Fundamentals of Wireless Communication

The Wireless ChannelLecture 3Large and Small Scale Propagation ModelsArea 2Area 1Transmitter

Log-normalshadowingShort-term fadingWireless Mulipath Channel

Channel varies at two spatial scales:large scale fadingsmall scale fadingLarge-scale fadingIn free space, received power attenuates like 1/r2.

With reflections and obstructions, can attenuate even more rapidly with distance. Detailed modelling complicated.

Time constants associated with variations are very long as the mobile moves, many seconds or minutes.

More important for cell site planning, less for communication system design.Small-scale multipath fadingWireless communication typically happens at very high carrier frequency. (eg. fc = 900 MHz or 1.9 GHz for cellular)Multipath fading due to constructive and destructive interference of the transmitted waves.Channel varies when mobile moves a distance of the order of the carrier wavelength. This is 0.3 m for Ghz cellular. For vehicular speeds, this translates to channel variation of the order of 100 Hz.PlanWe wish to understand how physical parameters such as carrier frequency, mobile speed, bandwidth, delay spread impact how a wireless channel behaves from the communication system point of view.

We start with deterministic physical model and progress towards statistical models, which are more useful for design and performance evaluation.Physical ModelsWireless channels can be modeled as linear time-varying systems:

where ai(t) and i(t) are the gain and delay of path i.The time-varying impulse response is:

Consider first the special case when the channel is time-invariant:

Impulse Rresponse Ccharacterizationt(t0)t0t2t(t2)t1t(t1)Time spreading propertyTime variations property Impulse response: Time-spreading : multipathand time-variations: time-varying environmentPassband to Baseband ConversionCommunication takes place at [fc-W/2, fc+ W/2].Processing takes place at baseband [-W/2,W/2].

Baseband Equivalent ChannelThe frequency response of the system

Each path is associated with a delay and a complex gain.

Sampling

Multipath propagationSignal can take many different paths between sender and receiverdue to reflection, scattering, diffraction

Time dispersion: signal is dispersed over timeinterference with neighbor symbols Inter Symbol Interference (ISI)

The signal reaches a receiver directly and phase shifteddistorted signal depending on the phases of the different partsThe Effects of Multipath Propagation Due to the different paths taken by the multipath components, they may arrive at different times

If the symbol period TS is smaller than the delay spread, i.e. TS < Tm, Inter-Symbol Interference (ISI) will occur

The receiver cannot determine which symbol each multipath component belongs to:

The Effects of Multipath Propagation

Delay SpreadThe Delay Spread Tm is defined as the difference between times-of arrivalof the first and last multipath components Typical values are as follows:

(Doppler shift)

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FadingCoherence Bandwidth The Coherence Bandwidth Bc is a statistical measure of the range of frequencies over which the attenuation of the channel is approximately constant

Two frequency components f1 and f2 will experience similar attenuation if (f1 f2) TsIntersymbol InterferenceSpectral chara. of transmitted signal not preservedMultipath components resolvedSignalChannelfreq.BSBCfreq.BCBSChannelSignalChannel ClassificationBased on Time-VariationsFast FadingHigh Doppler Spread1/Bd @ TC < TsSlow FadingLow Doppler Spread1/Bd @ TC> TsSignalfreq.BDBSfreq.BSBDDopplerSignalDopplerFlat and frequency selective fading Channels

Classification of fading ChannelStatistical Multipath Model

The Multipath Model

The tapped delay line model

Time Varying Impulse Response

Linear Time Varying System

Received Signal Characteristics

Multipath resolvability

The tapped delay line model revised

Narrowband Model

Statistical ModelsStatistical ModelsDesign and performance analysis based on statistical ensemble of channels rather than specific physical channel.

Recall that:

Additive Gaussian NoiseThe discrete-time baseband-equivalent model

Rayleigh ModelRayleigh flat fading model: many small scattered paths Complex circular symmetric Gaussian .

Rayleigh PDF:

Typical Rayleigh fading envelope @ 900 MHz

Rician Model

Used when LOS or other dominant non fading path exist.Characterized by Rician factor K that compare signal power of the non-fading path to variance of multipath.Rician Rayleigh

Distributions for Rayleigh and Rician fading channels

Nakagami model

Rician fading

Rayleigh fading

No fading, Constant power More practical modelMore about Narrow band Channel

Wide band Channel

Inter-symbol Interference (ISI)Time domain: dispersion (delay spread Tm)Frequency domain: non-flat response in the band of interestOne-tap filter: flat frequency responseMulti-tap filter: frequency selective responseWhen symbol time T >> Tm, no ISI (narrowband or low rate)For higher rate, T comparable to Tm , we need to deal with ISIEqualization, OFDM, CDMA with RAKE