doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 1 Time-Correlated Packet Errors in MAC Simulations Angelo Poloni and StefanoValle STMicroelectronics Gianluca Villa Politecnico di Milano

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 2 Introduction MAC simulations require time-correlated packet errors in order to emulate PHYs in a realistic way. Simple Markov chains (Good/Bad channel), proposed so far, seem to be a rough approximation of the channel behavior [1]. Information Theory provides the “Channel Capacity” (CC) concept; CC is a suitable metric to predict PHY performances [2]. The “instantaneous” value of the CC can be used to predict the “instantaneous” packet error probability.

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 3 Basic idea “Instantaneous” CC at time is a function of the channel transfer function and of the average SNR; The “instantaneous” CC can be considered a stochastic process. It can be proved experimentally that, once the PHY is defined, the instantaneous PER is a function of CC If PER versus CC is available from link-level simulations (e.g. as a Look-Up-Table[LUT]), it is sufficient to generate the stochastic process that represents the CC versus time in the MAC simulator. Its instantaneous value can be used to read the PER LUT.

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 4 CC for frequency selective SISO channel Assumption: channel flat in each OFDM sub- carrier (SC) bandwidth Capacity on k-th OFDM sub-carrier is given by CC can be considered as the sum of the Capacities on each SC

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 5 Simulation conditions u a standard u Rate 6 Mbps u Channel model “B” (as defined by n standard) u E s /N 0 = 8 dB Instantaneous PER versus instantaneous CC Erroneous packets are in correspondence of low CC

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 6 PER versus CC a Rate 6 Mbps Channel model “B” (802.11n standard) E s /N 0 [0:4:20] dB

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 7 CC stochastic process In order to simulate the CC stochastic process in MAC simulators it is necessary to have its statistical characterization. This is done in the next two slides. After that an approach to reproduce such process in a MAC simulator is proposed.

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 8 Characterization of CC: pdf Channel model “B” (802.11n standard)

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 9 Characterization of CC: mean and standard deviation Es/N 0 Capacity [Mbps] mean std

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 10 Generation of CC stochastic process Emulate the stochastic process with a Birth-Death Markov process [3] Pros : –easy to implement; –low loading of MAC simulator. Cons : –Relative high number of LUTs. 0 Mbps5 Mbps# Mbps …

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 11 Characterization of Markov chain 1/2 Transition probabilities are given by the following matrix (4 state Markov chain is assumed for simplicity) Matrix can be estimated form a discrete version of the CC versus time curve.

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 12 Characterization of Markov chain 2/2 Only contiguous states transitions are allowed Contiguous states are uniformly spaced; capacity step is  C. The assumption of transitions towards contiguous states only is not obvious. In order to guarantee that such assumption is correct, it is necessary that Markov chain time clock (  t) is sufficiently small. A conservative condition is obtained through the following considerations: –Assume the capacity process to be a sinusoid with frequency f D (Doppler Spread); –The condition for having a capacity step less than  C in a time step  t is

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 13 Example of Markov chain characterization 1/2   C = 15 Mbps   t = 1 ms  Channel: IEEE B  SNR = 0,4,8,12,16,20,24 dB  Transition probabilities for each SNR are plotted in the next slide

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide capacity [Mbps]  i i capacity [Mbps]  i,i capacity [Mbps]  i,i+1 SNR = Example of Markov chain characterization 2/2  i,i  i,i-1  i,i+1

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 15 Markov chain in MAC simulator Channel Capacity Emulation (Markov Chain) Erroneous Packet Rando m draw Packet OK Mean SNR Shadowing Propagation Law LUT: Markov chain transition probabilities LUT: PER vs SNR vs CC Distanc e

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 16 Erroneous packet event: drawing methods Random draw methods: –draw for erroneous packet event every new packet (Method 1); –draw for erroneous packet event every new capacity state (Method 2).

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 17 Preliminary Model validation Validation metrics are: –average PER; –Average Burst Error Length (ABEL); –Standard Deviation of Burst Error Length (STDBEL).

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 18 Validation results 1/3   C = 15 Mbps   t = 1 ms  Channel: IEEE B  Random draw: method 1

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 19   C = 15 Mbps   t = 1 ms  Channel: IEEE B  Random draw: method 2 Validation results 2/3 PER ABEL STDBEL SNR

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 20 Validation results 3/3 PER ABEL STDBEL SNR PHY behavior Markov model PHY behavior Markov model PHY behavior Markov model   C = 2 Mbps   t = 1 ms  Channel: IEEE B  Random draw: method 2

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 21 Comments on model validation PER matches the PHY behavior. Matching ABEL and STDBEL is the most critical aspect: –in the special case here presented, promising results have been obtained by shortening the Capacity Step of the Markov Chain and by using the Draw method number 2; –a general rule for calibrating the Capacity Step is still unknown.

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 22 Summary of the simulation method Link level simulator PER versus SNR CC Channel only simulator (SNR, channel model) CC versus TIME versus SNR CC MARKOV CHAIN (transition probabilities) Statistical analysis MAC simulator N.B., Channel only simulator, Link level simulator and MAC simulator run separately

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 23 Some comments Channel state is condensed in a single number (CC versus time): overloading of MAC simulators is avoided. CC versus time can be easily reproduced by other parties and thus it can be easily standardized. PHY behaviors (PER versus time) can be easily included and updated with LUTs (PER versus CC). A method for including the effects of interferers will be investigated in the near future. The same approach is applicable to MIMO channels and PHYs.

doc.: IEEE n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 24 References 1.J. M. McDougall, “Low Complexity Channel Models for Approximating Flat Rayleigh Fading in Network Simulations”, PhD Dissertation, Texas A&M University, August IST- FITNESS D4.3, “Simulation Platform Structure and System Level Performance Evaluation” ( ) 3.Hong Shen Wang, Moayeri, N., “Finite-state Markov Channel-a Useful Model for Radio Communication Channels”, IEEE Transactions on Vehicular Technology, Feb Volume 44 Number 1.