Ultra Wide Band Radio Fundamentals UWB Receiversin AWGN ...

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UWB Receivers in AWGN channels DIET Department Ultra Wide Band Radio Fundamentals Practice #7 – October 29, 2020

Transcript of Ultra Wide Band Radio Fundamentals UWB Receiversin AWGN ...

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UWB Receivers in AWGN channels

DIET Department

Ultra Wide Band Radio Fundamentals

Practice #7 – October 29, 2020

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AWGN Channel

Outline

Channel model

Simulation time!

Results

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AWGN Channel

Channel model

Outline

Channel model

Simulation time!

Results

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AWGN Channel

Channel model

Framework (1/3)

Channel model hypothesis

› multipath-free

› AWGN (and any other gaussian interference)

› amplitude gain:

Optimum receiver (for AWGN channels)

› Correlator: it correlates r (t), the rx noisy signal (input), with

the orthonormal waveforms (ψi )N−1 of the signal space basis,i =0

giving a vector Z ∈ RN of decision variables (output).

› Detector: it decides which waveform was transmitted by

applying the ML criterion, i.e. by maximizing p(Z|s(t)).

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AWGN Channel

Channel model

Framework (2/3)

Two decision detection strategies may be used in case of

multi-pulse signals:

› SOFT: only one decision based on the whole multi-pulse

signal

› HARD: Ns independent decisions (each with error probability p),

and final decision obtained by applying a majority criterion,

leading to:

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AWGN Channel

Channel model

Framework (3/3)

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AWGN Channel

Simulation time!

7

Transmitted

UWB signal

Received UWB

signal plus AWGN

noise

Multipath-free

radio channel

Remind:

Received signal

channel

gain

channel

delay

distance D

Reference channel gain

at distance D = 1 m

Path-loss exponent

Thermal noise: realization

of a stochastic Gaussian

process with bilateral PSD

N0/2

speed of light in vacuum

n(t)

c0

g

c

s(t) r(t)

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0 0.5 1 1.5 2 2.5 3

x 10-9

-3

-2

-1

0

1

2

3

4

5

6

7

x 10-4

Time [s]

Am

plit

ud

e [V

]

0 0.5 1 1.5 2 2.5 3

x 10-9

-3

-2

-1

0

1

2

3

4

5

6

7

x 10-4

Time [s]

Am

plit

ud

e [V

]

0 50 100 150-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

5

Received signal for

transmitted bit “0”

Received signal for

transmitted bit “1”

Correlator Mask

Z is positive

Z is negative

Case 1: single-pulse PPM signals

2PPM-TH receiver architecture based on a single correlator

Remind:

Z

Mask correlator:

AWGN Channel

Simulation time!

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Remind: Case 2: multi-pulse PPM signals with Soft Decision Detection

Transmitted

waveform

In soft decision detection, the signal formed by NS pulses is considered as

a single multi-pulse signal smp(t)

Received

waveform

AWGN Channel

Simulation time!

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for b=0

for b=1

2PPM-TH receiver architecture based on a single correlator

Case 2: multi-pulse PPM signals with Soft Decision DetectionRemind:

Z

AWGN Channel

Simulation time!

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Case 3: multi-pulse PPM signals with Hard Decision DetectionRemind:

• In hard decision detection, the receiver implements NS

independent decisions over the NS pulses that represent

one bit.

• The final decision is obtained by applying a simple majority

criterion.

• It can be shown that soft decision outperforms hard

decision when considering propagation over AWGN

channels

AWGN Channel

Simulation time!

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AWGN Channel

Simulation time!

Outline

Channel model

Simulation time!

Results

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AWGN Channel

Simulation time!

Schematic

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AWGN Channel

Simulation time!

Routines (1/2)

• To implement the transmission blocks, you will use the old

routines for the generation of PPM signals (see PW03)

• You will have to write functions for channel and receiver:

[sRX, alpha] = pathloss(sTX, c0, d, gamma)

[sRXwn, noise] = gnoise(sRXwon, ExN0dB, n_pulses_tot)

It implements the pathloss formula (where sTX is the PPM-TH

signal obtained from the function TX_BPPM_TH, while alpha is

the amplitude gain of the channel)

It adds noise with suitable power to attain the desired Eb/N0:

if Ns > 1, then Ex /N0 = Eb/(Ns N0).

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AWGN Channel

Simulation time!

Routines (2/2)

It takes decisions and measures the BER. The function should

implement both types of detection:

• DDT=1: hard detection

• DDT=2: soft detection

mask = corrmask(ref, smp_freq, num_pulses, dPPM)

It performs two tasks:

1) energy normalization of ref signal (that is the TH-code signal

from TX_BPPM_TH),

2) mask creation, by evaluating ref-sref, where sref is a

version of ref delayed by dPPM.

[RXbits,BER] = mod_receiver(sRx,mask, smp_freq,

bits, Ns, Ts, mod, DDT)

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Input parameters:

smp_freq = 50e9;

nBits = 20000;

Ts = 3e-9;

Ns = [1 3];

Tc = 1e-9;

Nh = 3;

Np = 60000;

IR_d = 0.5e-9;

tau = 0.25;

dPPM = 0.5e-9;

SNRb_dB = 0:2:10;

powdBm = -30;

c0= 10^(-30/20); %gain @1 m

d= 10; %[m]

gamma=2;

mod= 1;%PPM or mod=2%PAM

AWGN Channel

Simulation time!

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AWGN Channel

Results

Outline

Channel model

Simulation time!

Results

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AWGN Channel

Results

Expected result

0 1 2 3 4 5 6 7 8 9 10

Ex/N

0 [dB]

10-5

10-4

10-3

10-2

10-1

100

BE

R

PPM Ns=1

PPM Ns=3 - Hard Decision

PPM Ns=3 - Soft Decision

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AWGN Channel

Results

Questions

You should be able to answer to the following questions:

1. What is the effect of Ns on Pe ?

2. What is the performance difference between soft and hard

detection schemes?