comparison with the previous optimal power allocation schemes will be addressed in the fol lowing section of the proposed optimal method. 3. System Model and the Proposed Power Allocation Scheme In this section, we describe the proposed transceiver sys tem. 3.1. Review of Transceiver System and Conven tional Power Allocation Scheme In Figure 1, the data source is first separated into m sub streams and then encoded by different PCCC encoders. Subsequently, each coded substream can be beamformed by weight or coded by PMI mode. An inverse fast Fou rier transform (IFFT) is then applied to the signal and each coded substream is independently fed into its an tenna. In addition, the power of the transmitted signals can be controlled by base station through closedloop optimal power allocation based on CINR and the feed back of CPE. Figure 2 illustrates the proposed TBLAST receiver structure. The communications channel with the highest signaltonoise ratio (SNR) is chosen for detection by a linear adaptive MMSE scheme. In the decoder, a maxi
W. YIN ET AL. Copyright © 2009 SciRes. ENGINEERING 94 Figure 2. Block diagram of the proposed receiver system. mum aposteriori (MAP) or aposteriori probability (APP) based algorithm is utilized to extract the data from the received signal. After deriving soft decision and recon structing each transmitted substream, the detected signal is removed from the received signal by successive inter ference cancellation (SIC) algorithm before proceeding to the next iteration. In WiMAX beamforming (BF) or LTE precoding techniques, eigenvalue base techniques can be used for weight calculation or code book selection in the precoder design at base station. The conventional OPL algorithms are designed according to utility functions using SINR, BER performance or system capacity. The cost function of signal to interference and noise ratio (SINR) can be expressed as [16,17]: 2 2 2 2 j ii i jj i ji ii i ikjj ji ap pbp n p vp vH vH (5) where denotes the processing gain; i a j bdenotes the channel coefficient; is a zero mean Additive White Gaussian Noise (AWGN); is the nulling vector and is the power allocated to individual substreams in the transmitter. i n i v i p The maximum signal to noise ratio (MSNR) based precoding scheme is equivalent to the maximum capacity based scheme. The system capacity can be presented as follows [18]: N n nk H SINR C 1 , 2 1log detlog IHQH (6) where H is a normalised complexvalued channel nm matrix with unit variance, Q is the covariance matrix of the information data bits and the 2 denotes the variance of the noise In MIMO systems, the ergodic capacity, defined as the maximum average mutual information for identical inde pendent distribution (i.i.d) complex Gaussian channels with perfect CSI at receiver and no CSI information in transmitter can be expressed as [18]: 2 1 H 2 1log 1 b/s/HzIdetlog ii m i Hi p m m Epf HQH (7) where denotes the average SNR; stands for the complex conjugate operator. The channel gain is normal ized so as to meet the constant power constraint, m is the number of transmit antennas. H VBLAST is a technique that selects the received layer with the highest signal noise ratio (SNR) and then re moves the relevant layer by SIC till the last layer is de tected. Therefore, the first layer detection is critical to BLAST system performance. The principle of the opti mal power allocation in the proposed BLAST system is to allocate more power to the layers with high SNR, and a good system performance can be achieved in this manner. 3.2. Review of Optimal Theory on Wireless Communications Most optimization problems in practical wireless com munication environments fall into the category of convex optimization. IPM (interior point method), which con sists of quasi Newton method and Lagrangian method, has been regarded as the most efficient method in the optimal sense for resolving optimal convex problems with certain constraints. The applications of IPM are classified into three cata logues, i.e. primal IPM, dual IPM and primal dual IPM methods. The optimal source management solutions in practical wireless communication systems can be dealt with by optimal primalduality IPM theory that is actu ally a minimummaximum or minmax problem [17] with power constraint: m i iiii pgkpf 1 max (8) The automatic differentiation (AD) method is highly efficient to achieve optimal solution with low computa tion complexity compared to the conventional optimal schemes. In the wireless communication systems, it can be described in terms of multiple variables as follows
