Wireless Communication

Lecture 11—Multipath and Fading

What is Multipath Propagation?

- Assume that the signal from a mobile user propagates isotropically (equally in all directions).

- When it hits a reflector (building, ground, tree, person, car, etc.) it reflects. There are likely to be MANY such reflections.

- The signal received at any point is the sum of the incident and reflected signal(S), each with a different delay and attenuation.

- MOTION: Either the reflector or mobile or both will probably be moving, so the multipath will be constantly changing..

- These signals may interfere constructively or destructively, and the result will be a combination of large and small magnitudes, depending on the location. (FADING)

Received power looks like (smeared) set of delta functions

General combination of two multipath components (not restricted 2-ray propagation model)

h(t) = beta₁ * delta(t) + beta₂ * delta(t-tau)

H(f) = beta₁ + beta₂ * exp( -j 2 pi f tau ) (Table G.8)

|H(f)| = sqrt( beta₁² + beta₂² + 2 beta₁ beta₂ cos( 2 pi f tau ) )

plot |H(f)| vs f

periodic dips (even nulls) at

f = (2 n+1)/(2 tau)

if BW << 1/tau, minimal distortion of signal, receiver sees freq. flat fading

else it’s freq selective

even messier with more paths…

Now, let tau vary.

tau varies with location or motion

set signal to a single tone at f_c

plot |H(f)| vs tau

significant variations in location are anytime tau changes by 1/(2 fc)

d = v t

= c tau

= c / (2 fc)

but c/fc = lambda_c and we vary from max to min in moving just lambda_c/2 !

@ 900 MHz, compute lambda_c / 2 ( 8 cm! )

Fast vs. slow fading

Fig 5.15

compute how long in time between fades

Does signal change faster or slower than the coherence time of the channel?

t = d / v -- remember that this v is the speed of the user, not speed of light

t_coherence ~ 0.1 * time of significant change

~ 0.1 * time to move lambda_c/2

~ 0.1 * lambda_c / v

However, this is only true if the speed is in line with the link. There’s an angle dependence.

Compute Doppler frequency fd = v cos (theta) / lambda Hz.

Is this shift significant to the analog components in a mobile at 900 MHz or 1900 MHz?

Example 5.1

Follow-on example:

F = 915 MHz

V = 60 mph

Traveling towards RX: F = 1850.00008 MHz (smaller)

- Higher frequencies à More problems with Doppler Shift.

- This is NOT too much trouble for tuning/electronics, because it is small frequency change.

- This IS a problem for the modulation schemes.

- Narrow band systems (all the same Doppler shift) have more trouble than Broad band (spread spectrum) (different Doppler shifts) systems, in general.

Is it significant to our PSK waveforms?

if Ts << Tcoherence, we have slow fading

else we have fast fading.

Reminder: What factors affect multipath?

- Reflectors in the channel

- Speed of mobile and reflectors

- Bandwidth of the signal

- Symboling time

What are the effects of Multipath ?

- FADING: Rapid changes in signal strength over small change in distance or time.

- show Bessel correlation function

- look again at Fig 5.15

- DOPPLER SHIFT: Random change in frequency modulation because of motion

- look at Fig 5.20

- ECHOS: Time delay (dispersion) of signals.

Consider a fast-fading example from Sklar notes.

Consider the GSM TDMA signaling period and slot structure in Sklar notes and Figure 11.10

1) It is important to try to turn fast fading into slow fading for improved parameter estimation.

2) Then diversity techniques can lessen the impact of fading

3) Frequency selective fading can often be equalized out.

4) Frequency flat fading must rely on diversity techniques.

Types of Fading:

Figure 5.11

Measurements (want small scale averaged values)

- Measure time delays (t_k ) and amplitude variations (P_k) in the power at quarter wavelength increments (will average out to approximately the "sector average")

(Assume first detectable signal arrives at t₀ =0.)

- Measure over 6m outdoors, 2m indoors (If you measured more, you might see large scale effects rather than the small scale effects that represent multipath.)

1. Time Dispersion Parameters

-

Divide time delays (t_k ) into k "bins"

- Mean excess time delay:

Note: The exact value of P does not matter. It is normalized out. All that matters is the relative values of P for each multipath component.

- RMS Delay Spread

See Table on Rappaport P. 162 for examples.

- Maximum Excess Delay (XdB)

Measure time delays until power falls below XdB

t max = t_X - t_o

2. Frequency Domain Parameters : Coherence Bandwidth

(This is inversely proportional to RMS Delay spread. Constant of proportionality depends on structure of multipath.)

Coherence (statistical measure):

- All frequency components have approximately equal gain and phase.

- Channel is "flat."

- Two different frequencies are likely to be amplitude correlated ("fade" in the same way)

If frequency correlation = 0.9 then Bc » 1 / (50 s)

If frequency correlation = 0.5 then Bc » 1 / (5 s)

If Bc > than the bandwidth of your system (determined by the protocol), then the system does not need an equalizer (variable amplification). Broadband systems will require equalization.

