ECE 4371, Fall, 2014 Introduction to Telecommunication Engineering/Telecommunication Laboratory Zhu Han Department of Electrical and Computer Engineering Class 15 Oct. 22 nd, 2014

Outline BER and Decision Digital Carrier System –Carrier band vs. baseband –Baud rate, bit rate, bandwidth efficiency –Spectrum –Coherent, noncoherent receiver –BER –Comparison Homework 4 –7.2.6, 7.3.4, 7.4.2, 7.5.1, 7.7.4, 7.8.1, Due 11/18/ Lab #4 and #5 11/10, 4117 Lab #6 due at last class,

Bit Error Probability We assume: binary transmission with transmission system fulfills 1st Nyquist criterion noise, independent of data source Probability density function (pdf) of Mean and variance d(i) g Tx (t) Noise n a (t) g Rx (t)

Conditional pdfs The transmission system induces two conditional pdfs depending on if

Example of samples of matched filter output for some bandpass modulation schemes

Figure 5.8 Illustrating the partitioning of the observation space into decision regions for the case when N  2 and M  4; it is assumed that the M transmitted symbols are equally likely.

Probability of wrong decisions Placing a threshold Probability of wrong decision When we define and as equal a-priori probabilities of and we will get the bit error probability s

Conditions for illustrative solution substituting for equivalently with  With  and 

Special Case: Gaussian distributed noise many independent interferers central limit theorem Gaussian distribution Motivation: Definition of Error Function and Error Function Complement  no closed solution              0 2 de N N b P   0

Error function and its complement function y = Q(x) y = 0.5*erfc(x/sqrt(2)); x erf(x), erfc(x) erf(x) erfc(x)

Bit error rate with error function complement Expressions with and antipodal: unipolar  Q function

Bit error rate for unipolar and antipodal transmission BER vs. SNR BER theoretical simulation unipolar antipodal

Digital Carrier System Baseband analysis Signal in baseband: mean symbol energy: signal in carrier band: mean symbol energy: Conclusion: analysis of carrier band = base band. Fc=0 in project

Remember channel capacity C=Wlog2 (1+ SNR)> fb Baud Rate, Bit Rate, Bandwidth Efficiency

Power Spectrum, ASK Baseband Sy(W)=Sx(W) P(W) ASK: Sy(t)=b Acoswct, Square wave convolute with sinusoid.

FSK Spectrum FSK: two sinc added together

BPSK Spectrum BPSK: Sx(W): NRZ. P(t): raised cosine function. Sy(W)= P(W) Rb baud rate

QPSK Spectrum Same Rb Narrow BW

Pulse Shaped M-PSK Different 

Bandwidth vs. Power Efficiency Bandwidth efficiency high, required SNR is high and low power efficiency

QAM efficiencies For l =1  PSD for BPSK For l =2  PSD for QPSK, OQPSK … PSD for complex envelope of the bandpass multilevel signal is same as the PSD of baseband multilevel signals Same baud rate, higher bit rate. Same bit rate, less bandwidth. But higher power

Minimum Shift Keying spectra Continuous phase and constant envelop. So narrow spectrum

GMSK spectral shaping

Coherent Reception An estimate of the channel phase and attenuation is recovered. It is then possible to reproduce the transmitted signal, and demodulate. It is necessary to have an accurate version of the carrier, otherwise errors are introduced. Carrier recovery methods include:

Coherent BER PSK –BPSK QPSK –MPSK

Coherent BER performance ASK FSK MSK: less bandwidth but the same BER MQAM

Non-coherent detection –does not require carrier phase recovery (uses differentially encoded mod. or energy detectors) and hence, has less complexity at the price of higher error rate. No need in a reference in phase with the received carrier Differentially coherent detection –Differential PSK (DPSK) u The information bits and previous symbol, determine the phase of the current symbol. Energy detection –Non-coherent detection for orthogonal signals (e.g. M-FSK) u Carrier-phase offset causes partial correlation between I and Q braches for each candidate signal. u The received energy corresponding to each candidate signal is used for detection.

Differential Reception

Differential Coherent DBPSK 3dB loss

Non-coherent detection of BFSK Decision stage: + -

Non-coherent detection BER Non-coherent detection of BFSK Similarly, non-coherent detection of DBPSK Rayleigh pdf Rician pdf

BER Example

Example of samples of matched filter output for some bandpass modulation schemes

Comparison of Digital Modulation

Comparison of Digital Modulation

Spectral Efficiencies in practical radios GSM- Digital Cellular –Data Rate = 270kb/s, bandwidth = 200kHz –Bandwidth Efficiency = 270/200 =1.35bits/sec/Hz –Modulation: Gaussian Minimum Shift Keying (FSK with orthogonal frequencies). –“Gaussian” refers to filter response. IS-54 North American Digital Cellular –Data Rate = 48kb/s, bandwidth = 30kHz –Bandwidth Efficiency = 48/30 =1.6bits/sec/Hz –Modulation: pi/4 DPSK

Modulation Summary Phase Shift Keying is often used, as it provides a highly bandwidth efficient modulation scheme. QPSK, modulation is very robust, but requires some form of linear amplification. OQPSK and p/4-QPSK can be implemented, and reduce the envelope variations of the signal. High level M-ary schemes (such as 64-QAM) are very bandwidth efficient, but more susceptible to noise and require linear amplification. Constant envelope schemes (such as GMSK) can be employed since an efficient, non-linear amplifier can be used. Coherent reception provides better performance than differential, but requires a more complex receiver.