Link Layer Abstraction in MIMO-OFDM System Xin He, Kai Niu, Zhiqiang He and Jiaru Lin Beijing University of Posts and Telecommunications, Beijing, China, e-mail:
[email protected] Abstract—Link layer abstraction is crucial to the crosslayer simulation and design as the interface. EESM and MIESM are two kinds of algorithms which account for the instantaneous channel realization and other configurations and obtain the estimated packet error rate correspondingly. Enhanced versions of the algorithms with weighted training are brought out in this paper, which have shown great improvements compared to the original algorithms. Plenty of simulations have been made for verifications and the results show that the enhanced abstraction algorithms can reflect the performance of the link layer of MIMO-OFDM system with high precision for higher layer simulations. Keywords—Link layer abstraction, effective SNR, EESM, MIESM
I. INTRODUCTION In system level simulations, we will focus on making transmission adaptations to optimize system performance and get better understanding of the user performance in various deployment scenarios. For complexity reasons system level evaluations should avoid the heavy physicallayer simulations and rely on simplified PHY-layer models that still must be accurate enough to capture the essential behavior. Therefore, the modeling approach of link layer is very important in the cross-layer design and simulations. The PER performance versus SINR averaged over all channel realizations of one specific channel model has been widely used as the interface between the link- and system-level simulators. But in many cases, the specific channel realization encountered may perform significantly different from the average performance. Consequently, many novel modeling approaches accounting for the instantaneous channel and interference conditions, such as capacity effective SINR metric (CESM), exponential effective SINR metric (EESM) and mutual information effective SINR metric (MIESM) have been brought forward [1]~[3]. In this paper, enhanced versions of EESM and MIESM algorithms with weighted training are brought out and introduced to MIMO-OFDM system, which show great promise in the further communication such as WLAN 11n, Wimax 16e, LTE and so on. In the second part, the link-layer abstraction procedure taking MIMO and OFDM into consideration is explained. EESM and MIESM and their enhanced version are introduced in detail in the third part. The forth part presents some verification results and a conclusion follows.
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II. LINK-ABSTRACTION PROCEDURE
SNReff
Fig. 1. Link layer abstraction procedure The abstraction model adopted in this paper which can reflect the instantaneous link layer performance consists of three main parts as shown in Fig.1. The first one covers the calculation of quality measures SINRp for all relevant Resource Elements. In the second part, an appropriate compression of the SINRp to one single parameter SNReff is performed to facilitate further processing. Finally SNReff is mapped to PER in the last step. Post-detection SINR for each spatial stream is calculated after MMSE detection and FFT algorithm. One packet is assumed to consist of P constellation points in the time/frequency space and post-detection SINR is calculated for each resource element. Note that for a given channel allocation scheme the number of SINRp per block can be reduced according to the channel conditions by considering the coherence of the fading in the time and frequency domain. All the SINRp values belonging to a particular packet are compressed to a single scalar in the second step. For a given several-dimensional vector SNR, accounting for the instantaneous channel characteristics and other configurations, the scalar SNReff is defined as the SNR in an equivalent, constant signal-to-noise ratio AWGN channel that would yield the same packet error probability as in [4]. It is the most important part of the modeling. EESM and MIESM are two examples of those algorithms to get a good approximation for the effective SNR concept, which are explained in section3. Based on the concept of effective SNR, the mapping curves from effective SNR to PER in the last step should be simulated on the simple AWGN channel and stored as look-up tables for further consulting. The goal is to cover the channel impacts and pre-/post processing in the first part. The following two steps accounting for the modulation and coding parameters and should be independent of the channel characteristics. They should be well designed so that the final PER effectively models the modulation and coding performance.
III. ABSTRACTION ALGORITHMS EESM and MIESM are two kinds of abstraction algorithms used in the step 2 described in seciton1 to transform the SNRp s to one single scalar SNReff appropriately. They both use the nonlinear nature of the mapping curves accounting for the variance and shape of the SNR probability distribution, which turn out to be good approximations for the effective SNR. A.