See example p. 164

3. Doppler spread and coherence time

(Moving / time varying channels)

Doppler Spread (B_D)

If bandwidth of baseband (voice) signal is greater than B_D then it is negligible.

Coherence Time (Tc)

Measure of length of time that channel impulse response is almost invariant.

For a time correlation of 0.5:

How to Measure / Characterize the Communication Channel:

Linear Filter:

- The channel can be modeled as a linear filter that changes with time (and location of the RX,TX).

- TX(t) is transmitted signal, RX(t) is received signal

Both are assumed to be bandlimited.

Hb(t) is the "impulse response" of the channel. Since the TX/RX signals are bandlimited, the Hb(t) can be also (don't need a REAL broadband impulse)

TX(t) à Hb(t) à RX(t)

RX(t) = TX(t) Ä Hb(t)

What can Linear Filters (and hence the channel) do?

- Delay signals (multipath)

- Attenuate signals (fading)

- Amplify signals (multipath constructive interference, although you can never amplify above what the original signal WOULD have provided)

Discrete vs. Continuous Channel Characterization:

(What kinds of analysis can be used for "Cell Planning"?)

- It is easy to imagine a discrete number of signals modeled as "rays" that bounce off of buildings, etc. and end up at the RX location.

- In reality, this is more continuous than discrete. "Rays" are really spherical waves that are interfering with eachother. Full-wave (field) analysis has been done, but the computational resources required are immense. Success is limited to small local environments such as hospital rooms. In general, and particularly in outdoor applications, the discrete "ray" type analysis is used more often.

- Statistical models (as we will see next lecture) are also commonly used in practice.

Discrete Channel Impulse Response:

- Channel impulse response is assumed to be made up of a sum of "rays" representing waves that have different amplitude, time delay, and phase (perhaps from phase shift through foliage or phase shift from reflection at dielectric interface)

- Rather than considering a continuous variation in time between waves, they are divided into discrete "bins" of excess time delay for convenience.

-

Power Received:

- Received power is the sum of the received power from each multipath signal. This is true for both narrowband (pulsed) and CW systems.

- If the bandwidth of the TX is LARGER than the bandwidth of the channel (filter), the channel WILL reduce the signal (it will be filtered). You can think of this as "some of the TX power is reflected away from the RX." BUT this affect does not vary significantly over space…. All points in space have about the same RX power (though it would not have arrived at the same TIME). There are no deep nulls.

- If the bandwidth of the TX is SMALLER than the bandwidth of the channel (a CW signal, and most cell phone signals), the signal will still be filtered, and this filtering WILL vary strongly with location. There will be deep fading nulls.

(Students please read through example 4.3)

How is the Channel Measured:

- In practice, channels are more often measured than predicted. There are too many parameters to be considered for predication models unless the scope of the location is very localized.

- Three Types of Measurements:

- Direct RF Pulse

- Spread Spectrum Sliding Correlator Channel Sounding

- Frequency Domain Channel Sounding

Direct RF pulse:

Viewgraph. P. 154

- Advantages:

Simple, equipment readily available

Broad band Antennas are used.

- Disadvantges:

Wide band band pass filter (BPF) also picks up noise and interference (imagine trying to measure a cell phone channel in downtown LA with everyone else's cell phone turning on and off at random. The other cell phones are not part of the channel, yet they are definitely going to corrupt the measurements. Consequently, this system can only be practically used in isolated environments (inside buildings where users can be controlled, in an area without present coverage, etc.)

Spread Spectrum Sliding Correlator Channel Sounding

Viewgraph p. 155

- Review Frequency Hopped Spread Spectrum. This is the TX.

The Data is modulated (as in FSK) at baseband and will be mixed with the carrier wave.

The total frequency band available for the phone is divided into hundreds or thousands of subbands. The carrier wave will be "pseudo-randomly" HOPPED around these subbands. Fast hopping means it hops within the time one bit of data is transmitted. Slow hopping means it sends several bits of data on each of its frequency hops.

The PN (pseudo noise) code generator determines which of these subbands the frequency is hopped to.

The CODE CLOCK determines how fast the PN code generator changes (fast or slow hopping).

IF the code clocks on RX and TX are synchronized, the system will pick up ONLY the primary signal, no multipath. (Assuming the multipath elements are delayed by more than a clock cycle.)

- In order to pick up each multipath element individually, the RX chip clock is run slightly slower than the TX chip clock. The signal is constant value, not a varying data stream, so no modulator is used. Each time the PN codes of the RX and TX are the same, the TX signal is received (they are correlated). For each delayed multipath element, a later version of the PN code will "pick up" this delayed signal. Thus, individual multipath elements can be received.

Frequency Domain Channel Sounding:

Viewgraph p. 159

- Advantages:

MOST COMMON method for indoor channel sounding

- Disadvantages:

Requires hard-wired synchronization between RX and TX

Time-varying channel will not be correctly analyzed (missed waiting for the stepped frequencies in the network analyzer)