AN EFFICIENT LINK PERFOMANCE ESTIMATION TECHNIQUE FOR MIMO-OFDM SYSTEMS

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1 AN EFFICIENT LINK PERFOMANCE ESTIMATION TECHNIQUE FOR MIMO-OFDM SYSTEMS 1 K. A. Narayana Reddy, 2 G. Madhavi Latha, 3 P.V.Ramana 1 4 th sem, M.Tech (Digital Electronics and Communication Systems), Sree Vidyanikethan Engineering College, Tirupathi (aswartha.kn@gmail.com). 2 Asst. Professor Dept. of ECE, Sree Vidyanikethan Engineering College, Tirupathi. 3 HOD, Dept. of ECE, Sree Vidyanikethan Engineering College, Tirupathi Abstract_Adaptive modulation and coding (AMC) is a powerful technique to enhance the link performance by adjusting the transmission power, channel coding rates and modulation levels according to channel state information. In order to efficiently utilize the AMC scheme, an accurate signalto-noise ratio (SNR) value is normally required for determining the AMC level. In this paper, we propose an efficient link performance estimation technique for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with maximum likelihood (ML) receiver. The performance of ML detection (MLD) is estimated by using capacity bounds of two simple linear receivers. By analyzing the relation between the upper bound and the lower bound of the ML detector performance, we introduce an efficient way to determine the SNR for the ML receiver. I. INTRODUCTION Most wireless communication systems have been designed to support high-speed packet data transmissions. Those high speed packet services can be provided by employing efficient usages of the transmission bandwidth and mitigating intersymbol interference in frequency selective fading channels. In such environments, much attention has been paid to multi-input multi-output (MIMO) systems [1] and orthogonal frequency division multiplexing (OFDM) [2]. MIMO systems can exhibit a significant throughput gain over single antenna systems by transmitting multiple independent data streams [1]. Also, the OFDM makes it possible to transmit packets over frequency selective channels without equalizers. Moreover, MIMO systems combined with OFDM, which is called as MIMO-OFDM, can guarantee high spectral efficiency and better link error performance by associating with bit-interleaved coded modulation (BICM) [3] [5]. If channel state information (CSI) is available at the transmitter, it is possible to enhance the system throughput by adjusting the transmit power level, channel coding rates and/or modulation levels, which is the basic concept of an adaptive modulation and coding (AMC) technique [6]. When adopting the AMC, accurate link quality estimation at the receiver side is crucial. Exponential effective signal-tonoise ratio (SNR) mapping (EESM) proposed in [7] is a simple prediction method for the AMC. However, the EESM technique was originally developed for single-input singleoutput (SISO) systems. For the case of MIMO systems with maximum likelihood detector (MLD), referred to as MIMO-MLD, it is difficult to estimate the link error performance based on the EESM mapping, since the received signal is jointly detected over all spatial sub channels. Recently, two alternative link prediction methods for the MIMO-MLD were proposed based on mean mutual information per bit (MMIB) [8] and received bit mutual information rate (RBIR) [9]. While these methods achieve better prediction in the MIMO case, higher computational complexity is required for performing eigen value decomposition and computing some other approximation parameters. A number of ESM methods have been introduced in order to provide a more effective way of predicting the link quality of coded OFDM systems in single-input single-output 1

2 (SISO) cases [10] [12]. Since maximum likelihood detection (MLD) provides the optimum MIMO detection performance, the MLD or near-ml detectors have widely been considered to be adopted as a powerful receiver algorithm. However, it is well recognized that accurate link estimation becomes challenging for MIMO systems when an ML detector is applied. Although a couple of extensions of existing ESM methods to the MIMO-MLD have been introduced [13][14], they require high computational complexity or do not provide reasonable estimation accuracy. In [15], a new approach of the PHY abstraction for the MIMO-MLD was proposed for horizontal encoding structures, where each transmit antenna is connected to separate channel encoders. The same idea was applied to the vertical encoding case [16], where all data streams are simultaneously encoded by a single channel encoder. In this paper, by extending the general SISO ESM approach, we propose an improved link error prediction technique for MIMO-OFDM systems with ML receiver. First, utilizing capacity upper and lower bounds, we develop a simple yet accurate stream wise SNR representation process for vertical encoding MIMO-MLD systems. After obtaining the SNR estimates per each stream, the corresponding block error rate (BLER) performance is found for each encoding block through the SISO ESM using the received bit information rate (RBIR) metrics [12]. From simulation results, we confirm that the proposed method is quite accurate in the MIMO-MLD link performance evaluation while preserving very low computational complexity. The remainder of this paper is organized as follows: In Section II, we describe the system model of adaptive MIMO-OFDM systems. Section III, we explain the proposed link error prediction technique for the MIMO-MLD. Section IV verifies the accuracy of the proposed method from extensive simulation results, and we finish the paper with conclusions in Section V. Throughout this paper, we use the following notations. Boldface upper-case letters and boldface lower-case letters indicate matrices and column vectors, respectively. Also, and are denoted as transpose and Hermitian transpose, respectively. The notation indicates the k-th diagonal entry of a matrix A and an N N identity matrix is defined by. The expectation operation is represented as E[.]. II. SYSTEM MODEL We consider an adaptive MIMO-OFDM system with transmit and receive antennas. In each time slot, a receiver chooses a proper modulation and coding set (MCS) according to the current channel condition and feeds back its index to the AMC controller at the transmitter. The MCS levels consist of the quadrature amplitude modulation (QAM) level and the channel code rate, which are predetermined depending on system requirements. Then, at the transmitter, based on the BICM structure, the information bits are encoded either vertically or horizontally, bit-wise interleaved and mapped to symbol constellations after serial-to-parallel conversion. After the mapping, the data symbols are modulated by the -size inverse fast Fourier transform (IFFT). Assuming proper cyclic prefix (CP), the dimensional received signal vector at the k-th subcarrier after the FFT demodulation is given by (1) where is the transmitted symbol vector, denotes the additive white Gaussian noise (AWGN) vector with zero mean and the covariance matrix, and equals the MIMO Rayleigh fading channel matrix whose entries have an independent and identically distributed (i.i.d.) complex Gaussian distribution with CN(0,1). In the absence of the channel state information at the transmitter, satisfies E[ ] = with 2