W. YIN. ET AL. Copyright © 2009 SciRes. ENGINEERING 95 1112n mm12n F(p)=f(p ,p,p,) F(p) = F(p)=f (p,p,p,) (9) The derivative matrix that depends on the Jacobian ma trix can be described as F(p) = J (10) 111 1 12 n mm m n 12 n F (p)F (p)F (p) ypp p = F(p) F(p)F(p) ypp p J (11) where the function is set up to meet the require ments of the wireless communication system functions; p i F m,, pppp 21 is the allocated power in the trans mission system. The symbolic derivative (SD) method has been re garded as a new area in mathematics and has been widely applied in industry, commerce and academia. It can be implemented by the solver package, which is an efficient software depending on IPM method, for resolv ing optimal convex solution by Newton method, in the processing of derivative. SD algorithms calculate deriva tive and estimate an approximate optimal solution in the formulas with less computational complexity and accu racy compared to conventional optimal schemes. 3.3. Proposed Optimal Method and Comparison with Conventional Schemes In the classical singleuser or multiuser Waterfilling scheme, the power is allocated for each individual sub stream in the transmitter iteratively until all Karush KuhnTucker (KKT) conditions are satisfied, which is a necessary condition and resolved by first order deriva tive in a nonlinear equation and is actually a simplified application of IPM [19]. However, the conventional wa terfilling schemes have many issues that will prevent their application and will be explained in the following paragraphs. The proposed optimal power allocation scheme in the BLAST systems is different from the conventional wa terfilling or any other power allocation schemes. Firstly, in the classical waterfilling scheme, the power will be cut off when the power allocated for individual sub stream is less than the waterfilling level u 0,max uppi (12) Consequently, the classical waterfilling will result in a reduced spectral efficiency due to the loss of spatial mul tiplexing gain when applied to the BLAST systems. Sec ondly, considering the error propagation problem inher ent in the interference cancellation based receiver, the first layer detection is crucial for the system performance in terms of achievable system capacity and BER per formance. For this reason, the substream with the highest SNR should be allocated more power. Thirdly, the con ventional BLAST detection algorithms are only deter mined by the SINR. However, in coded BLAST systems with variable transmission rate, the choice of channel code and code rate in each substream will affect the BLAST systems performance significantly. The conventional optimal power allocation algorithms for VBLAST have been investigated in [14,15], the SINR that can be expressed as 2 2 2 2 p ap ii i ii pibp n jj i ji vp ikjj j ji vH vH (13) where i a denotes the processing gain; j bdenotes the fading channel gain; i n is a zero mean AWGN; is the nulling vector and i v i p is the power allocated to in dividual substream in transmitter. The BER ie pP can be approximated and reduced to a simplified formula as [22, 23] 12 5.1 exp 5 1 i R i p i p e P (14) where is the data rate of the transmit stream. The derivatives are subsequently taken for the Equations (3) (41) subject to (3)(39) i Rth i 0 i dp i p e Pd i dp i pfd i dp i pJd (15) Then the power allocation solution can be derived from an exhaustive search [23] p p p i i R ii ln2625.0 1 ij jm i R paf pM i 1 2125.3 1 1 (16) where
W. YIN ET AL. Copyright © 2009 SciRes. ENGINEERING 96 m ii j jm i R m ii i R p af pm p p mi i 1 1 1 1 1 1 1 2125.3 ln 2 6.1 exp (17) where the power allocation can be derived by an adap tive method such as LMS k i ii i p pJ iukpkp 1 m ii k p i pJ m i k p i pJ m iuk i p 1 2 11 ) (18) where denotes the step function and m is the trans mit antenna size. iu It can be observed that the disadvantage of this opti mal power allocation scheme is its heavy computational load to obtain the derivatives in the equation, which is impractical for real time communication environments. One solution is to employ the SD, which is efficient in the derivation and differential algebraic operations for optimal solution with less computational complexity compared to the conventional optimal methods. The power allocated to each individual substream can be expressed in the form of eigenvalues as gppkp m iic iii il (19) where are the lagrangian coefficients. Subsequently, we can obtain the first order of derivative as: i k dl(p,k,r )df(p,r)dg(p,r ) k dp dpdp iii iiii ii ii e i i (20) we can then derive the following equations 1 () () m iii i pkg p ) i (21) where and are the gradient of the func tions and . The allocated power {} can be derived from solving following equations i pf i pf i g i p i gi p 1212 12 {}( mi pp psolveeeeggg (22) In the conventional VBLAST detection algorithm, the ordering procedure that is determined by SINR is ex pressed as [13] HH GHIHH 1 2 maxarg (23) With optimal power allocation, the equation for ordering selection is replaced by HH GHPIHPHP1 2 1 (24) Finally, we obtain the eigenmode power allocation for individual substream in the transmission system as mi pppdiagP 21 , (25) Table 1. Simulation environment. Simulation model Transmit antenna Receive antenna Fading channel Doppler frequency Encoder & rate Data modulation Decoding algorithm Constraint length Feedback polynomial Feedforward polynomia Number of iterative CSI System Monte Carlo 3 elements 6 elements Rayleigh. Jakes model 20 Hz CTC 1/2 OFDM QPSK LogMap, extrinsic information transfer (EXIT) 4, 6 111 (L=4), 11011 (L=6) 101 (L=4), 11001 (L=6) 6 Perfect known PCCC, Closedloop Figure 3. BER Performance comparison: OPL versus equal power allocation.
