EE4900/EE6720: Digital Communications 1 Lecture 10 Performance of Communication System: Bit Error Rate (BER)
Block Diagrams of Communication System Digital Communication System 2 Informatio n (sound, video, text, data, ) Transducer & A/D Converter Source Encoder Channel Encoder Modulator Tx RF System Channel Output Signal D/A Converter and/or output transducer Source Decoder Channel Decoder Demodulator Rx RF System
Performance Metrics: Power and Bandwidth Baseband Modulation is done before the information (bits) is sent out using a carrier signal Carrier signal is received (and down-converted to the baseband signal) Baseband signal is demodulated and information is recovered How do we know the performance of a modulation scheme? Bandwidth: measured from power spectral density of the baseband signal, proportional to the bit rate Power: Measured from probability of bit error (Bit Error Rate or BER) 3 Trade-off between Bandwidth and Power
EE4900/EE6720: Digital Communications 4 Bandwidth
Bandwidth: PAM To find Bandwidth, we first need the Fourier transform of the pulse shape p(t) in continuous-time domain Pulse shapes: NRZ, RZ, MAN, HS, SRRC PAM Modulator 5 Bandwidth
Bandwidth: QAM To find Bandwidth, we first need the Fourier transform of the pulse shape p(t) in continuous-time domain Pulse shapes: NRZ, RZ, MAN, HS, SRRC 6 QAM Modulator Bandwidth Same Bandwidth (shifted by Ω 0 ) Direct Digital Synthesizer
Bandwidth: Pulse Shapes NRZ, RZ, MAN, and HS pulses 7 Frequency at which 10log 10 P(f) 2 <-60dB RZ NRZ HS MAN
Bandwidth: Pulse Shapes Continuous-time SRRC α = Roll-off factor: indicates excess BW α = 0: 0% excess BW α = 0.5: 50% excess BW α = 1: 100% excess BW 8 Smaller α = Smaller lobes in Frequency Domain t
Discrete-time SRRC When you truncate the pulse in time-domain it creates side-lobes in freq. domain L p =# of Symbols used to create the SRRC pulse Goal: -40 db side-lobe level Bandwidth: Pulse Shapes Decreasing α 9 L p =3 L p =6 L p vs α to achieve -40 db attenuation in freq. domain L p =12
Bandwidth for PAM and QAM Bandwidth is determined from Power Spectral Density (PSD) of PAM pulse: Eq. 6.1: PSD equation Eq. 6.2: BW of NRZ, RZ, MAN, and HS pulses Eq. 6.3: BW of SRRC pulse 10 Bandwidth is determined from Power Spectral Density (PSD) of QAM pulse: Eq. 6.29: PSD equation Eq. 6.30 : BW of NRZ, RZ, MAN, and HS pulses Eq. 6.31: BW of SRRC pulse
EE4900/EE6720: Digital Communications 11 Probability of Bit Error and Power
Probability of Bit Error for PAM The received baseband signal (after down-converting from the carrier signal) is demodulated and detected (decoded) The 1-D decision regions determine the amplitudes of the approximated received signal The probability of error is computed from the conditional probabilities of error and applying the total probability theorem Discrete-time PAM Demodulator Probability of Error is computed based on the decision regions 12
Probability of Bit Error for 4-PAM Decision Regions for 4-PAM (M=4) Probability of Symbol Error, P(E), given that original symbols were transmitted: Eq. 6.22, Eq. 6.23 Probability of Bit Error, P b : Eq. 6.25, Eq. 6.26 13
PDF for Matched Filter Output for 4-PAM Received symbols will be shaped by randomness introduced by noise which is defined by Gaussian R.V. 14
Probability of Bit Error for M-ary PAM Probability of Symbol Error, P(E): Eq. 6.27 Probability of Bit Error, P b : Eq. 6.28 15 M=8 4 8 M=4 Probability of Bit Error M=2 P b is also known as Bit Error Rate (BER) E b /N o : ebno (rhymes with elbow) is the required power Average Bit Energy over Noise Level
