Properties of the Mobile Radio Propagation Channel Jean-Paul M.G. Linnartz Nat.Lab., Philips Research

Statistical Description of Multipath Fading Mobile Radio Propagation Channel Statistical Description of Multipath Fading The basic Rayleigh / Ricean model gives the PDF of envelope But: how fast does the signal fade? How wide in bandwidth are fades? Typical system engineering questions: What is an appropriate packet duration, to avoid fades? How much ISI will occur? For frequency diversity, how far should one separate carriers? How far should one separate antennas for diversity? What is good a interleaving depth? What bit rates work well? Why can't I connect an ordinary modem to a cellular phone? The models discussed in the following sheets will provide insight in these issues 99-09-21 Multipath fading

The Mobile Radio Propagation Channel A wireless channel exhibits severe fluctuations for small displacements of the antenna or small carrier frequency offsets. Amplitude Frequency Time Channel Amplitude in dB versus location (= time*velocity) and frequency 99-09-21 Multipath fading

Some buzz words about Time Dispersion and Frequency Dispersion Mobile Radio Propagation Channel Some buzz words about Time Dispersion and Frequency Dispersion Time Dispersion Frequency Dispersion Time Domain Channel variations Delay spread Interpretation Fast Fading InterSymbol Interference Correlation Distance Channel equalization Frequency Doppler spectrum Frequency selective fading Domain Intercarrier Interference Coherence bandwidth Interpretation 99-09-21 Multipath fading

Fading is characterised by two distinct mechanisms Mobile Radio Propagation Channel Fading is characterised by two distinct mechanisms 1. Time dispersion Time variations of the channel are caused by motion of the antenna Channel changes every half a wavelength Moving antenna gives Doppler spread Fast fading requires short packet durations, thus high bit rates Time dispersion poses requirements on synchronization and rate of convergence of channel estimation Interleaving may help to avoid burst errors 2. Frequency dispersion Delayed reflections cause intersymbol interference Channel Equalization may be needed. Frequency selective fading Multipath delay spreads require long symbol times Frequency diversity or spread spectrum may help 99-09-21 Multipath fading

Time dispersion of narrowband signal (single frequency) Mobile Radio Propagation Channel Time dispersion of narrowband signal (single frequency) Transmit: cos(2p fc t) Receive: I(t) cos(2p fc t) + Q(t) sin(2p fc t) = R(t) cos(2p fc t + f) I-Q phase trajectory As a function of time, I(t) and Q(t) follow a random trajectory through the complex plane Intuitive conclusion: Deep amplitude fades coincide with large phase rotations 99-09-21 Multipath fading

Mobile Radio Propagation Channel Doppler shift All reflected waves arrive from a different angle All waves have a different Doppler shift The Doppler shift of a particular wave is Maximum Doppler shift: fD = fc v / c Joint Signal Model Infinite number of waves Uniform distribution of angle of arrival f: fF(f) = 1/2p First find distribution of angle of arrival the compute distribution of Doppler shifts Line spectrum goes into continuous spectrum 99-09-21 Doppler

Mobile Radio Propagation Channel Doppler Spectrum If one transmits a sinusoid, … what are the frequency components in the received signal? Power density spectrum versus received frequency Probability density of Doppler shift versus received frequency The Doppler spectrum has a characteristic U-shape. Note the similarity with sampling a randomly-phased sinusoid No components fall outside interval [fc- fD, fc+ fD] Components of + fD or -fD appear relatively often Fades are not entirely “memory-less” 99-09-21 Doppler

Autocorrelation of the signal Mobile Radio Propagation Channel Autocorrelation of the signal We now know the Doppler spectrum. But how fast does the channel change? Wiener-Kinchine Theorem: Power density spectrum of a random signal is the Fourier Transform of its autocorrelation Inverse Fourier Transform of Doppler spectrum gives autocorrelation of I(t) and Q(t) 99-09-21 Autocorrelation

Autocovariance of amplitude Mobile Radio Propagation Channel Autocovariance of amplitude ( ) C J 2 f D = p t 99-09-21 Autocorrelation

How to handle fast multipath fading? Mobile Radio Propagation Channel How to handle fast multipath fading? 99-09-21 Multipath fading

Frequency Dispersion Frequency dispersion is caused by the delay spread of the channel Frequency dispersion has no relation to the velocity of the antenna 99-09-21 Multipath fading

Frequency Dispersion: Delay Profile Mobile Radio Propagation Channel Frequency Dispersion: Delay Profile 99-09-21 Multipath fading

Mobile Radio Propagation Channel Typical Delay Spreads 99-09-21 Multipath fading

Channel Parameters at 1800 MHz Environment Delay Spread Angle spread Max. Doppler shift Macrocellular: Rural flat 0.5 ms 1 degree 200 Hz Macrocellular: Urban 5 ms 20 degrees 120 Hz Macrocellular: Hilly 20 ms 30 degrees 200 Hz Microcellular: Factory, Mall 0.3 ms 120 degrees 10 Hz Microcellular: Indoors, Office 0.1 ms 360 degrees 2..6 Hz 99-09-21 Multipath fading

Typical Delay Profiles Mobile Radio Propagation Channel Typical Delay Profiles 99-09-21 Multipath fading

How do systems handle delay spreads? Mobile Radio Propagation Channel How do systems handle delay spreads? 99-09-21 Multipath fading

Frequency and Time Dispersion Mobile Radio Propagation Channel Frequency and Time Dispersion 99-09-21 Multipath fading