W. YIN. ET AL. Copyright © 2009 SciRes. ENGINEERING 97 11.5 22.5 33.5 4 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 Signal to Noise Ratio (SNR) in dB Spectral Efficiency (Bits/Sec/Hz) Optimal power allocation Uniform power allocation Figure 4. Comparison of spectral efficiency: OPL versus uniform power allocation. In the VBLAST system, we selected the layer with the highest SINR and perform SIC to remove the detected layer. This procedure continues for subsequent iterations of detection and decoding process till the last substream is detected layer. The solution can be derived by setting Equation (9) to zero, then we can perform optimal search within certain steps or iterative number that depends on the AD method [16]. As a result, the derived solution can be applied to the transmitter to optimize resource alloca tion or relocate the power to the modulation and coding of transmission in the base station. 4. Numerical Results In this section, the performance of different systems is evaluated by computer simulations and numerical results are provided to demonstrate the effectiveness of the pro posed schemes. The simulation parameter setting is tabu lated in Table 1. In Figure 3, we show the comparison of the BER per formance between the proposed OPL and the equal power allocation scheme. Simulation results indicate that there is a considerable improvement by the proposed scheme compared to the conventional equal power scheme. A gain of 4.5 dB has been observed at target BER= , and the gain becomes more obvious as SNR increases. 3 10 One can also see from Figure 4 that the spectral effi ciency, which depends on received CINR, can be im proved by the proposed scheme compared to the equal (uniform) power allocation. This is due to the fact that more power in the base station is allocated to the trans mit layers with high SNR, leading to the improved sys tem performance with SIC based layered processing. In practical wireless communication systems such as LTE and WiMAX IEEE802.16e, only equal power allo cation has been considered so far. However, this simple algorithm is highly suboptimal as indicated by our re sults. Also considering the fact that the conditions for performing iterative waterfilling can not always be ful filled in practical situations, the proposed algorithm pro vides an effective means to allocating transmit power for the 4G systems. 5. Conclusions In this paper, a closedloop TBLAST system with eigen mode and optimal power allocation is proposed and evaluated by means of simulations. Results show that it achieves a substantial performance gain in system per formance with reasonable computational complexity compared to the conventional schemes. The work pre sented in this paper provides a useful source of informa tion for the optimization of power allocation in the future 4G systems. 6. References [1] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE Selected Areas in Communica tions, Vol. 17, pp. 17471758, October 1999. [2] K. Kim, Y. Han, and S.L. Kim, “Joint subcarrier and power allocation in uplink OFDMA systems,” IEEE Communications Letters, Vol. 9, No. 6, pp. 526528, 2005. [3] R. Raghunath and A. Chockalingam, “SIR analysis and interference cancellation in uplink OFDMA with large carrier frequency and timing offsets,” Wireless Commu nications & Networking Conference, 2007 IEEE, Kow loon, China. [4] B. Hamid, L. Jonathan, P. Jules, and U. Raner, “A study on UL potential issues,” WiMAX Forum, Technical working group, 2008. http://www.WiMAXforum.org. [5] H. Jin and Y. X. Na, “Physical carrier to interference plusnoise ratio techniques for wideband wireless com munications networks,” Cisco Technology, INC, USPC Class: 375346. [6] G. J. Foschini, “Layered spacetime architecture for wire less communication in a fading environment when using multielement antennas,” Bell Labs Technical Journal, Vol. 1, No. 2, Autumn 1996. [7] R. M. Buehrer and B. D. Woerner, “Analysis of adaptive multistage interference cancellation for CDMA using an improved Gaussian approximation,” IEEE Transactions on Communications, Vol. 44, No. 10, pp. 13081321, October 1996. [8] M. Sellathurai and S. Haykin, “TurboBLAST for wire less communications: Theory and experiments,” IEEE Transactions on Signal Processing, Vol. 50, No. 10, pp. 25382546, October 2002.
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