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?