Physical Layer: Channel models and digital modulation techniques Maria Papadopouli Department of Computer Science University of Crete Thanks to G. Fortetsanakis for generating most of these slides 1

Multi-path A signal transmitted from a transmitter may have multiple copies traversing different paths to reach a receiver The received signal: sum of all these multi-path signals The paths traversed by these signals are different (of various length) The one at the direction of light of signal (LOS) should be the shortest Channel fading: interaction of these signals with each other: If signals are in phase, they would intensify the resultant signal Otherwise, the resultant signal is weakened due to out of phase This phenomenon is called channel fading. Criteria to measure channel fading: Doppler spread delay spread

Delay spread The signals on shorter paths reach the receiver earlier than those on longer paths The direct effect of these unsimultaneous arrivals of signal causes the spread of the original signal in time domain This spread is called delay spread It constrains the maximum transmission capacity on the wireless channel If the period of baseband data pulse is larger than the delay spread, inter-symbol interference (ISI) will be generated at the receiver The data signals on two neighbouring pulse periods are received at the same timethe receiver is unable to distinguish them

Channel models Large-scale propagation models Predict the mean signal strength at large transmitter-receiver distances Small-scale or fading models  Characterize the rapid fluctuations of the received signal strength over very short distances or time durations 4

Large-scale models Log distance path-loss or in dB The average large scale path loss is a function of distance or in dB d: transmitter-receiver distance d0: reference distance n: path loss exponent 5

Path loss exponents for different environments 6

Log-normal shadowing Surrounding environment varies at different locations Measured signals are different from the average value predicted by the log-distance model Path loss is random, distributed log-normally (mean distance-dependent value) Xσ : zero mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB) 7

Parameter estimation Parameters n & σ are estimated using linear regression  The difference between the measured and estimated path losses is minimized in a mean square error sense 8

Path loss model for various cities in Germany Parameters n=2.7 σ= 11.8 dB correspond to all cities 9

Fading models Fading describes the rapid fluctuations of amplitudes, phases or multipath delays of a radio signal Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at different times 10

Channel impulsive response By sending a pulse of very small duration to the channel, the impulsive response can be estimated  At the output, the duration of the pulse is extended due to multipath Η έξοδος που παίρνομε όταν βάλομε ως είσοδο ένα παλμό Dirac. 11

Analytical expression If the channel is stationary over a small time interval, the channel impulsive response (h) may be written as: αi & θi : the amplitude & phase of the ith multipath copy ti corresponds to the time of arrival of the ith copy 12

Time dispersion parameters Power delay profile: Received power as a function of the excess (additional) delay Mean excess delay: The first moment of the power delay profile. It can be expressed as: P(τi) is the received power at time τi (arrival of the i-th multipath copy). Excess delay: distasthma pou vlepome isxy ston diaulo (megalyterh diarkeia apo authn pou stelnome ena symvolo). 13

Time dispersion parameters (con’td) rms delay spread: Square root of the second central moment of the power delay profile. It can be defined as: where Maximum excess delay (X dB): The time delay during which the multipath energy falls to X dB bellow the maximum. 14

Example of Time Dispersion 15

Flat Channel Definition When the channel gain remains the same across all the frequencies of the transmitted signal The channel impulsive response is approximately the same in all the frequencies of the transmitted signal The “manner” that the transmitted signal fades at each frequency is the same

Frequency-selective time-varying fading Frequency-selective time-varying fading causes a cloudy pattern to appear on a spectrogram signal strength as grey-scale intensity Frequency Time

Coherence Bandwidth The range of frequencies over which the channel is considered flat The channel passes all spectral components with approximately equal gain Frequency components have strong potential for amplitude correlation If the coherence bandwidth is defined as the zone over which the amplitude correlation> 0.9: If the coherence bandwidth is defined as the zone over which the amplitude correlation> 0.5 : Ena kanali einai flat otan dinei to idio kerdos se oles tis syxnothtes tou shmatos. Otan h apokrish syxnothtas tou kanaliou einai sxedon sta8erh se olo to euros twn syxnothtwn tou pros metadosh shmatos, tote leme oti to kanali einai flat. Auto shmainei oti to pros-metadosh shma den 8a ypostei paramorfwsh apo to kanali. Dhladh se olo to euros twn syxnothtwn tou shmatos h exas8enhsh einai h idia… 18

Flat vs. frequency selective fading Flat fading: Bandwidth of transmitted signal < coherence bandwidth (Bs < Bc) The channel gain is equal for all frequency components of the transmitted signal Frequency selective fading: Bandwidth of transmitted signal > coherence bandwidth (Bs > Bc)  The channel gain may vary for different frequencies of the transmitted signal 19

Doppler spread fd: Doppler spread: When a sinusoidal pulse of frequency fc is transmitted over a multi-path channel, the received spectrum will have components in the range fc- fd to fc- fd fd: Doppler spread: v: velocity of the receiver θ: direction of arrival of the received signal λ: wavelength 20

Coherence time Definition: The time interval over which the channel impulsive response is considered stationary Typical assumption: Doppler spread and coherence time are related by the formula: K: constant in the range of 0.25 to 0.5 21