3 uniform power allocation across the transmit antennas, where P is the total transmit power. We assume that all sub channel matrices are perfectly known at the receiver. III. IMPROVED PSSR TECHNIQUE PSSR method estimates the post-detection SNR values of the MLD, denoted by,..., for a given channel matrix. First, we define the information rate of the n-th data stream from the SNRs as Then, the artificial capacity of the MIMO-MLD can be written as CML = = Here, CML means the maximum achievable rate when the MLD is employed at the receiver, which must be distinguished from the MIMO openloop capacity where (2), we simply conjecture that. Because the true values of are unknown, we adopt two simple bounds to estimate. First, an upper bound of is derived by assuming that interference among data symbols is perfectly removed at the receiver, which is called perfect interference cancellation (PIC). Also, as a lower bound, the linear minimum meansquare error (MMSE) receiver is considered. The received SNR of the PIC and the signalto-interference-plus-noise ratio (SINR) of the MMSE receiver for the n-th stream are given respectively, as (3) -1 (4) then, the corresponding instantaneous capacities and are represented as and, from these bounds, it follows that is bounded as which leads to the same relationship among the capacities as CMMSE CML CPIC. On the other hand, we can easily prove that CMMSE Copen CPIC. As a consequence, we have CMMSE CML Copen CPIC (5) where the equalities hold if all columns of H are orthogonal. Note that for a given channel H, CMMSE, Copen and CPIC are known values, while CML is unknown. From now on, we will explain how to determine the SNR values for MLD,..., by utilizing the relation (5) for vertical encoding systems. First, we introduce two parameters and to denote the ratios of the capacity gaps from (5), respectively, as α =, 0 (6) β =, 0 (7) modulation level Code rate 1/2 2/3 3/4 5/6 7/8 4-QAM QAM QAM Table I : The optimum values of β for different MCS levels where the ranges of α and β are obtained from Copen CPIC and CML Copen. In order to formulate an expression of, we also define 3

4 as the ratio of the capacity gaps for the n-th data stream as for n=1,..., naturally, may be different for all individual streams. However, these different values of,..., can not be quantitatively evaluated since is unknown. Accordingly, to simplify the derivation, we assume that all sub-streams have the same ratio of (8) for any H as =., for n=1,..., (9) SNRs and BLERs, as many as the number of FEC encoding blocks. Among existing ESM models, we adopt the RBIR approach [12] since it is simple. The RBIR of each substream can be represented by where, for n = 1,..,...(11) denotes the number of bits allocated to the k-th subcarrier at the n-th stream and SI(γ,m) is the symbol mutual information (SI) with the modulation level m derived as [12] dl. for vertical encoding systems where a single MCS is employed across streams, this approximation is true in an average sense over all channel realizations. Moreover, simulations show that,..., are not very distinct, even if H is ill-conditioned. Now, by rearranging (8) and (9), we have αβ + (1- αβ). Consequently, the SNR of the n-th substream for the MIMO- MLD is finally represented as...(10) note that in (10), and α are directly obtained from (3), (4) and (6) as a function of H, respectively. Then, only β needs to be optimized in advance via an offline process. In Table I, the optimal values of β over 15 different MCS levels are listed. Table I is valid for any MIMO antenna configurations and β is insensitive to the channel power delay profile and depends on the employed channel code. This is a very desirable feature for a good PHY abstraction method. So far, we have investigated how to estimate the post-processing SNR values of MIMO-MLD for each subcarrier from the proposed PSSR techniques. The next step is to map those SNR estimates to the effective Here, represents the probability density function of the symbol level loglikelihood ratio (LLR) of the j-th constellation point with SNR equal to [12]. To avoid repeated complex calculations, (12) is computed once for a wide range of SNRs and saved in a lookup table after scaling to [0, 1] [25, Table 25]. According to (11) and the SNR-to-SI mapping table, for each stream is obtained based on 4. Then, is inversely mapped after normalization by to get the effective SNR. In the vertical encoding case, we only need a single effective SNR estimate. This can be simply resolved by averaging RBIR values obtained from (11) over the spatial domain as Then, in the same way, RBIR is inversely mapped to the effective SNR. Finally, as the last step, the BLER of each encoding block can be directly mapped from for the vertical encoding by looking up the AWGN look-up table.

