# New experiment 4

## Simulation of various important transmission parameters

-BASIC CONDITIONS

-MODULATION

-TRANSMISSION ATTENUATION

-DEMODULATION

-OFFSET CORRECTION

-DIFFERENCE TO REAL TRANSMITTION

## Basic conditions

This simulation shows how an optical QPSK (quadrature phase shift keying) works with an homodyne receiver (with this modulation type, we can transfer more bits per symbol("2bits")). So we ignore phase shift of the different components, ignore the influence of temperature, use ideal lasers with the exact wavelength and the exact phase for an better comprehension of the theoretical knowledge. The mechanism of action in the optical transmission is that you change the electrical signal into an optical signal with a modulator. Then send it through an optical fiber. The signal is demodulated at the receiver and converted back into an electrical signal by using a photodiode. In this simulation, we use the homodyne transmission. The important thing in this transmission type is the intermediate frequency with 0 difference between the local laser and the receive signal. In a real QPSK, a phase measurement with subsequent phase correction is necessary.

Illustration: optical QPSK simulation>

## Modulation

The modulator consists of a signal generator, an I/Q splitter, a rectpulse shaper for the I and the Q ways, a local laser and a "Mach-Zehnder-Interferometer" (see Wikipedia) with $LiNb{O}_{3}$ The signal goes to the I/Q splitter and gets separated into the I way and the Q way. Then it goes into the rectpulse shaper for a defined form and a voltage level on the both ways of the Mach-Zender-Interferometer that is feeded with the local laser. The used effect is that, $LiNb{O}_{3}$ changes its refractive index (changes the phase) and you can calculate the phase shift with the formula. $\phi =\frac{{\omega }_{0}L\Delta {n}_{eff}}{c}$ In the Q way it is 90° or 270° and in the I way it is 0° or 180°. At the end of the interferometer, we add both ways and produce the four phase shifts( +-45° and +-135°). This signal goes to the optical fiber.

Illustration: optical QPSK modulator>

## TRANSMISSION ATTENUATION

In this simulation,we use the transmission attenuation of the optical fiber with the length and the attenuation per km. Further you can add an additional attenuation such as a radius. To keep the simulation easier, we ignore the dispersion and the phase shift of the optical fiber. The transmission can be calculated using the following formulas. $S E = S S *a²= r ^ ²⇒ r ^ = S S *a MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa aaleaacaWGfbaabeaakiabg2da9iaadofadaWgaaWcbaGaam4uaaqa baGccaGGQaGaamyyaiaacklacqGH9aqpceWGYbGbaKaacaGGYcGaey O0H4TabmOCayaajaGaeyypa0ZaaOaaaeaacaWGtbWaaSbaaSqaaiaa dofaaeqaaaqabaGccaGGQaGaamyyaaaa@48B8@$ $a=d*m$

## DEMODULATION

For the demodulation we split the signal into two ways. To one way you add a local laser with 90° phase shift and to the other way you add a local laser with 0° phase shift. The power is added or subtracted by interference. After mixing, the signals are sent to two photodiodes and are changed into an electrical signal. There is now an electrical Q-signal and I-signal. To form a correlation piont both signals are combined. $c=10V; c ^ ² 2 =50V²→Locallaser=100V²→Locallaser=20dBm MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaiabg2 da9iaaigdacaaIWaGaamOvaiaacUdadaWcaaqaaiqadogagaqcaiaa cklaaeaacaaIYaaaaiabg2da9iaaiwdacaaIWaGaamOvaiaacklacq GHsgIRcaWGmbGaam4BaiaadogacaWGHbGaamiBaiaadYgacaWGHbGa am4CaiaadwgacaWGYbGaeyypa0JaaGymaiaaicdacaaIWaGaamOvai aacklacqGHsgIRcaWGmbGaam4BaiaadogacaWGHbGaamiBaiaadYga caWGHbGaam4CaiaadwgacaWGYbGaeyypa0JaaGOmaiaaicdacaWGKb GaamOqaiaad2gaaaa@6320@$ The difference between the optical and the electrical demodulation is, that we add the signal and not multiply it, this is really important. ${P}_{Q/I}={\left(\stackrel{^}{r}\mathrm{cos}{\phi }_{r}+\stackrel{^}{c}\mathrm{cos}{\phi }_{c}\right)}^{2}={\stackrel{^}{r}}^{2}\mathrm{cos}{\phi }^{2}+{\stackrel{^}{c}}^{2}\mathrm{cos}{\phi }_{c}{}^{2}+2\stackrel{^}{r}\stackrel{^}{c}\mathrm{cos}{\phi }_{r}*\mathrm{cos}{\phi }_{c}$ $Average=\int \stackrel{^}{r}²\mathrm{cos}\left({\phi }_{r}\right)²+\stackrel{^}{c}²\mathrm{cos}\left({\phi }_{c}\right)²+2\stackrel{^}{r}\stackrel{^}{c}\mathrm{cos}\left({\phi }_{r}\right)\mathrm{cos}\left({\phi }_{c}\right)$ $Average= r ^ 2 2 + c ^ 2 2 + r ^ c ^ 2 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadA hacaWGLbGaamOCaiaadggacaWGNbGaamyzaiabg2da9abbaaaaaG+a cXwDLbWdbmaalaaabaGabmOCayaajaWaaWbaaSqabeaacaaIYaaaaa GcbaGaaGOmaaaacqGHRaWkdaWcaaqaaiqadogagaqcamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdaaaWdaiabgUcaRabbOpaaaaaasvgza8 GaceWGYbGbaKaaceWGJbGbaKaadaWcaaqaamaakaaabaGaaGOmaaWc beaaaOqaaiaaikdaaaaaaa@4D15@$

