Transcript
Lecture ( 4 Mar. 2015)
4/25/2015
Modelling Multipath Signals
Direct Signal, Angle of Arrival and Doppler Shift
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Lecture ( 4 Mar. 2015)
4/25/2015
Direct Signal, Angle of Arrival and Doppler Shift
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Direct Signal, Angle of Arrival and Doppler Shift
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Lecture ( 4 Mar. 2015)
4/25/2015
Direct Signal, Angle of Arrival and Doppler Shift
Direct Signal, Angle of Arrival and Doppler Shift
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Lecture ( 4 Mar. 2015)
4/25/2015
Direct Signal, Angle of Arrival and Doppler Shift
Direct Signal, Angle of Arrival and Doppler Shift
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Lecture ( 4 Mar. 2015)
4/25/2015
Direct Signal, Angle of Arrival and Doppler Shift
Matlab Code [1/4] clear all; close all; clc; % basic inputs ============================= fc=2e9; % Hz Carrier frequency F=16; % sampling rate: fraction of wave length V=10; % m/s MS1 speed NFFT=128; % Number of points in FFT Nsamples=100; % Number of samples % geometry inputs =========================== dBS=1000; % distance of BS to origin alpha = 180; % degree. Angle of BS-MS with MS route % inidirect gemeotric parameters ================ BSx=dBS*cosd(alpha); % loc of BS x-coord BSy=dBS*sind(alpha); % loc of BS y-coord
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Matlab Code [2/4] % indirect parameters =========================== c=3e8; lambdac=c/fc; % m wavelength Dx=lambdac/F; % m sampling spacing ts=Dx/V; % s time sampling interval fs=1/ts; % Hz sampling frequency kc=2*pi/lambdac; % propagation constant timeaxis=ts.*[0:Nsamples]; disaxis=Dx.*[0:Nsamples];
% s elapsed time axis % n traveled distance axis
MSx=V.*timeaxis; % MS route sampling points % radio path length============================== distBSMS=sqrt((BSx-MSx).^2+(BSy).^2);
Matlab Code [3/4] % complex envelope: amplitude and phase =============== r=1*exp(-j*kc.*distBSMS); % complex envelope spectrum ====================== spectrumr=fftshift((abs(fft(r,NFFT))).^2); freqaxis=[0:NFFT-1]*fs/NFFT-fs/2;
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Matlab Code [4/4] % Plots ===================================== figure,plot(timeaxis,abs(r)) xlabel('Time (s)') ; ylabel('Magnitude of complex envelope'); figure,plot(disaxis,unwrap(angle(r))) xlabel('Traveled distance (m)'); ylabel('Absolute phase of complex envelope (rad)'); figure,plot(disaxis,angle(r)) xlabel('Traveled distance (m)'); ylabel('Modulo-\pi phase of complex envelope (rad)') figure,plot(freqaxis,10*log10(spectrumr)-max(10*log10(spectrumr))) xlabel('Doppler shift (Hz)') ylabel('Normalized frquency response (dB)')
Direct and Reflected Signals
D=
DR=
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Lecture ( 4 Mar. 2015)
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Direct and Reflected Signals
DR=
D=
Direct and Reflected Signals
D=
DR=
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4/25/2015
Direct and Reflected Signals
D=
DR=
Dropping fixed phases,
Direct and Reflected Signals
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Direct and Reflected Signals
Two Scatterers
No LoS signal
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Two Scatterers
Two Scattering points
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Two Scattering points
Multiple Scattering points
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Multiple Scattering points
Multiple Scattering points
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Mobile-to-Mobile Communications
Assignment 2 Question No. 1: Find a relationship for the Doppler shift frequency and complex envelopes of the received signal if the transmitted signal is an unmodulated RF signal. • mobile-to-mobile communication scenario, i.e., both ends are moving. • Initial distance between M1 and M2 is d. • Only LoS path exist (single path). • M1 is moving with a velocity v1 and M2 is moving with a velocity v2, directly towards/away-from each other. Question No. 2: Repeat question no. 1 for a the direction of MSs’ motion generalized by parameter α, i.e., • M1 is moving in a direction α1 w.r.t. LoS path with a velocity v1. • M2 is moving in a direction α2 w.r.t. LoS path .with a velocity v2. Question No. 3: Extend simulations in question no. 2 by taking multipath into account. Take fixed number of reflectors at fixed locations.
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The Clarke’s Model
p(α)
0
α
The Clarke’s Model
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Fading Statistics • Second order statistics • Level Crossing Rate (lcr). The average number of times the signal crosses a given threshold, R, within a given observation time, T, with either a positive or negative slope
• Average Fade Duration (afd). The ratio between the total time the received signal is below a reference level, R, and the total number of fades. o These two parameters are of interest since they can help in the selection of the most suitable error protection coding scheme and interleaving algorithm. o The afd helps determine the most likely number of bits that may be lost during a fade.
Second order statistics (lcr)
R
lcr: ;
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Second order statistics (afd)
R
afd: For Rayleigh distribution case:
Second order statistics
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Second order statistics
In order to detect about 50% of the fades (i.e., 30 dB) below the rms level, the signal must be sampled every 0.0126λ, which means a fraction, F, of the wavelength of approximately 79.
Random FM • Channel gives rise to random amplitude and phase variations, together with Doppler shifts. • One further effect caused by the channel is random frequency modulation. • Random FM, which is more marked at the deep fades, can be considered as an additional noise source affecting the transmitted signal, especially if a frequency-sensitive detector is used. • The random FM caused by the channel can be calculated as,
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Random FM
Autocorrelation of complex envelops.
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Directional Antenna A directional antenna is an antenna which radiates higher power in selective directions.
Using Directional Antenna p(α) γ 0
α
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Using Directional Antenna
A narrower spectrum means slower variations.
Using Directional Antenna
A wider spectrum means faster variations.
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Angle- and Time- of-Arrival Statistics (USM) AoA: Distribution of power w.r.t. physical angles of arriving multipath signals. ToA: Distribution of power w.r.t. delay of arriving multipath signals.
Angle- and Time- of-Arrival Statistics (GSM).
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Angular Shape factors • Angular Span • Angular Spread.
• Shape factor
Angular Shape factors • Mean of AoA
• Direction of Maximum fading.
• Angular Constriction
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Angular Spread (Shape factor)
Angular Constriction
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