Multipath Simulation Models for Sub-GHz PHY Evaluation

1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: [Multipath Simulation Models for Sub-GHz PHY Evaluation] Date Submitted: [October 2004] Source: [Paul Gorday] Company: [Motorola] Address: [8000 W. Sunrise Blvd., Plantation, FL, 33322, USA] Voice:[+1 561 723 4047], E-Mail:[paul.gorday@motorola.com] Re: [ IEEE 802.15.4 ] Abstract: [This contribution presents two multipath simulation models for use in evaluating and comparing optional sub-GHz PHYs.] Purpose: [To document channel models used for PHY evaluation.] Notice: This document has been prepared to assist the IEEE P802.15. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15. Paul Gorday, Motorola

2. Two Multipath Models • Two analytical multipath channel models are defined for evaluating optional sub-GHz PHY performance. • Diffuse exponential model • Presented in 802.11 Handbook [1] and recommended for narrowband systems by TG3a channel modeling sub-committee [2] • Preferred for baseband simulations • Discrete exponential model • Sampled version of diffuse model • Acceptable alternative for simulations with high sampling rates Paul Gorday, Motorola

3. Diffuse Exponential Model • Diffuse – each delay bin • contains multipath energy • Exponential – average power • decays exponentially • Fading - each delay bin has • independent Rayleigh fading • Single Parameter: • RMS delay spread   • Mean excess delay  • Max excess delay (10 dB)  2.5 • Max excess delay (20 dB)  5 k2 = Normalized Average Power C = Normalization Constant Ts = Simulation Sample Period k = Bin Number kmax 5/Ts Normalized Average Power (Depicted:  = 4Ts) k (Bin #) Power-Delay Profile Paul Gorday, Motorola

4. Diffuse Exponential ModelBaseband Simulation • Each channel realization can be simulated using an FIR filter (tapped delay line), where the tap weights are independent complex Gaussian random variables with zero mean and variance given by the power delay profile. In other words, the FIR coefficients are: where N(m,2) is the normal, or Gaussian, random variable. • Assume quasi-static channel, such that h(k) is constant during packet. • One or more packets are sent for each channel realization. • At least 1000 random channel realizations for each PER value. Paul Gorday, Motorola

5. Diffuse Exponential ModelExample Matlab Code for Baseband Simulation • Variable description signal_in = input to channel model signal_out = output of channel model profile = power-delay profile channel = random realization of the channel kmax = maximum tap index for power-delay profile tau = RMS delay spread Ts = simulation sampling period • Sample Matlab Code kmax = ceil (5*tau/Ts); profile = exp(-(0:kmax)*Ts/tau); profile = profile/(sum(profile)); channel = sqrt(profile/2).*(randn(size(profile))+j*randn(size(profile))); signal_out= conv(channel,signal_in); Paul Gorday, Motorola

6. Discrete Exponential Model • For simulations with high sampling rates, the diffuse model leads to long FIR filters when modeling large delay spreads. This increases complexity and reduces simulation speed. • An acceptable alternative in such cases is to use a discrete, or sampled version of the diffuse exponential model. • The taps (rays) are uniformly spaced by L samples, such that: • RMS delay spread = 1.85LTs • Max excess delay = 10LTs • Avg. power of last ray is 22 dB lower than avg. power of first ray Paul Gorday, Motorola

7. Discrete Exponential ModelPower-Delay Profile • The power-delay profile for this discrete model is tabulated below. Paul Gorday, Motorola

8. Discrete Exponential ModelBaseband Simulation • Each channel realization can be simulated using a tapped delay line, where the tap weights are independent complex Gaussian random variables with zero mean and variance given by the power delay profile. In other words, the tap weights are: • The taps are uniformly spaced by L samples. • Assume quasi-static channel, such that h(k) is constant during packet. • One or more packets are sent for each channel realization. • At least 1000 random channel realizations for each PER value. Paul Gorday, Motorola

9. Discrete Exponential ModelExample Matlab Code for Baseband Simulation • Variable description signal_in = input to channel model signal_out = output of channel model profile = power-delay profile channel = random realization of the channel L = number of samples between rays (RMS delay spread = 1.85LTs) • Sample Matlab Code profile = zeros(1,10*L+1); profile(1:L:end) = exp(-(0:10)/2); profile = profile/(sum(profile)); channel = sqrt(profile/2).*(randn(size(profile))+j*randn(size(profile))); signal_out = zeros(size(signal_in)); for k = 0:10 signal_out=signal_out+channel(k+1)*[zeros(1,k*L) signal_in(1:length(signal_in)-k*L)]; end Paul Gorday, Motorola

10. References [1] B. O’Hara and A. Petrick, IEEE 802.11 Handbook – A Designer’s Companion, IEEE Press, 1999. [2] J. Foester, “Channel Modeling Sub-committee Report (Final),” IEEE P802.15-02/490r1-SG3a, Feb. 2003. Paul Gorday, Motorola