Spatial, Spectral and Temporal Adaptation for Fast Fading MIMO-OFDMA Systems

Transcription

1 Workshop on Moile Computing and Emerging Communication Networks Spatial, Spectral and Temporal Adaptation for Fast Fading MIMO-OFDMA Systems Balkan Kecicioglu, Wenxun Qiu, Hlaing Minn and John H. L. Hansen Dept. of Electrical Engineering, The University of Texas at Dallas Astract Modern wireless communication systems are designed to operate in diverse propagation conditions. Adaptive transmission techniques are powerful tools for achieving this ojective. We propose a new adaptive transmission method for fast fading channels. The new method comines enefits of closed loop and open loop transmission techniques y efficient utilization of resources in time, frequency and spatial domains. In the new approach we consider how to allocate different MIMO schemes and alternative suchannelization methods in a given frame depending on the moile speed, numer of antennas and signal-to-noise ratio SNR). Numerical results show effectiveness of the proposed method for a wide range of moile speeds. I. INTRODUCTION In designing wireless communication systems, efficient utilization of andwidth resources is very crucial. In MIMO-OFDMA ased communication systems, these resources are in time, frequency and spatial domains. If the channel knowledge is not availale at the transmitter, open loop OL) transmission techniques are employed which distriute andwidth resources uniformly in frequency and spatial domains to achieve diversity gain in the channel. On the other hand, if channel knowledge can e acquired at the transmitter with a reasonale cost, then MIMO transmission method can e adapted to changing channel conditions in order to otain power gain in spatial domain and the channel can e adaptively assigned to the desired user to otain multiuser diversity gain in the frequency domain. These methods are termed closed loop CL) transmission techniques. In OFDMA system, as adjacent sucarriers experience almost the same channel gain, channelization or resource partitioning among users can e ased on groups of contiguous sucarriers known as resource locks RBs). The channel gains on the sucarriers within an RB can e considered to e the same. Although an RB can e defined over several OFDM symols, in this paper we define it over one OFDM symol to allow adaptation for fast fading channel. These RBs are divided into suchannels to e allocated to users. Suchannel structure is designed according to the desired operating conditions to take advantage of underlying channel characteristics. If the channel is slow fading, then channel information can e otained at the transmitter with sufficient reliaility. In this case, consecutive sucarriers are grouped together in frequency domain to form and-type suchannels. This structure allows implementation of CL transmission techniques. When the channel is fast fading, it is usually assumed that acquiring channel knowledge at the transmitter is not feasile. In this scenario, the suchannels are formed from sucarriers distriuted in the availale spectrum which can e termed as interleavedtype suchannels. Interleaved-type suchannel structure is suitale for OL transmission techniques. It can e shown that neither CL nor OL transmission is optimum in certain scenarios etween very fast fading and slow fading channels. Therefore the transmission scheme and the suchannel structure should e carefully designed to consider the operating conditions of the system. [1]-[2] study optimum MIMO transmission scheme when the channel is not perfectly known at the transmitter. In [3]-[5], authors propose multiple antenna transmission schemes roust to channel knowledge imperfections which comines enefits of eamforming and space diversity techniques. In [6]-[7], resource allocation for OFDMA systems is studied when the channel knowledge is imperfect at the transmitter. In all of these works, channel imperfection is considered to e a constant value in a frame duration. This model is suitale for channel perturations due to feedack delays, quantization errors or channel estimation errors. In fast fading channels, the channel can change within a frame duration. This fast fading channel can e oserved in moile speeds that are supported y next generation cellular wireless standards [13]-[15]. In such fading conditions, even if the initial channel knowledge