Doppler shift in wireless communications

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The base station sends a carrier signal. The car receives the signal.

The base station sends a carrier signal s( t )=cos( 2π f c t ) . Where f c is the carrier frequency.

The wave needs the time t 0 to reach the car.

The car receives a delayed signal r t = r ^ cos 2π f c (t t 0 ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaa5dqaaaaa aaaaWdbiaadkhadaqadaWdaeaapeGaamiDaaGaayjkaiaawMcaaiab g2da9iqadkhapaGbaKaapeGaci4yaiaac+gacaGGZbWaaeWaa8aaba WdbiaaikdacqaHapaCcaWGMbWdamaaBaaaleaapeGaam4yaaWdaeqa aOGaaiika8qacaWG0bGaeyOeI0IaamiDa8aadaWgaaWcbaWdbiaaic daa8aabeaakiaacMcaa8qacaGLOaGaayzkaaaaaa@4B1B@ .

When the car moves away an additional signal propagation delay occurs.
When the car moves further away an additional signal propagation delay occurs: t 1

Now the car receives the signal r t = r ^ cos 2π f c (t t 0 t 1 ) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaa5dqaaaaa aaaaWdbiaadkhadaqadaWdaeaapeGaamiDaaGaayjkaiaawMcaaiab g2da9iqadkhapaGbaKaapeGaci4yaiaac+gacaGGZbWaaeWaa8aaba WdbiaaikdacqaHapaCcaWGMbWdamaaBaaaleaapeGaam4yaaWdaeqa aOGaaiika8qacaWG0bGaeyOeI0IaamiDa8aadaWgaaWcbaWdbiaaic daa8aabeaak8qacqGHsislcaWG0bWdamaaBaaaleaacaaIXaaabeaa kiaacMcaa8qacaGLOaGaayzkaaaaaa@4E11@

Where

The received signal yields to:

r( t )= r ^ cos( 2π f c ( t vt c ) φ 0 )= r ^ cos( 2π( f c v c f c )t φ 0 )

Where we can identify a frequency shift that is known as Doppler shift:

f D = v f c c

Note that an angle between wave propagation and velocity needs to be considered.

The Doppler frequency shift is proportional to the relative velocity and the carrier frequency.

f D = v f c cos( α ) c

Where

In channels where transmitter and receiver move relative to each other the signal frequency is shifted depending on the velocity. This so-called Doppler effect can be observed on passing cars, moving stars (redshift of light) and wireless communications.

Start

In addition to the video Doppler shift the received signal can be analyzed in the simulation. Start the simulation. Note that the setup is exactly the scenario in the video:

Doppler
The transmission frequency is 1 GHz.
doppler shift
After the car has accelerated the Doppler shift is 40 Hz in the scenario in the video and this simulation.

Experiment

In the video you were asked to calculate the speed of the car. Now check your result: The car moves with a speed of 12 m/s towards the transmitter.

That can be verified experimentally by changing the speed of the car. Click on Doppler multipath channel in the block diagram. Watch the impact on the Doppler shift.

Furthermore change the angle e.g. 180, 90, 30.

Video Doppler shift: Calculate the speed of the car!

All details you need for doing that are given in the video:

The car's speed yields to:

v= f D c f c = 40Hz3 10 8 m/s 1GHz =12m/s

Next Steps

Due to reflections, fading and shadowing there are more transmission paths than the direct one. Think about how the spectrum looks under this condition.

Start the simulation Doppler shift in wireless communications - 2 paths