Scatter Function of a Multipath Mobile Channel Mobile Radio Propagation Channel Scatter Function of a Multipath Mobile Channel Gives power as function of · Doppler Shift (derived from angle ) f · Excess Delay Example of a scatter plot Horizontal axes: · x-axis: Excess delay time · y-axis: Doppler shift Vertical axis · z-axis: received power 99-09-21 Multipath fading

Scatter Function of a Multipath Mobile Channel Mobile Radio Propagation Channel Scatter Function of a Multipath Mobile Channel Example of a scatter plot Excess Delay Doppler Shift derived from angle f 99-09-21 Multipath fading

Correlation of Fading vs. Frequency Separation Mobile Radio Propagation Channel Correlation of Fading vs. Frequency Separation 99-09-21 Multipath fading

Mobile Radio Propagation Channel 99-09-21 Multipath fading

Mobile Radio Propagation Channel Coherence Bandwidth 99-09-21 Multipath fading

Effects of fading on modulated radio signals

Effects of Multipath (I) Mobile Radio Propagation Channel Effects of Multipath (I) Frequency Time Narrowband Frequency Time Wideband Frequency Time OFDM Multipath reception and user mobility lead to channel behavior that is time and frequency dependent. In the following frequency-time diagrams, we depict where in frequency and when in time most of the bit energy is located. It is important to select a modulation scheme that is appropriate for the Doppler Spread and the Delay Spread of the channel. In narrowband communication (NB), the occupied bandwidth is small and the bit duration is long. The bit energy footprint is stretched in vertical direction. Intersymbol interference is neglectable is the bit duration is, say, ten times or more longer than the delay spread. However, due to multipath the entire signal (bandwidth) may vanish in a deep fade. Is fading is very fast, the channel may change during a bit transmission. This can occur if the Doppler spread is large compared to the transmit bandwidth. In wideband transmission (WB), i.e., transmission at high bit rate, the signal is unlikely to vanish completely in a deep fade, because its bandwidth is so wide that some components will be present at frequencies where the channel is good. Such frequency selective fading, however, leads to intersymbol interference, which must be handled, for instance by an adaptive equalizer. In MultiCarrier or OFDM systems, multiple bits are transmitted in parallel over multiple subcarriers. If one subcarrier is in a fade, the other may not. Error correction coding can be used to correct bit errors on faded subcarriers. Rapid fading (Doppler) may erode the orthogonality of closely spaced subcarriers.

Effects of Multipath (II) Mobile Radio Propagation Channel Effects of Multipath (II) Frequency Time + - DS-CDMA Frequency Time + - Hopping Time Frequency + - MC-CDMA Direct Sequence intentionally broadens the transmit spectrum by multiplying user bits with a fast random sequence. The wideband signal is unlikely to fade completely. If frequency selective fading occurs, the receiver sees a series of time-shifted versions of the chipped bit. A ‘rake’ receiver can separate the individual resolvable paths. Frequency Hopping: The carrier frequency is shifted frequently, to avoid fades or narrowband interference. While the signal may vanish during one hop (at a particular frequency), most likely other hops jump to frequencies where the channel is good. Error correction is applied to correct bits lost at faded frequencies. Slow and fast hopping methods differ in the relative duration spent at one frequency, compared to the user bit duration. Orthogonal MC-CDMA is a spectrum-spreading method which exploits advantages of OFDM and DS-CDMA. Each user bit is transmitted simultaneously (in parallel) over multiple subcarriers. This corresponds to a 90 degree rotation of a bit energy map in the frequency-time plane, when compared to DS-CDMA. While the signal may be lost some subcarriers, reliable communication is ensured through appropriate combining of energy from various subcarriers, taking into account the signal-to-interference ratios. In an interference-free environment, Maximum Ratio Diversity combining is the preferred receive strategy. In a noise free environment, equalization (i.e. making all subcarrier amplitudes equal) is preferred.

Time Dispersion Revisited The duration of fades and the optimum packet length

Time Dispersion Revisited: Duration of Fades Mobile Radio Propagation Channel Time Dispersion Revisited: Duration of Fades 99-09-21 Multipath fading

Mobile Radio Propagation Channel Two-State Model 99-09-21 Multipath fading

Average Fade / Nonfade Duration Mobile Radio Propagation Channel Average Fade / Nonfade Duration 99-09-21 Fade duration

Level Crossings per Second Mobile Radio Propagation Channel Level Crossings per Second 99-09-21 Level crossing

Average nonfade duration Mobile Radio Propagation Channel Average nonfade duration 99-09-21 Fade duration

How to handle long fades when the user is stationary? Mobile Radio Propagation Channel How to handle long fades when the user is stationary? 99-09-21 Fade duration

Mobile Radio Propagation Channel Optimal Packet length 99-09-21 Fade duration

Mobile Radio Propagation Channel Optimal Packet length fc = 900 MHz 72 km/h (v=20 m/s) fade margin 10 dB 99-09-21 Fade duration

Derivation of Optimal Packet length Mobile Radio Propagation Channel Derivation of Optimal Packet length 99-09-21 Fade duration

Mobile Radio Propagation Channel Average fade duration 99-09-21 Fade duration

Conclusion Time and Frequency Dispersion The multipath channel is characterized by two effects: Time and Frequency Dispersion Time Dispersion effects are proportional to speed and carrier frequency System designer needs to anticipate for channel anomalies 99-09-21 Multipath fading