is reliale in the eginning of the frame, it will ecome outdated in later part of the frame. Considering this fast fading channel, we recently proposed a transmission scheme that allocates eamforming BF) and space frequency coding SFC) schemes depending on the time selectivity of the channel [9] and an evolving suchannel structure that incorporates and-type and interleaved-type structures to accommodate different moile speeds in SISO systems [8]. The former considered spatial and temporal adaptation within each frame while the latter addressed spectral and temporal adaptation. In this work, we propose an adaptive transmission strategy for fast fading channels in which oth /11/$ IEEE 597

2 user channelization and MIMO transmission mode are adapted in a given frame. Although the new user suchannel structure is not static within the frame, it just needs to e designed offline once. On the other hand, MIMO transmission mode adaptation is performed ased on the initial channel knowledge in each frame. Taking advantage of oth OL and CL transmissions, the proposed method performs etter than individual transmission methods in all moile speeds. The rest of the paper is organized is as follows. The system and channel model are introduced in Section II. In Section III, the proposed method is explained. Performance of the proposed method is demonstrated with numerical simulations in Section IV and the paper is concluded in Section V. II. SYSTEM MODEL In this paper, we consider downlink DL) of a wireless network employing OFDMA as multiple access method. Base station BS) is equipped with n t antennas and each moile user has single receive antenna, i.e. n r =1 1.The received signal of user k on sucarrier q at symol time n is given y yq k n) =h k q,nx k q n)+wq k n) 1) where wq k n) is the noise which is complex Gaussian distriuted with zero mean and unit variance. h k q n) is the 1 n t vector containing channel coefficients of user k on sucarrier q. It is assumed that the channels are statistically independent and identically distriuted iid) etween different users. Each channel coefficient is distriuted as complex Gaussian with zero mean and unit variance. x k q is the transmitted signal vector for user k on the sucarrier q with average power E[ x k q n) 2 ]=η, therefore η is the average SNR on each sucarrier per receive antenna. A. Channel Model The channel is fast fading. We assume that quasi-static fading assumption is not valid in a frame level ut the OFDM sucarrier spacing is properly chosen to avoid inter-carrier interference such that the channel stays essentially the same during one OFDM symol duration. The transmitter can otain the channel knowledge either through uplink measurements for TDD systems or with feedack from the receiver for FDD systems. In either case, our analysis focuses on channel knowledge imperfections at the transmitter due to the time selectivity of the channel. Channel vector at symol time n, h k q,n is given y h k q,n = ρ n h k q,0 + 1 ρ 2 nh k e,q,n 2) 1 In this paper we are concerned aout how to utilize channel knowledge at the transmitter for single stream transmission. In this case, finding optimum comining weights at the receiver is trivial. Also, the performance for n r > 1 shows a similar trend to the case of n r =1. Therefore, we consider single receive antenna case in this work to simplify the analysis. where h k q,0 is the channel knowledge availale at the eginning of the frame and h k e,q,n is the perturation term due to decorrelation effect. ρ n is the correlation coefficient etween the initial channel knowledge h k q,0 and current channel realization h k q,n at symol time n. Although channel is changing during a frame, the receiver can estimate the channel with pilot tones inserted into the frame in time-frequency grid. Thus, in this work we assume that the receiver has perfect channel knowledge for all decoding purposes. In the following analysis we adopt a channel with uniform power delay profile with independent taps. Although this assumption is necessary for the analysis, other power delay profiles can e accommodated y finding degrees of freedom in the frequency selective channel. B. Alternative Suchannelization Methods We consider an OFDM modulated system with Discrete-Fourier-Transform DFT) size N dft, out of which N used of them are used. Availale spectrum is divided into N suchan