September 2000 doc IEEE 802 11 00296 r

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Suggested Phase Noise Model for 802. 11 HRb Mark Webster and Mike Seals Intersil Corporation September, 2000 Submission 1 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Overview • This presentation recommends a phase-noise model for 802. 11 HRb proposals. • Phase noise impacts packet-error-rate. • The model is a fair representation of phase noise behavior and “ideal” carrier recovery loops. • The model is easy to use. • Used by 802. 11 a. Submission 2 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 VCO Phase Noise and Ideal 2 ndorder Carrier Recovery Loops F 3 d. B freq VCO d. Bc/Hz -20 d. B/dec VCO PLL Trk Resp. 2 nd-order PLL freq +20 d. B/dec F 3 d. B Output Composite freq -20 d. B/dec Assumes Ideal Phase Detector Submission 3 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Equivalent Phase Noise Model F 3 d. B Randomly Pre-energize to prevent Startup Transient 1 st-order LPF AWGN freq AWGN PSD Submission 1 storder LPF freq Output Composite -20 d. B/dec F 3 d. B freq -20 d. B/dec Matches Composite Hardware Effect 4 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Two Free Parameters F 3 d. B Composite Phase Noise freq Pssb d. B -20 d. B/dec Free Parameters 1. 3 d. B bandwidth 2. SSB Phase noise level at 0 Hz (or RMS Phase noise) Submission 5 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Equivalent Noise Bandwidth of 1 -pole Butterworth Filter used for phase noise shaping. R C Submission 6 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Compute RMS Phase Noise as Function of Flat SSB Power Pssb d. B F 3 d. B freq Pssb d. B Phase Noise Submission -20 d. B/dec 7 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code Usage % Settable parameters. vco. Pn. Deg. Rms = 1; vco. Pn. Bw. Hz = 10 e 3; n. Samples = 1 e 6; chan. Samp. Rate. MHz = 44; % % Desired RMS phase error in degree. LPF 3 d. B bandwidth in Hz. Length of transmit signal (packet). Signal (packet) sample rate. %---------------------------------* % Monte-Carlo simulation to verify model. % Note, the 1 -pole filter has a start-up transient. % But, that is OK for examining effects of phase deviations. % Output samples have the form exp(j*radian_deviation). %---------------------------------* % Generate a VCO sample waveform. vco. Pn. Phasor = Phz. Noise. Gen( vco. Pn. Deg. Rms, vco. Pn. Bw. Hz, . . . n. Samples, chan. Samp. Rate. MHz); % Phase-noise distort signal out. Sig = in. Sig. * phz. Noise. Submission 8 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code for Generator (page 1 of 3) %*********************************** % Phz. Noise. Gen. m % % VCO Phase Noise modeled using a 1 -pole Butterworth filter to % give 20 d. B/dec slope. Gaussian white noise is passed % through the Butterworth filter, with the correct level % to generate the radian variation. Output samples have % the form exp(j*radian_deviation). % % Input parameters: % % vco. Pn. Deg. Rms % Desired RMS phase error in degrees. % vco. Pn. Bw. Hz % LPF 3 d. B bandwidth in Hz. % n. Samples % Size of output vector. % chan. Samp. Rate. MHz % Simulation sample rate. % % Output parameters: % % phz. Noise % n. Samples length complex vector. % % Each sample has abs() equal to 1; % % Example usage: % % out. Sig = in. Sig. * phz. Noise. % % % Mark Webster September 19, 2000 %*********************************** function phz. Noise = Phz. Noise. Gen( vco. Pn. Deg. Rms, vco. Pn. Bw. Hz, n. Samples, chan. Samp. Rate. MHz) Submission 9 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code for Generator (page 2 of 3) % Design VCO phz noise filter. % 1 -pole Butterworth. vco. Pn. NPoles = 1; % Gives 20 d. B/dec phase-noise roll-off. chan. Samp. Rate. Hz = chan. Samp. Rate. MHz * 1 e 6; Wn = 2 * vco. Pn. Bw. Hz / chan. Samp. Rate. Hz; [vco. Pn. B, vco. Pn. A] = butter( vco. Pn. NPoles, Wn); % Compute the resulting RMS phz noise in d. Bc/Hz. vco. Pn. Radians. Rms = vco. Pn. Deg. Rms * pi/180; vco. Pn. Var = vco. Pn. Radians. Rms ^ 2; excess. Bw 1 Pole. Butter = pi/2; % Relative excess bandwith of 1 -pole filter. vco. Pn. Pwr. Per. Hz. One. Sided = vco. Pn. Var / (vco. Pn. Bw. Hz * excess. Bw 1 Pole. Butter) ; vco. Pn. Pwr. Per. Hz. Ssb = vco. Pn. Pwr. Per. Hz. One. Sided / 2; vco. Pn. Lvld. Bc. Per. Hz. Ssb = 10 * log 10( vco. Pn. Pwr. Per. Hz. Ssb ); % Compute AWGN source level feeding Butterworth filter. awgn. Pwr = vco. Pn. Pwr. Per. Hz. Ssb * chan. Samp. Rate. Hz; awgn. Pn. Rms = sqrt(awgn. Pwr); Submission 10 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code for Generator (page 3 of 3) % Pre-energize lowpass filter to eliminate start-up transient % by setting initial lowpass filter state. % Energize with Gaussian variable equal to desired rms phase noise. lp. Filt. Init. State = vco. Pn. Radians. Rms*randn; % Generate a VCO phase-noise sample waveform. awgn. Pn = awgn. Pn. Rms * randn(n. Samples, 1); colored. Gaussian. Pn = filter(vco. Pn. B, vco. Pn. A, awgn. Pn, lp. Filt. Init. State); phz. Noise = exp(j*colored. Gaussian. Pn); Submission 11 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code for Test Shell (page 1 of 3) %*********************************** % Main. Phz. Noise. Test. m % % This routine tests the procedure for simulating phase noise % using 1 -pole LPF spectral shaping. In this routine, the user % sets % % (1) The 3 d. B bandwidth of the LPF filter % (2) The desired RMS phase noise in degrees. % (3) The number of phase noise samples desired. % (4) The simulation channel sample rate. % % Simulation verifies the model. % % Mark Webster September 9, 2000 %*********************************** clear all close all % Settable parameters. vco. Pn. Deg. Rms = 1; vco. Pn. Bw. Hz = 10 e 3; n. Samples = 1 e 6; chan. Samp. Rate. MHz = 44; Submission % % Desired RMS phase error in degree. LPF 3 d. B bandwidth in Hz. Length of transmit signal (packet). Signal (packet) sample rate. 12 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code for Test Shell (page 2 of 3) %---------------------------------* % Monte-Carlo simulation to verify model. % Note, the 1 -pole filter has a start-up transient. % But, that is OK for examining effects of phase deviations. % Output samples have the form exp(j*radian_deviation). %---------------------------------* % Generate a VCO sample waveform. vco. Pn. Phasor = Phz. Noise. Gen( vco. Pn. Deg. Rms, vco. Pn. Bw. Hz, . . . n. Samples, chan. Samp. Rate. MHz); % Estimate the VCO's output phz noise in degrees RMS. deg. Rx = angle(vco. Pn. Phasor) * 180/pi; deg. Rms. Est = sqrt(mean(deg. Rx. ^2)); Submission 13 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Matlab Code for Test Shell (page 3 of 3) %-------------------* % Plot and print stochastic results. %-------------------* figure plot(deg. Rx) grid xlabel('sample #') ylabel('Degrees') str = sprintf('Phz Noise Sample: %2. 2 f degrees', deg. Rms. Est); title(str) disp(' ') disp('***********') str = sprintf('Target RMS phz error (degrees): %d', vco. Pn. Deg. Rms); disp(str) str = sprintf('Estimated RMS phz error (deg) using %d samples: %d', . . . n. Samples, deg. Rms. Est); disp(str) disp('**********') disp(' ') Submission 14 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Example Test Shell Output *********** Target RMS phz error (degrees): 1 Estimated RMS phz error (deg) using 1000000 samples: 1. 005964 e+000 ********** Submission 15 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Zoomed Plot of Test Shell Output Start-up Transient Avoided by Pre-energizing Lowpass Filter with Gaussian variable having desired RMS degree phz noise. Submission 16 M. Webster, Mike Seals

September 2000 doc. : IEEE 802. 11 -00/296 r 1 Summary • • Recommend 1 -pole phase noise shaping. Use 3 d. B bandwidth of 20 KHz. Sweep RMS phase noise in degrees. Show influence on Carrier Degradation in AWGN. • Start-up transient is avoided. • Caveat: assumes “ideal” carrier recovery loop. Submission 17 M. Webster, Mike Seals