and Multipath Random frequency modutation due to (ii) different multipath signals, and varying Doppler shifts on ip Time dispersion (echoes) caused by multipath propagation delays jp built-up urban areas, normally fading occurs because of the height of the mobile antennas are well below the height of the surrounding structures, so there iano single line-of-sight path exist to the base station. a When line-of-sight exists, then the multipath still occurs due to the reflections from the ground and surrounding structures, The incoming radio waves arrive at different directions with the different propagation delays. a The signal received by the mobile at any point in space may consist of a large number of plane waves having randomly distributed amplitudes, phases, and angles of an arrival. a These multipath components combine vectorially at the receiver antenna, and can cguse the signal received by the mobile to distort (or) fade. a Ifa mobile receiver is stationary, then the received signal may fade duc to movement of surrounding objects in the radia channel. & Doppler Shift Due to the relative motion between the mobile and the base station, each mudtipath wave experiences an apparent shift in frequency, The shift in received signal frequency due to the motion is called ax Doppler shift it is directly proportional to the velocity and direction of motion of the mobile with respect to the direction of arrival of the received multipath wave. 3.2.2 Factors Influencing Small-Scale Fading The following physical factors in the radio propagation channel that influence small-scale fading. are: [i) Multipath Propagation © The presence of reflecting objects and scatterers in the channel ereates a constantly changing environment that dissipates the signal energy in terms of amplitude, phase, and time.Gy] mi Sy (10 one anothers = ‘ite ty Feceiving antenna which is displaced with respec Spatial orientation, Buliding Signal on direet ath Destructive (self) Interference WYN + Constructive (sell-) imterterence NW W AN Fig.3.2 Principte of smatt-scate fading © The random phase and amplitudes of the different multipath componers Cause fluctuations in signal strength and thereby introducing small-sca fading, signal distortion (or) both, oO The multipath Propagation increases the time Tequited for the baschand factual information) Portion of the signal to Teach the receiver due toa Inter Symbol Interference (181). (2) Speed of the Mobile o The relative motion between the base station and the mobile results it random frequency modulation due to the different Doppler shifts on each t the multipath component. Doppler shift is simply defined as the movement of the mobile termi iffre towards or away from the base station transmitter, It may either be posirr Fading and Multipath val scale or negative depending on whether the mobife receiver is moving towards or from the base station. away a speed of Surrounding Objects ¢ Ifabjects in the radio channel are in motion, then they induce a time varying Doppler stift on multipath components. o The Doppler shift effect dominares the smati-scale fading, when the surrounding objects move at a greater rate than the mobile. o If the rate of variations of the signal in frequency then it is described as Doppler spread. o The coherence time defines the staticness of the channel and it is directly impacted by the Doppler shift. 9 Wireless channels change both in time and frequency. The dime coherence shows us how quickly the channel changes iu time, and similarly, the frequency (bandwidth) coherence shows fhaw quickly it changes in frequency? o The femporat correlation function is defined as a measure of how fast a channel changes? % Coherence Time {Tc} Coherence time (Te) ix usually defined as, “the required time interval to obtain an amplitude correlation of 0.9 (or) less between two received signals in imuhipath propagation”. © Simply it is the time duration over which the two received signals have a slong potential for an amplitude correlation and Wis inversely proportional to the maximum Dopplee frequency (fn) 8s, 1)ry = Wireless Communica 36] Mian (4) Transmission Bandwidth of the Signal 0 Uf the transmitied radio signal bandwidth is greater than the handwidtj, of the multipath channel, then the received signal will be distorted. Signal Channel Fig 3.3 Transmission bandwidth of the signet ie 12 kHz. >| © The small scale signal will not be significant in local area, so the received signal strength will not fade much. © The bandswidih of the channel can be quantified by the coherence bandwidth which is related 10 the specific multipath structure of the channel, & Coherence Bandwidth {B,J The coherence bandwidih is a measure of the maximum frequency difference (bandwidths for which the received signals strongly correlated in amplitude, This bandwidth is inversely: proportional 1a the rms value of time delay spread falas, o (2) 3.2.3 Doppler Shift * Due to the relative motion between the mobile and the base station, each multipath wave experiences an apparent shift in frequency. 3 Doppler shift The shift in the received signal frequency due to the motion is called as Doppler shift.jpScale Fading and Multipath a7 si Doppler shift is directly proportional to the velocity and direction of motion of the mobile with respect to the direction of arrival of the received multipath wave. x vA vl 44 s ! fy | »’ I J 7 N. { N. 7 N‘ eyo ‘a? a B Bs Fig 3.4 Iltustration of Doppler shift * In the Fig 3.4, a mobile moving at a constant velocity v, along a path segment having distance ‘d' between points A and B. + Itreceives the signal from a remote source X. The difference in path distances traveled by the wave from source X to the mobile at points 4 and B is Al. From the Fig 3.4, cos8 = a Al = dcos@ se Ga) where, Distance = Velocity x Time d=vat --- (3b) By substituting equation (3b) in equation (3a) and il becomes Al = v Arcos 0 wes (4) Where, A/ is the time required for the mobile to travel from A to B.oo” Wireless Communicay; On Here, 0 is assumed to be the same at points A and B since the source js 88m) to be very far away. The phase change (A9) in the received signal due loth y difference in path lengths is then expressed as, Al ag 6) By substituting equation (4) in equation (5), we can get 2nw dt Ag fe * 35 ar = ) By substituting equation (6) in equation (7), we can get, J 2nvAt ji = in hat cos 0 Sy = [e050 18) & Equation (8) relates the Doppler shift to the mobile velocity and the spatial angle between the direction of motion of the mobile and the direction of arrival of the wave, 4% We can observe from equation (8), if the mobile is moving towards the direction of arrival of the wave, the Doppler shift becomes positive, that is, the apparent received frequency is increased. + When the mobile is moving away from the direction of arrival of the wave, the Doppler shift becomes negative, that is, the apparent received frequency is decreased. + Multipath components ftom a Continuous Wave (CW) signal that arrives from the different directions contribute to Doppler spreading of the received sign! thus increasing its signal bandwidth.