suchannels and each suchannel is constructed from N r RBs, each consisting of N scr sucarriers. Therefore, N used = N suchan N r N scr. Suchannels are formed y grouping N rchan resource locks. Permutation of the resource locks in a given suchannel results in different suchannelization user channelization) structures. In this paper, we consider two different reference suchannelization methods as depicted in Figure 1. First, consecutive resource locks are grouped to form suchannels, which is called andtype suchannelization. Second, suchannels are constructed from resource locks which are non-adjacently distriuted in the frequency domain. This approach is called interleaved-type suchannelization. The third suchannelization structure shown in Figure 1 is related to the proposed transmission approach in this work and will e explained in the following. III. PROPOSED TRANSMISSION METHOD In this work, we propose a practical transmission strategy for fast fading channels. In the new approach we jointly consider adapting multiple antenna transmission scheme and suchannel structure. The proposed method is designed to improve reliaility, i.e. it-errorrate ) for a fixed transmission rate. Benefits of OL and CL methods are utilized y allocating alternative transmission methods in a given frame depending on the time-selectivity of the channel and SNR. We choose eamforming BF) and space-frequency coding SFC) as alternative multiple antenna techniques. First the channel structure is determined ased on the desired operating point which is determined y average SNR and moile speed. Then, BF and SFC is allocated in a frame ased on initial channel knowledge. In the sequel, we look into approximate performance metrics of 598

3 gain in addition to the diversity gain that can e otained with OL systems. When the initial channel knowledge is acquired at the transmitter, the suchannel with the highest gain is selected and eamforming vector coefficients are calculated for this suchannel. However, this initial channel knowledge ecomes outdated throughout the frame when the channel is fast fading. Therefore enefits of CL transmission decreases towards the end of the frame. In state of the art systems, CL transmission is avoided if channel does not stay static at least for a frame duration. In this work, we show that enefits of CL transmission can e partially otained when the user channelization structure is carefully designed. For this purpose, we first start y deriving approximate performance of BF with alternative suchannel structures when channel is following the fast fading channel model in 2). Following analysis focuses on a given user that is assigned to its est channel. Hence, we omit user index for clarity. The transmitter calculates eamforming coefficients v q for the given sucarrier q with the initial channel knowledge h q,0 at the eginning of the frame as v q = h H q,0/ h q,0. The received signal is then given y y q n) =h q,n v q x q n)+w q n) 4) Fig. 1. Alternative suchannel structures alternative transmission methods with different channelization structures. By knowing these metrics, we propose adaptive suchannelization and MIMO mode allocation algorithm. Approximate expressions are derived for M-QAM modulated signal. The approximation P γ) 0.2e 1.5γ M 1 from [10] is used in the analysis where γ is the SNR per symol. For the fading channel, the average performance can e otained from P e 1.5γ M 1 fγ γ)dγ 3) where f γ γ) is proaility density function PDF) of the effective SNR. A. of BF with Alternative Suchannel Structures If perfect channel knowledge is availale at the transmitter, adaptive channel selection and BF provide power where x q n) is the transmitted symol and w q n) is the AWGN noise. Note that the received SNR is given y γ q,n = η h q,n v q 2. According to the channel model in 2), the random variale z q,n = ηh q,n v q is given y z q,n = ηρ n h q,0 + 1 ρ 2 nh e q,n)v q = ηρ n h q,0 + 1 ρ 2 nh e q,n) 5) where h e q,n = h e q,nv q. SNR on sucarrier q at symol time n is given y γ q,n = z q,n 2. Note that SNR at the symol time n =0is γ q,0 = η h q,0 2. We implement it level interleaving and coding in time-frequency grid to capture time and frequency diversity of the system. It is difficult to otain closed form performance metrics for an aritrary coding method. For simplicity of analysis we derive metrics ased on repetition coding in frequency domain. When different coding schemes are applied, a correction coefficient should e introduced to the effective SNR. The effective SNR is given y γ n = β γ q,n, 6) q=l 1 where l 1,...,l Q are the sucarrier indices in the given suchannel and β is the correction factor. Since the channel is highly correlated in consecutive sucarriers, effective SNR in 6) simplifies to γ n = Qβγn for andtype suchannel where γn is the SNR in the sucarrier which is located in the middle of the given suchannel. Conditioned on the initial channel knowledge h q,0, z q,n l Q 599