Illustration: optical QPSK modulator>

## OFFSET CORRECTION

Offset correction is important for this modulation type, because light can't have a negative power. The lowest point is zero power. This only exists if the local laser and the received signal eliminate each other completely. So we use the offset correction to set the center for the correlations diagram to zero.

The Offset correction of the optical QPSK is based on the math formula

$Offset: r ^ ² 2 + c ^ ² 2 = S S 2 *a²+ c ^ 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4taiaadA gacaWGMbGaam4CaiaadwgacaWG0bGaaiOoamaalaaabaGabmOCayaa jaGaaiOSaaqaaiaaikdaaaGaey4kaSYaaSaaaeaaceWGJbGbaKaaca GGYcaabaGaaGOmaaaacqGH9aqpdaWcaaqaaiaadofadaWgaaWcbaGa am4uaaqabaaakeaacaaIYaaaaiaacQcacaWGHbGaaiOSaiabgUcaRm aalaaabaGabm4yayaajaaabaGaaGOmaaaaaaa@4C43@$ $Δd= r ^ c ^ 2 2 = S S a c ^ 2 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam izaiabg2da9iqadkhagaqcaiqadogagaqcamaalaaabaWaaOaaaeaa caaIYaaaleqaaaGcbaGaaGOmaaaacqGH9aqpdaGcaaqaaiaadofada WgaaWcbaGaam4uaaqabaaabeaakiaadggaceWGJbGbaKaadaWcaaqa amaakaaabaGaaGOmaaWcbeaaaOqaaiaaikdaaaaaaa@437B@$ $v*Δd= 2 2 ⇒v* S s a c ^ 2 2 = 2 2 ⇒v= 1 S s a c ^ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaiaacQ cacqqHuoarcaWGKbGaeyypa0ZaaSaaaeaadaGcaaqaaiaaikdaaSqa baaakeaacaaIYaaaaiabgkDiElaadAhacaGGQaWaaOaaaeaacaWGtb WaaSbaaSqaaiaadohaaeqaaaqabaGccaWGHbGabm4yayaajaWaaSaa aeaadaGcaaqaaiaaikdaaSqabaaakeaacaaIYaaaaiabg2da9maala aabaWaaOaaaeaacaaIYaaaleqaaaGcbaGaaGOmaaaacqGHshI3caWG 2bGaeyypa0ZaaSaaaeaacaaIXaaabaWaaOaaaeaacaWGtbWaaSbaaS qaaiaadohaaeqaaaqabaGccaWGHbGabm4yayaajaaaaaaa@5215@$

 Illustration: Constelation diagram without offset Illustration: Constelation diagram with offset

In this experiment the bit error rate (BER) vs $E b / N 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw eadaWgaaWcbaGaamOyaaqabaGccaGGVaGaamOtamaaBaaaleaacaaI Waaabeaaaaa@3B6D@$ of M-QAM over an AWGN channel is analyzed.

