SmallScale Fading PROF MICHAEL TSAI 20150424 RX just

Small-Scale Fading PROF. MICHAEL TSAI 2015/04/24

RX just sums up all Multi Path Component (MPC). 2 Multipath Propagation

Multipath Channel Impulse Response An example of the time-varying discrete-time impulse response for a multipath radio channel hb(t, ) Maximum excess delay: the delay of latest arriving signal t t 0 0 1 2 3 4 5 6 (t 0)

Time-Variant Multipath Channel Impulse Response Because the transmitter, the receiver, or the reflectors are moving, the impulse response is time-variant. hb(t, ) t t 3 (t 3) t 2 (t 2) t 1 0 1 2 3 4 5 6 (t 0) 4 t 0 (t 1)

Multipath Channel Impulse Response • The channels impulse response is given by: Summation over all MPC Amplitude change (mainly path loss) Additional phase change due to reflections Phase change due to different arriving time • If assumed time-invariant (over a small-scale time or distance):

e. im t er rs) v o to s e lec g n ref a ch the l ne nd n ha X, a c e R hb(t, ) st th the fa TX, ow the t h f y o d tu ed t 3 s e e p w gs , s xi vin a is mo t 2 h t e ng o th i w t t 1 lo ted l Fo ela (r t 0 Two main aspects of the wireless channel 1 2 3 4 5 6 (t 2) (t 1) (t 0) Following this axis, we study how “spread-out” the impulse response are. (related to the physical layout of the TX, the RX, and the reflectors at a single time point) 6 0 (t 3)

Two main aspects of the wireless channel hb(t, ) t t 3 (t 3) t 2 (t 2) t 1 0 1 2 3 4 5 6 (t 0) Following this axis, we study how “spread-out” the impulse response are. (related to the physical layout of the TX, the RX, and the reflectors at a single time point) 7 t 0 (t 1)

Power delay profile • To predict hb( ) a probing pulse p(t) is sent s. t. • Therefore, for small-scale channel modeling, POWER DELAY PROFILE is found by computing the spatial average of |h. B(t; )|2 over a local area. RX Average over several measurements in a local area 8 TX

Example: power delay profile 9 From a 900 MHz cellular system in San Francisco

Example: power delay profile 10 Inside a grocery store at 4 GHz

Time dispersion parameters • Power delay profile is a good representation of the average “geometry” of the transmitter, the receiver, and the reflectors. • To quantify “how spread-out” the arriving signals are, we use time dispersion parameters: Already talked about this 11 • Maximum excess delay: the excess delay of the latest arriving MPC • Mean excess delay: the “mean” excess delay of all arriving MPC • RMS delay spread: the “standard deviation” of the excess delay of all arriving MPC

Time dispersion parameters • RMS Delay Spread First moment of the power delay profile Square root of the second moment of the power delay profile Second moment of the power delay profile 12 • Mean Excess Delay

Time dispersion parameters • Maximum Excess Delay: • Original version: the excess delay of the latest arriving MPC • In practice: the latest arriving could be smaller than the noise • No way to be aware of the “latest” • Maximum Excess Delay (practical version): • The time delay during which multipath energy falls to X d. B below the maximum. • This X d. B threshold could affect the values of the timedispersion parameters 13 • Used to differentiate the noise and the MPC • Too low: noise is considered to be the MPC • Too high: Some MPC is not detected

14 Example: Time dispersion parameters

Coherence Bandwidth • Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered “flat” a channel passes all spectral components with approximately equal gain and linear phase. Recall this: Transfer function

• Bandwidth over which Frequency Correlation function is above 0. 9 • Bandwidth over which Frequency Correlation function is above 0. 5 Those two are approximations derived from empirical results. 16 Coherence Bandwidth

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18 Typical RMS delay spread values

Signal Bandwidth & Coherence Bandwidth Transmitted Signal f t 0 0 1 2 3 4 5 6 19 t

Frequency-selective fading channel f TX signal t Channel t 0 0 1 2 3 4 5 6 These will become intersymbol interference! RX signal 20 f

Flat fading channel f TX signal t Channel t 0 0 1 2 3 4 5 6 No significant ISI RX signal f

Equalizer 101 • An equalizer is usually used in a frequency-selective fading channel • When the coherence bandwidth is low, but we need to use high data rate (high signal bandwidth) • Channel is unknown and time-variant 22 • Step 1: TX sends a known signal to the receiver • Step 2: the RX uses the TX signal and RX signal to estimate the channel • Step 3: TX sends the real data (unknown to the receiver) • Step 4: the RX uses the estimated channel to process the RX signal • Step 5: once the channel becomes significantly different from the estimated one, return to step 1.

Example P( ) Would this channel be suitable for AMPS or GSM without the use of an equalizer? 0 d. B -10 d. B -20 d. B -30 d. B 0 1 2 3 4 5

Example • Therefore: • Since BC > 30 KHz, AMPS would work without an equalizer. • GSM requires 200 KHz BW > BC An equalizer would be needed.

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