4 is a complex Gaussian distriuted random variale with mean ρ n η h0 and variance η1 ρ 2 n). Therefore it is easy to see that γ n is a noncentral Chi-square random variale with 2 degrees of freedom and noncentrality parameter s = ρ n ηβq h0. PDF of SNR at symol time n for a given channel knowledge h 0 can e expressed as f γn γ 0 γ n γ 0 ) = 1 ηβq1 ρ 2 n) exp 2ρ n I 0 ηβq1 ρ 2 n) ρ2 nγ 0 + γ n ηβq1 ρ ) 2 n) γn γ 0 where I m.) is the m-th order modified Bessel function of the first kind. Average performance for M-QAM at symol n conditioned on the current channel realization h 0 as can e easily derived using the approximation in 3) as ) 31 ρ P BF and 2 1 n, M n,γ 0 ) 0.2 n )ηqβ +1 2M n 1) 3ρ 2 ) exp nγ 0 31 ρ 2.7) n)ηqβ +2M n 1) If the suchannel structure is interleaved-type, coding across frequency efficiently captures diversity in the frequency selective channel. Therefore the effective SNR as expressed in 6) is a Chi-square random variale with 2d f degrees of freedom, where d f is the frequency diversity order. Following similar steps to arrive at 7), average metric for the BF scheme in an interleavedtype suchannel is given as ) 31 ρ P BF int 2 df n, M n,γ 0 ) 0.2 n )ηβ +1 2M n 1)d f 3ρ 2 ) exp nγ 0 d f 31 ρ 2 8), n)ηβ +2M n 1)d f where d f =minl, Q) and L is the numer of independent time domain taps of the channel. B. of SFC with Alternative Suchannel Structures If channel knowledge cannot e otained with sufficient reliaility, diversity techniques are implemented to extract degrees of freedom in the system. Since the transmitter does not know the channel, the est approach is to distriute transmission power uniformly in all dimensions as much as possile. In this study, we choose space frequency lock coding SFBC) as spatial diversity technique due to its simple decoding method. In SFBC, a lock of m modulated symols are coded across n f sucarriers and coded vectors are simultaneously transmitted from n t antennas. Rate of such a SFBC is R = m/n f. In this paper, we optimize transmission mode to minimize for a fixed rate and fixed power transmission. If the rate of SFBC is R<1, then modulation order of SFBC should e increased to satisfy constant rate requirement. Considering the ) system model in 1), we can write the received signal on symol time n and sucarrier q as y q n) =h q,n x q n)+w q n) 9) where x q n) is n t 1 transmitted signal vector generated according to a given SFBC matrix. As the channel is highly correlated across consecutive sucarriers, receiver can decode symols with linear complexity. Symols from each antenna are normalized y 1/ n t to satisfy constant power requirement, i.e., E[ x q n) 2 ]=η. Thus, the received SNR on sucarrier q is given y γ q,n = a η n t h q,n 2 F [12], where a is a parameter that is a function of SFBC code. a = 1 for Alamouti code and a = 2 for rate 1/2 code designed for 4 transmit antennas. Encoding across frequency extracts frequency diversity of the channel. When a and-type channel structure is employed together with SFBC transmission, it captures multiuser diversity gain from the adaptive channel selection and diversity gain in the spatial domain. Following the steps to arrive at 7), we can easily otain average metric of SFBC transmission on and-type suchannel structure as ) 3a1 ρ P SFC and 2 nt n, M n,γ 0 ) 0.2 n )ηqβ +1 2M n 1)n t 3ρ 2 ) exp nγ 0 n t 3a1 ρ 2.10) n)ηqβ +2M n 1)n t SFBC when used with interleaved-type suchannel provides diversity in spatial and frequency domain. Rememering that the diversity order of the frequency selective channel is d f, it can e noted that γ n now is a central Chi-square distriuted random variale with 2n t d f degrees of freedom. PDF of SNR conditioned on the initial channel knowledge can e written as n t d f f γ γ) = aηγn t d f ) γntd f 1 exp n td f aη γ ), where