EESM A generalized exponential ESM is stated in (1) including a parameter β that can be adjusted to match the ESM to a specific combination of modulation scheme and coding rate. A suitable value for β for each modulation scheme and coding rate of interest can then be found through adequate link-level simulations. The exponential ESM is derived based on the Union-Chernoff bound of error probabilities, and the details can be consulted in [5]. 1 P − SNPi (1) SNReff = − β ln ∑ e β P i =1 B. MIESM MIESM uses the nonlinear mapping relationship from SNR to mutual information to approximate the effective SNR. The key formula used is expressed in (2):
1 P SINR p SNReff = α1 ⋅ I −1 ∑ I P p =1 α 2 Here, I denotes mutual information
(2)
function, accounting for the modulation type. α1 = α 2 = β is assumed for simplification in most cases, which could be optimized through simulations. In (3), mp is the bits per symbol, X is the set of symbols, Xbi is the set of symbols for which bit i equals b. Y is zero mean unit variance complex Gaussian variable. exp(− | Y − x(xˆ − z)|2 ) ∑ 1 mp 1 xˆ∈X Imp (x) = mp − EY mp ∑∑∑ log2 2 i Y x x z 2 exp( | ( )| ) − − − i=1 b=0 z∈Xb ∑ x∈Xbi (3) The mutual information function values shall be calculated off line and stored in tabular with high revolutionary for further consulting.
C. Enhanced Algorithms with Weighted Training The training of the parameter β is involved in both EESM and MIESM algorithms and the accuracy of the values obtained influence the abstraction performance directly. Up to now the β value is normally optimized by minimizing the square difference between SNReff obtained from abstraction algorithms and the effective SNR from AWGN performance curves through adequate link layer simulations as in [5]~[6]. However, it is well known that the influences of SNR distance on the PER performance varies a lot in different parts of the performance curve. And when the SNR value gets higher from a low start
point, the PER performance is more sensitive to the SNR difference. Therefore, the algorithms are enhanced by minimizing a weighted square difference between SNReff estimated and ideal effective SNR, which highlights the influences of the SNR differences in the high SNR region on the PER performance. The weight values are established by the square of relative SNR difference between the current SNR value and the SNR value where PER begins to drop on AWGN performance curve. F ( β ) = ( SNReff - SNReesm ( β ))iW
SNReff − SNRstart SNRstart
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(4)
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W =
(5)
In the cost function needed to be minimized in (4), SNReff and SNReesm are two vectors with the size of the number of simulated channel realization, and W is the weight vector with the same size expressed in (5). SNRstart is the SNR point where the PER begins to drop from 1 (PER=0.99 for example) on the AWGN performance curve. The minimization algorithm is implemented based on golden section search and parabolic interpolation. The enhanced version with weighted training shows great improvements on the abstraction performance through adequate simulations. IV. SIMULATIONS FOR VERIFICATIONS Some verifications are presented in this section to show the abstraction performance when the enhanced abstraction algorithms are applied to MIMO-OFDM system. A.
Simulation condition
Fig. 2.Transmitter architecture The link layer architecture at the transmitter side in our simulation is shown in Fig.2. The beta training and verifications are taken under SCM Channel with 2 transmitting antennas and 2 receiving antennas and the velocity of 3Km/h. Ideal channel estimation is assumed. Only one spatial stream is used with spatial spreading as the MIMO precoding scheme. CTC is adopted as channel coding. The modulation and code set is shown in table1. Table 1: Modulation and code rate set Index Mod 1 QPSK 2 QPSK 3 16QAM
Rate Encoded data block size (bytes) 1/2 12 3/4 72 1/2 72
Post-detection SINR after MMSE detection is defined as: MH
2
(4) 2 2 σ M M is the weight vector used in the MMSE detection. 2 σ is the power of the white Gaussian noise involved in the system and H is the effective equivalent channel here. H=HrealQ, while Hreal is the real MIMO channel and Q is 2 represents calculating the MIMO precoding matrix. the norm of a vector. The curves of PER (from the link layer simulations) vs. the effective SNR (transformed from the second step of the abstraction modeling approach with the same SNR in the link layer simulation as its input) are compared with those PER performance curves simulated in the AWGN channel to show the abstraction performance. 300 independent channel realizations are simulated and marked with dots in each figure.