BER Plot for PAM How do we interpret the BER curves? 1) Find number of error bits given a certain power (E b /N o ) 2) For constant power, BER increases as M increases 3) For constant BER, Power increases as M increases Example: P b =10-6 ** 2-PAM: E b /N o =10.6 db 4-PAM: E b /N o = 14.6 db 8-PAM: E b /N o = 19.2 db M=8 M=4 4 8 16 BER M=2 Trade-off between M (faster transmission) and BER ** 10-6 or one in million bits is a standard E b /N o
BER Plot for PAM What about bandwidth? For P b =10-6 and R b =1 kbits/s : 2-PAM: E b /N o = 10.6 db, BW=750 Hz 4-PAM: E b /N o = 14.6 db, BW=375 Hz 8-PAM: E b /N o = 19.2 db, BW=250 Hz 17 Bigger M = Faster Transmission M=8 4 8 M=4 BER Bigger the M (# of bits per symbol), Smaller the BW, Bigger the Power BW Decreases E b /N o M=2
Probability of Bit Error for QAM The received baseband signal (after down-converting from the carrier signal) is demodulated into I & Q signals The 2-D decision regions determine the amplitudes of the approximated I & Q signals The probability of error is computed from the conditional probabilities of error and applying the total probability theorem Discrete-time QAM Demodulator 18 Probability of Error is computed based on the decision regions
Probability of Bit Error for 16-QAM Decision Regions for 16-PAM (M=16) Probability of Symbol Error, P(E), given that original symbols were transmitted: Eq. 6.61, Eq. 6.62 Probability of Bit Error, P b : Eq. 6.63 19
Probability of Bit Error for M-ary QAM For MPSK, Probability of Bit Error, P b : Eq. 6.72 For square MQAM, Probability of Bit Error, P b : Ex. 6.5 For irregular MQAM, Probability of Bit Error, P b : Eq. 6.91 20 M=256 (8 bits/symbol) Probability of Bit Error M=64 (6 bits/symbol) M=16 (4 bits/symbol) M=4 (2 bits/symbol) Average Bit Energy over Noise Level
Which one is better? BER Plot for MPSK** 21 M=16 (4 bits/symbol) M=8 (3 bits/symbol) M=4 (2 bits/symbol) ** Recall that MPSK is a special case of MQAM
Which one is better? BER Plot 22 4-PAM Y-QAM M=4, 2 bits/symbol QPSK
Which one is better? BER Plot 23 M=8, 3 bits CCITT V.29 (9600 bps modem)
Measured BER Plot How to measure BER for an actual comm. system? 1) Compare transmitted bits with received bits (from the received symbols) and find BER. Repeat for different power levels 2) Example: Tx: [1 0 0 1 0 1 0 0 1 1] Rx: [1 1 0 0 0 1 0 0 1 1] Example: Measured BER performances of IMDD-OOFDM** systems 24 BER= Number of error bits/ Total number of bits BER= 2/10=0.2=20% Interpretation: 2 out of 10 bits are erroneous 20% chance of getting errors ** intensity-modulated and direct-detection optical OFDM
Use BER Test Meters Tektronix BitAlyzer Bit Error Rate Tester BA BER Meters Reach Technologies BER Tester 25 Example: NI s PXI-6552 box Cool Low-cost and Home-made BER Tester (Senior/M.S. Project)
Usefulness of BER Performance Metric Determine the integrity of the communication system Key parameter that is used in assessing digital comm. systems that transmit data from one location to another Determine what degrades the digital signal: noise, interference, changes to the propagation path, phase jitter, etc. How to improve the communication system? A: Reduce BER by reducing BW, increasing transmitter power, decreasing data speed, etc. 26
Link Budget Usefulness of BER System design: Find Eb/No (C/No) in terms of transmitter power, distance, antenna gain, noise level, losses, etc. Link budget equation: Eq. 6.126 Example: 3G uplink in suburban environment 27
Matlab/Simulink Exercise 1) Find bandwidth of SRRC pulse 28 2) Find BER of either of the comm. system in Assignment 5
Assignment 6 [10] Simulate and generate BER plot for either of the comm. system in Assignment 5 [10] 29 Submit the following: 1) BER plot: Compare ideal BER (Formula based) with your system Example