γ) is the Gamma function. The average performance of SFC transmission with interleaved-type suchannel structure can e written as P SFC int η, M n ) a d f n t M n 1) η ) ntd f. 11) Since this transmission mode does not utilize channel knowledge for adaptive channel selection or eamforming, performance is independent of symol index n. C. Adaptive Transmission Mode and Suchannel Allocation In the new method, we propose to adapt suchannel structure as well as multiple antenna transmission scheme to changing channel conditions. The transmission mode is adapted as a function of initial channel knowledge, modulation order, SNR and time correlation properties of the channel. It should e noted that it may not e practical to have different suchannel structures 600

5 in different portions of the OFDMA frame. Therefore it is etter to determine suchannel structure ased on unconditional performance rather than conditioned on the channel knowledge. In the proposed method, we follow a two step approach for transmission adaptation. First, the suchannel structure is designed offline for a given average SNR η and moile speed. This decision is ased on unconditional performance of completely CL BF with andtype suchannel) and OL SFC with interleaved-type suchannel) transmissions. The same suchannel structure is maintained in a given frame for all users. Second, multiple antenna schemes are allocated in each frame with conditional metrics otained in 7),8),10) and 11). Therefore, multiple antenna schemes can vary etween different users. The first step requires knowledge of unconditional performance metrics. As explained in the previous section, performance of OL transmission in 11) is already an unconditional metric. Due to the space limitations, we cannot include unconditional performance of BF with and-type suchannel structure here, ut it is availale in [9]. Once the suchannel structure is fixed, 7),8),10) and 11) are used to estimate switching points inside the frame to allocate different transmission modes as m n) =argmin P m n, M n,γ 0 ) mn) where m n) is the transmission mode index on symol n and mn) {BF-and, BF-int, SFC-and, SFCint}. Power gain due to adaptive channel selection and eamforming is still oserved in the eginning of the frame. As the channel knowledge ecomes outdated at later part of the frame, these gains can drop elow performance of OL scheme. When it occurs, the proposed scheme switches to the open loop scheme. Note that the transmission mode selection for each symol of a frame is done on a frame y frame asis. IV. SIMULATIONS AND RESULTS In this section we demonstrate the performance of the proposed transmission method with numerical simulations. Channel coefficients are independent identically distriuted etween different antennas and they are generated according to the Jakes s model [11], where ρ n = J 0 2πf d T s n) with T s eing the OFDM symol duration and f d eing the Doppler frequency. In our simulations, f c =2GHz and T s =71.35 μs. DFT size is 1024, where out of 1024 sucarriers, 576 of them are used as in LTE. Three different suchannelization methods are used in the simulations. For n t =2, used sucarriers are grouped into 144 RBs each consisting of 4 consecutive sucarriers. Each suchannel is allocated 6 RBs. For n t = 4, used sucarriers are grouped into 72 RBs each consisting of 8 consecutive sucarriers. Each suchannel has 3 RBs. RB for 4 antennas uses more adjacent sucarriers ecause the SFBC encodes 4 symols over 8 sucarriers. Suchannels are formed from consecutive RBs for and-type structure and from distriuted RBs for interleaved-type structure. The suchannel structure of the proposed approach is a mixture of the two as shown in Figure 1. Numer of OFDM symols in each frame is taken as 14 and 28 for different simulations. It is assumed that the receiver has perfect channel knowledge throughout the frame and the transmitter otains channel knowledge at the eginning of the frame without feedack delay 2. When performing BF in a suchannel, BF vector are computed for each sucarrier. When implementing SFBC, full rate Alamouti code is used for n t = 2, however rate 1/2 code is used if n t =4. Therefore, the modulation order of BF, M CL, is equal to the modulation order of SFBC, M OL, when n t =2, whereas M OL = MCL 2 when n t =4to maintain the same data rate. The information is encoded with rate 1/2 convolutional code