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Fig.3(a): Abstraction performance comparison (original EESM) beta=1.4
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Fig.3 (b): Abstraction performance comparison (enhanced EESM) beta =1.6 abstraction performance enhanced MIESM for format1
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Simulation results We can see from the figures that the dots simulated under different independent channel realizations are distributed closely around the AWGN curve which is marked with a solid line. It means that the abstraction model which estimate its PER from the AWGN curve for all channel realizations is quite close to the performance getting from simulations. From the comparison of Fig.3(a) and Fig.3(b), we can see that estimated PER from the enhanced EESM is much more close to the real PER when the SNR is high. The beta value optimized through the original EESM algorithm and the enhanced version are 1.4 and 1.6 respectively. And the mean square of PER estimation errors among all channel realizations is 0.05 and 0.03 respectively. Note that the major advantage of enhanced version is the improvements of performance when SNR is higher which is more interested in the higher level simulation. Comparing Figure3 (b) with Fig.4, Fig.5(a) with Fig.5(b) and Fig.6(a) with Fig.6(b), in which mean square of PER estimation errors are 0.03,0.008, 0.08, 0.04, 0.09, 0.07 respectively, we can see that in most cases, enhanced MIESM algorithm outperforms the enhanced EESM algorithm in link layer abstraction. And also we can see that abstraction performance of both algorithms declines when higher order modulation is adopted from format 1 to format 3. That is because the higher-order modulation in itself can be seen as a multi-state channel from a binary- symbol transmission point-of-view and both algorithms can not provide such tight error probability bounds for higher-order modulations as for QPSK modulation. Adequate simulations have been done to verify abstraction performance in our work, but we cannot put out all the results here. The simulation results show that the stand deviations from the abstraction of the enhanced algorithms to the real performance are less than 0.1dB in most cases, which means that the enhanced abstraction algorithms can reflect the characteristics of the link layer
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with high accuracy degrees and, therefore, guarantee high reliability for system-layer design and simulations.
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Fig.4: Abstraction performance of enhanced MIESM for format 1beta=1.0
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Fig.5 (a): Abstraction Performance of Enhanced EESM for format 2 beta=1.7
Fig. 6(b): Abstraction Performance of Enhanced EESM for format 3 beta=1.0
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V. CONCLUSION
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Fig.5 (b): Abstraction Performance of Enhanced MIESM for format 2 beta=1.1 abstraction performance enhanced EESM for format 3
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The link layer abstraction is crucial for the higher layer simulation to focus on the adaptations and other techniques. The enhanced versions of EESM and MIESM algorithms with weighted training are brought out in this paper, which are applied to MIMO-OFDM system and have shown great improvements in the abstraction performance compared to the original algorithms. The link layer abstraction procedure based on the enhanced algorithms turns out to be excellent with high accuracy of the PER estimation performance in MIMO-OFDM system. However, we have to know that the whole theory of the abstraction algorithm is just a good kind of approximation but could never be exactly the same to the real system, especially when the modulation and code rate is high. Through plenty of simulations in our work, we can conclude that the stand deviations from the enhanced abstraction algorithm to the real performance are less than 0.1dB and enhanced MIESM outperforms enhanced EESM in most cases. They are both accurate enough to reflect the performance of the real link layer for higher layer simulations. REFERENCES [1]
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Fig.6 (a): Abstraction Performance of Enhanced EESM for format 3 beta=5.2 [4]
[5] [6]
IST–2000–30116 FITNESS Project, “MTMR Baseband Transceivers Needs for Intra-system and Inter-system (UMTS/WLAN) Reconfigurability”, Deliverable D3.3.1 “Effective SNR mapping for modelling frame error rates in multiple-state channels”, 3GPP2-C30-20030429-010, April 2003 K. Brüninghaus, D. Astely, Th. Sälzer, S. Visuri, A. Alexiu, St. Karger, G. A. Seraji, “Link Performance Models for System Level Simulations of Broadband Radio Access Systems”, PIMRC, Berlin 2005 S. Nanda and KM. Rege, ”Frame Error Rates for Convolutional Codes on Fading Channels and the Concept of Effective Eb/N0”, IEEE Trans. On Veh. Techn., Vol. 47, No. 4, pp. 1245–1250, November 1998 “System-level evaluation of OFDM – further considerations”, R10313103, RAN WG1 #35 “Effective SINR approach of link to system mapping in ofdm/multi-carrier mobile network”, Esa Tuomaala, 2005