Fast vs. slow fading Fast fading: The symbol duration > the coherence time (Ts> Tc)  The channel impulsive response varies during the symbol duration Slow Fading: The symbol duration is much less than the coherence time (Ts<<Tc) The channel impulsive response does not change for many symbol intervals 22

Fading phenomena Range of frequencies of the transmitted signal Coherence bandwidth 23

Observations Strong destructive interference is frequently referred to as a deep fade and may result in temporary failure of communication due to a severe drop in the channel signal-to-noise ratio Since different frequency components of the signal are affected independently, it is highly unlikely that all parts of the signal will be simultaneously affected by a deep fade

Rayleigh fading In flat-fading channels, the envelope of the received signal follows a Rayleigh distribution σ2 : time averaged power of the received signal before envelope detection 25

Ricean fading When there is a dominant signal component present, such as a line of sight propagation path, the received signal envelope follows the Ricean distribution A: peak amplitude of the dominant signal I0(): modified Bessel function of the first kind & zero order 26

Digital Modulation Frequency Shift Keying (FSK) Use of different carrier frequencies to encode the various symbols Phase Shift Keying (PSK) Use of a single carrier frequency The various symbols are encoded by the phase Quadrature Amplitude Modulation (QAM) Both phase & amplitude are used for encoding the various symbols

FSK modulation An alphabet of M symbols is used (M = 2K for some KN) Each symbols corresponds to a combination of K bits ith symbol is mapped to carrier frequency Fi = (n+i)/2T T: symbol duration, n: an arbitrary integer To transmit the ith symbol, the following signal is used E: ενέργεια amplitude

Example BFSK Bit 0 corresponds to: Bit 1 corresponds to:

FSK demodulation Consider a vector space with base vectors: The transmitted & received signal correspond to different points on this vector space This is due to noise & channel gain The largest coordinate of the received signal corresponds to the transmitted signal with high probability

BFSK demodulation Assumptions: When the received signal is bellow the dashed line, bit 0 is transmitted Otherwise, bit 1 is transmitted

PSK modulation Assume an alphabet of M = 2K different symbols To transmit the ith symbol, we send the following signal: Signals Si(t) are linearly dependent & can be represented by linear combination of the vectors:

Example BPSK Bit 0 corresponds to : Bit 1 corresponds to:

QPSK Assumptions: If the received signal lies in the: 1st quadrant, 00 is transmitted 2nd quadrant, 01 is transmitted etc…

8PSK If the received signal lies in the first area it is assumed that the combination 000 is transmitted. If it lies in the second area it is assumed that 001 is transmitted etc.

QAM modulation This modulation scheme is an expansion of PSK Again a single carrier frequency is used (Fc) Transmitted & received signal are represented as linear combinations of: Difference: not only the phase but also the amplitude of the carrier signal may vary

Example: 16QAM The constellation point that is closer to the received signal is assumed to correspond to the transmitted bit combination

The matched filter Suppose that r(t) is the received signal which corresponds at a particular symbol interval. The estimation of the transmitted symbol is done using the matched filter. r(t) is multiplied with each signal that belongs to the basis of the signal space. The result of each multiplication is then integrated into the whole symbol interval. That way the coordinates of the received signal can be estimated.

The matched filter for QPSK

PDF of the received signal The probability that the received signal would lie at a particular point is given by a 2-D Gaussian distribution The probability space of the PDF is the vector space of the signals The peak of the distribution corresponds to the transmitted signal 40

BER calculation To calculate BER: compute the integral of signal PDF in red zone For 8PSK: the red zone is larger & yields higher BER Also the additional red zones in 8PSK have large probability mass which means that the BER is significantly higher than in QPSK 41

OFDM Demodulation At the receiver the inverse procedure is followed. First the signal is brought down to baseband and is converted from analog to digital. Then FFT is performed which produces the estimations of the transmitted symbols. Finally parallel to serial conversion is performed resulting in an estimation of the transmitted bit stream. 42

Orthogonal frequency division multiplexing (OFDM) When the bandwidth of a communication system is larger than the coherence bandwidth of the channel, ISI is introduced (Frequency Selective Fading) To reduce the effect of frequency selective fading, we use OFDM The total available bandwidth is divided into N frequency bins N is selected such that the channel frequency response is almost constant at each bin (Flat fading)

OFDM modulation Bit stream is divided into N parallel sub-flows Bits of each sub-flow are modulated using MPSK or MQAM After modulation, symbols are mapped to points on a signal constellation These points can be represented as complex numbers which are then fed to the module which performs FFT-1 The resulted signal is converted from analog to digital brought to the RF frequencies fed to the antenna of the transmitter

OFDM Demodulation At the receiver the inverse procedure is followed The signal is brought down to baseband It is converted from analog to digital FFT is performed, producing the estimations of transmitted symbols Parallel to serial conversion is performed resulting in an estimation of the transmitted bit stream

References Theodore S. Rappaport “Wireless communications principles and practice”, Chapters 4,5. Simon Haykin “Communication systems”, chapter 10. John G. Proakis Masoud Salehi “Telecommunication systems”, Chapter 8. 46