EEE 441 Wireless And Mobile Communications Lecture 11 EEE 441 Wireless And Mobile Communications

Mobile Multipath Channel Parameters Time Dispersion Parameters Mean Access Delay RMS Delay Spread Coherence Bandwidth Doppler Spread and Coherence Time

Time Dispersion Parameters Measured from Power Delay Profiles Plots of relative received power as a function of excess delay Found by averaging intantaneous power delay measurements over a local area Outdoor local area usually no greater than 6 metres Indoor local area usually no greater than 2 metres Samples taken at l/4 metres approximately

Outdoor Power Delay Profile

Indoor Power Delay Profile

Noise Threshold The values of time dispersion parameters also depend on the noise threshold Noise level = the level of power below which signal is considered noise If noise threshold is set too low, then the noise will be processed as valid multipath component Thus causing the parameters to be higher

Time Dispersion Parameters: Eqns Determined from a power delay profile Mean excess delay( ): Rms delay spread (st):

Example 1 Pr(\tau) in dB -10 -20 \tau in microseconds 1 2 5 -10 -20 \tau in microseconds 1 2 5 E[\tau] = [(0.01)(0)+(0.1)(1)+(0.1)(2)+(1)(5)]/[0.01+0.1+0.1+1] = 4.38 microseconds; E[\tau^2] = [(0.01)(0^2)+(0.1)(1^2)+(0.1)(2^2)+(1)(5^2)]/[0.01+0.1+0.1+1] = 21.07 microseconds; RMS delay spread = sqrt[ E[\tau^2] – {E[\tau]}^2 ] = 1.37 microseconds.

Coherence Bandwidth Bc = Range of frequencies over which the channel can be considered flat i.e. channel passes all spectral components with equal gain and linear phase Is a function of the RMS delay spread Two sinusoids with frequency separation > Bc are affected differently by the channel f1 Receiver f2 Multipath Channel Frequency Separation: |f1-f2|

Coherence Bandwidth (cont’d) Frequency correlation between two sinusoids: 0 <= C[f1, f2] <= 1 If we define Coherence Bandwidth (BC) as the range of frequencies over which the frequency correlation is above 0.9, then: s is rms delay spread. If we define Coherence Bandwidth as the range of frequencies over which the frequency correlation is above 0.5, then: s is rms delay spread.

Example 1 (cont’d) For a multipath channel, s is given as 1.37ms Then 50% coherence bandwidth will be: 1/5s = 146 kHz This means that, the range of transmission frequency (channel bandwidth) should not exceed 146kHz Then all frequencies in the band will experience the same channel characteristics This coherence bandwidth enough for AMPS channel (30kHz channels), but not GSM channel (200kHz channels)

Doppler Spread and Coherence Time Time Dispersion Parameters and Coherence Bandwidth describe the time-dispersive nature of the channel with a stationary receiver Doppler Spread and Coherence Time describe the time varying-nature of the channel with relative motion between the Tx and Rx, or by motion of objects in the channel Coherence Time is time-domain dual of Doppler Spread

Doppler Spread Measure of spectral broadening caused by relative motion We know how to compute Doppler shift: fd Doppler Spread, BD = fm is defined as the maximum possible Doppler shift If the Signal Bandwidth >> BD = fm, then effect of Doppler Spread negligible at receiver

Doppler Spread and Coherence Time: Equations Doppler shift : fd = (v/).cos, where wavelength  = c / fc Doppler Spread, BD = fm = Max possible Doppler shift = v/ Coherence Time,

Doppler Spread and Coherence Time: Equations (cont’d) Coherence time is also defined as: Coherence time definition implies that two signals arriving with a time separation greater than TC are affected differently by the channel

Minimum Symbol Rate needed to counter Doppler Spread Coherence Time is the time duration over which the channel impulse response is essentially invariant If symbol period of baseband signal Ts > coherence time TC , then the signal will distort, since channel will change during the transmission TS TC f2 f1 Dt=t2 - t1 t1 t2

Doppler Spread and Coherence Time: Summary Doppler Spread definition implies that if the signal bandwidth is much greater than BD = fm, then effect of Doppler frequency shift is negligible at the receiver Coherence time definition implies that two signals arriving with a time separation less than TC are affected similarly by the channel

Types of Fading

Types of Small-scale Fading

Flat Fading Occurs when Signal BW, BS << coherence BW, BC Implies that channel has constant gain and linear phase response over BW which is > signal BW Usually manifested by amplitude falling with distance according to the Rayleigh distribution Counteract problem by increasing Tx power

Flat Fading: Figures t << TS Occurs when: h(t,t) s(t) r(t) t << TS TS t TS+t S(f) R(f) H(f) fC fC fC Occurs when: BS << BC and TS >> st BC: Coherence bandwidth BS: Signal bandwidth TS: Symbol period st: Delay Spread

Frequency Selective Fading Occurs when Signal BW, BS > Coherence BW, BC Then symbol period < channel multipath delay spread Leads to symbols facing Time Dispersion channel facing Intersymbol Interference (ISI)

Frequency Selective Fading: Figures h(t,t) s(t) r(t) t >> TS TS t TS TS+t Causes distortion of the received baseband signal Causes Inter-Symbol Interference (ISI) Occurs when: BS > BC and TS << st As a rule of thumb: TS < 10st

Fast Fading Due to Doppler Spread Occurs when rate of change of signal < rate of change of channel characteristics Happen when symbol period TS > coherence time TC Only occurs for very low data rates (i.e. large TS) Occurs when: BS < BD and TS > TC BS: Bandwidth of the signal BD: Doppler Spread TS: Symbol Period TC: Coherence Bandwidth

Slow Fading Due to Doppler Spread Occurs when rate of change of signal >> rate of change of channel characteristics Happen when symbol period TS << coherence time TC Velocity of mobile determines BD, hence determines if fading is Fast or Slow Occurs when: BS >> BD and TS << TC BS: Bandwidth of the signal BD: Doppler Spread TS: Symbol Period TC: Coherence Bandwidth

Different Types of Fading TS Flat, Fast Flat, Slow Symbol Period of Transmitting Signal st Frequency Selective, Slow Frequency Selective, Fast TS TC Transmitted Symbol Period w.r.t SYMBOL PERIOD

Different Types of Fading (cont’d) BS Frequency Selective, Fast Frequency Selective, Slow Transmitted Baseband Signal Bandwidth BC Flat, Fast Flat, Slow BS BD Transmitted Baseband Signal Bandwidth w.r.t BASEBAND SIGNAL BANDWIDTH

Notices Read Rappaport, Ch. 5.4-5.5 Special Attn: Rappaport, Examples 5.4-5.6