with constraint length of 7. Correction coefficient of β = 0.5 is chosen to account for differences etween the repetition code used in the analysis and the convolutional code in the simulations. In Figures 2 and 3, performances of individual OL and CL transmissions and proposed transmission method are shown. The average SNR is 15dB for n t = 2 and 8 db for n t = 4. It can e seen that performance of OL transmission improves while the performance of CL transmission degrades with increasing moile speed. The proposed method is seen to perform etter than oth schemes in all moile speeds. Figures 4 and 5 demonstrate the performance for a fixed moile speed of 200km/h for n t =2and 250km/h for n t =4. It is again seen that the proposed method has a performance gain over individual schemes. V. CONCLUSIONS A novel approach of spatial, spectral and temporal adaptation is proposed for fast fading channels in which oth user channelization and MIMO transmission modes are adapted in a given frame. The user channelization is designed ased on average SNR and moile speed. On the other hand, MIMO transmission mode is adapted on frame-y-frame asis as a function of initial channel knowledge. Taking advantage of oth OL and CL transmissions, the proposed method performs etter than individual transmission methods in wide range of moile speeds. REFERENCES [1] S. A. Jafar and A. Goldsmith, Transmitter optimization and optimality of eamforming for multiple antenna systems, IEEE Trans. Wireless Commun., vol. 3, no. 4, pp , Jul A feedack delay of τ symols can easily e incorporated into the analysis y modifying correlation coefficient at symol time n as ρ n+τ. 601

6 10 3 SFC int. BF and Proposed method 10 1 BF and SFC int. Proposed Method Moile Speed km/h) Fig. 2. performance for 16-QAM modulation with rate 1/2 convolutional code, n t=2, n r=1, SNR=15dB SNRdB) Fig. 4. performance for 16-QAM modulation with rate 1/2 convolutional code, n t=2, n r=1, moile speed=200km/h BF and SFC int Proposed method 10 1 BF and SFC int Proposed method Moile speed km/h) Fig. 3. performance for 16-QAM modulation with rate 1/2 convolutional code, n t=4, n r=1, SNR=8dB SNRdB) Fig. 5. performance for 16-QAM modulation with rate 1/2 convolutional code, n t=4, n r=1, moile speed=250km/h. [2] E. Visotsky and U. Madhow, Space-time transmit precoding with imperfect feedack, IEEE Trans. Inform. Theo., vol. 47, no. 6, pp , Sep [3] G. Jongren and M. Skoglung, Comining eamforming and orthogonal space-time lock coding, IEEE Trans. Inform. Theory, vol. 48, no. 3, pp , Mar [4] S. Ektaani and H. Jafarkhani, Comining eamforming and space-time coding using quantized feedack, IEEE Trans. Wireless Commun., vol. 7, no. 3, pp , Mar [5] S. Zhou and G. B. Giannakis, Optimal transmitter eigeneamforming and space-time lock coding ased on channel mean feedack, IEEE Trans. Sig. Process., vol. 50, no. 10, pp , Oct [6] H. Zhong-Hai; L. Yong-Hwan, Opportunistic scheduling with partial channel information in OFDMA/FDD systems, IEEE 60th Vehicular Technology Conference, vol.1, no., pp Vol. 1, Sept [7] I. C. Wong and B. Evans, Optimal resource allocation in the OFDMA downlink with imperfect channel knowledge, IEEE Trans. on Commun., vol.57, no.1, pp , January [8] W. Qiu, H. Minn and C. -C. Chong, An Efficient Diversity Exploitation in Multiuser Time-Varying Frequency-Selective Fad- ing Channels, accepted in IEEE Transactions on Communications, Hlaing.Minn/Wenxun.pdf. [9] B. Kecicioglu, H. Minn, and C. -C. Chong, Intra-Frame Transmission Adaptation for Fast Fading MIMO-OFDM Systems, accepted in IEEE Transactions on Communications, Hlaing.Minn/Balkan.pdf. [10] M. K. Simon and M.-S. Alouini, Digital communications over fading channels, New York: Wiley, [11] R. Clarke, A statistical theory of moile reception, Bell Syst. Tech. J., vol. 47, pp , July, [12] G. Femenias, performance of linear STBC from orthogonal designs over MIMO correlated Nakagami-m fading channels, IEEE Trans. Veh. Tech., vol. 53, pp , Mar [13] WP5D, Draft report on requirements related to technical performance for IMT-Advanced radio interfaces) [IMT.TECH], Working Party 5D Su-Working Group Radio Aspects, 2nd Meeting, Duai, United Ara Emirates, July [14] IEEE e, Air Interface for Fixed and Moile Broadand Wireless Access Systems. [15] 3GPP, LTE-Advanced, Requirements for further advancements for E-UTRA Release 8), 3GPP TR v8.0.1, Mar