5 IV. SIMULATION RESULTS We consider an OFDM system with Nc = 64 and the CP length of 16 samples, and a coding block is set to one OFDM symbol. The channel we assumed is Rayleigh fading channel. Here we are considering vertical encoding 2 2 MIMO-OFDM system with different quadrature amplitude modulation levels. The optimum values of for different modulation levels and different code rates are tabulated in table I. Figures 1 and 2 shows the simulation results for vertically encoded 2 2 MIMO-OFDM system. From the simulation results we observe that the SNR values of the 64QAM samples are slightly more than 16QAM samples it is desirable factor. Fig 1. Link prediction accuracy for 2 2 MIMO-OFDM system using 16QAM Fig 2. Link prediction accuracy for 2 2 MIMO-OFDM system using 64QAM V. CONCLUSION In this paper, we have proposed an efficient link abstraction technique for MIMO-OFDM systems with ML receiver. With improved PSSR procedure an efficient link error prediction has been made with very low computational complexity. From the simulations we confirmed that the proposed method is quite effective. 5 VI. REFERENCES [1] G. J. Foschini and M. Gans, On Limitsof Wireless Communications in a Fading Environment when Using Multiple Antennas, Wireless Personal Communications, vol. 6, pp , March [2] R. V. Nee and R. Prasad, OFDM for wireless multimedia communications. London, UK: Artech House Publishers, [3] G. Caire, G. Taricco, and E. Biglieri, Bit- Interleaved Coded Modulation, IEEE Transactions on Information Theory, vol. 44, pp , May [4] I. Lee, A. Chan, and C.-E. W. Sundberg, Space-Time Bit-Interleaved Coded Modulation for OFDM systems, IEEE Transactions on Signal Processing, vol. 52, pp , March [5] H. Lee, B. Lee, and I. Lee, Iterative Detection and Decoding with an Improved V-BLAST for MIMO-OFDM Systems, IEEE Journal on Selected Areas in Communications, vol. 24, pp , March 2006 [6] A. J. Goldsmith and S.-G. Chua, Adaptive Coded Modulation for Fading Channels, IEEE Transactions on Communications, vol. 46, pp , May [7] R. Elliott, A. Arkhipov, R. Paulefs, and W. Krymien, Effective SINR Mapping

6 for an MC-CDMA Systems, in Proc. 5 th International Workshop on Multi-Carrier Spread Spectrum, pp , September [8] K. Sayana, J. Zhuang, and K. Stewart, Link Performance Abstraction based on Mean Mutual Information per Bit (MMIB) of the LLR Channel, IEEE Broadband Wireless Access Working Group, [9] H. Zheng and et al, Link Performance Abstraction for ML Receivers Based on RBIR Metrics, IEEE Broadband Wireless Access Working Group, [10] Ericsson, System-level evaluation of OFDM further considerations, TSG- RAN WG1 #35, R , Nov [11] K. Sayana, J. Zhuang, and K. Stewart, Link performance abstraction based on mean mutual information per bit (MMIB) of the LLR channel, IEEE C802.16m- 07/097, May [12] H. Zheng and et al., Link performance abstraction for ML receivers based on RBIR metrics, IEEE C802.16m-08/119, Mar [13] K. Sayana, J. Zhuang, and K. Stewart, Short term link performance modelling for ML receivers with mutual information per bit metrics, in Proc IEEE Globecom. [14] IEEE m Evaluation Methodology Document (EMD), Jan [15] J. Kim, K.-J. Lee, C. K. Sung, and I. Lee, A simple SNR representation method for AMC schemes of MIMO systems with ML detector, IEEE Trans. Commun.,vol. 57, pp , Oct [16] J. Kim, S.-H. Moon, C. K. Sung, and I.Lee, A new SNR prediction method for MIMO-OFDM systems with maximum likelihood detector, in Proc IEEE ICC. 6

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