## Start

The simulation starts with 4-QAM and $E b N 0 =0dB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaala aabaGaamyramaaBaaaleaacaWGIbaabeaaaOqaaiaad6eadaWgaaWc baGaaGimaaqabaaaaOGaeyypa0JaaGimaiaadsgacaWGcbaaaa@3E44@$ - see marked cell in table below.

Measured BER approximates the analytical bit error probability $p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$

$E b N 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaala aabaGaamyramaaBaaaleaacaWGIbaabeaaaOqaaiaad6eadaWgaaWc baGaaGimaaqabaaaaaaa@3AC9@$

[dB]

4-QAM

$p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$

16-QAM

$p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$

64-QAM

$p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$

256-QAM

$p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$

-2 1,306E-01 1,873E-01 2,464E-01 2,909E-01
0 7,865E-0 1,410E-01 2,002E-01 2,561E-01
2 3,751E-02 9,774E-02 1,570E-01 2,178E-01
4 1,250E-02 5,862E-02 1,185E-01 1,786E-01
6 2,388E-03 2,787E-02 8,382E-02 1,412E-01
8 1,909E-04 9,247E-03 5,233E-02 1,079E-01
10 3,872E-06 1,754E-03 2,653E-02 7,860E-02
Analytical bit error probability $p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$ for M-QAM considering $2 nd MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaik dadaahaaWcbeqaaiaad6gacaWGKbaaaaaa@39DF@$ bit errors

## Experiment

Adjust $E b / N 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw eadaWgaaWcbaGaamOyaaqabaGccaGGVaGaamOtamaaBaaaleaacaaI Waaabeaaaaa@3B6D@$ and M. Measure the corresponding BER and compare it to the analytical bit error probability.

Simulation - Settings (F11)

Simulation - Setup (F12): Set M, the size of the modulation constellation.

## Note

• This BER simulation is quite slow as it implements quadrature modulation and pulse shaping.
To boost simulation speed switch to modem none in Simulation - Setup (F12)
• Adjusting $E b / N 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw eadaWgaaWcbaGaamOyaaqabaGccaGGVaGaamOtamaaBaaaleaacaaI Waaabeaaaaa@3B6D@$ adapts the noise power spectral density. These settings are not modified:
 Transmitting power $1 V 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaik dacaWGwbWaaWbaaSqabeaacaaIYaaaaaaa@399A@$ Bit duration $T b i t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaads fadaWgaaWcbaGaamOyaiaadMgacaWG0baabeaaaaa@3AED@$ $1 μ s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaik dacqaH8oqBcaWGZbaaaa@3A84@$ Energy per bit $E b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw eadaWgaaWcbaGaamOyaaqabaaaaa@38F7@$ $1 μ V s 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaik dacqaH8oqBcaWGwbGaam4CamaaCaaaleqabaGaaGOmaaaaaaa@3C48@$

## Next steps

• The analytical bit error probability $p b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaaaaa@3922@$ considering $2 nd MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaik dadaahaaWcbeqaaiaad6gacaWGKbaaaaaa@39DF@$ bit errors is a much better approximation in cases of low signal quality. For instance, $E b / N 0 =−2 dB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw eadaWgaaWcbaGaamOyaaqabaGccaGGVaGaamOtamaaBaaaleaacaaI Waaabeaakiabg2da9iabgkHiTiaaikdacaaMc8Uaamizaiaadkeaaa a@4161@$ and 16-QAM: $p b =0,1873 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadc hadaWgaaWcbaGaamOyaaqabaGccqGH9aqpcaaIWaGaaiilaabaaaaa aaaapeGaaGymaiaaiEdacaaI5aGaaGimaaaa@3EB5@$
Measured BER

Select the modulation scheme, enter Eb/N0 and start the QAM baseband transmission. This simulation app implements an M-QAM baseband transmission. The bit error rate over an AWGN channel can be measured. The baseband simulation is highly performant.

QAM modulator demodulator baseband

## Start the QAM baseband transmission

Modulation Eb/N0 = dB

Adjust $E b / N 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9fr Fj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYx e9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadw eadaWgaaWcbaGaamOyaaqabaGccaGGVaGaamOtamaaBaaaleaacaaI Waaabeaaaaa@3B6D@$ and measure the corresponding BER.

Simulation - Settings (F11)
Simulation - Setup (F12): Set M, the size of the modulation constellation
All symbol transitions are possible.