UWB Receivers in AWGN channels

DIET Department

Ultra Wide Band Radio Fundamentals

Practice #7 – October 29, 2020

AWGN Channel

Outline

Channel model

Simulation time!

Results

AWGN Channel

Channel model

Outline

Channel model

Simulation time!

Results

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)).

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:

AWGN Channel

Channel model

Framework (3/3)

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)

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!

9

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!

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!

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!

AWGN Channel

Simulation time!

Outline

Channel model

Simulation time!

Results

AWGN Channel

Simulation time!

Schematic

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).

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)

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!

AWGN Channel

Results

Outline

Channel model

Simulation time!

Results

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

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?