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Chapter 5 Small-Scale Multipath Propagation Small-Scale Fading Chapter 5 Small-scale Multipath Propagation Multi-path Propagation 10 0 -10 dB time or wavelength Wireless Communication Small-scale Fading and Multipath Rapid fluctuation of the amplitude of a radio signal over a short period of time or travel distance Fading is caused by multipath waves • Transmitted signal which arrive at the receiver at slightly different times Effects: factors influencing small-scale fading • Rapid changes in signal strength over a small travel distance or time interval – Random frequency modulation varying Doppler shift – Speed of the mobile or speed of surrounding objects. • Time dispersion Multipath delay : depends on bandwidth of the signal. Fading • No single line-of-sight (LOS): mobile antennas are below the height of surround structures • With LOS, multipath still occurs • Multipath random distributed amplitude, phases and angles. • A mobile is stationary, the signal may fade due to movement of surrounding objects. • A receiver moving at high speed can pass through several fades in a small of time. • Doppler shift Chapter 5 –Small-scale multipath propagation 1 Dr. Sheng-Chou Lin Page 1 Wireless Communication Multipath Fading Slow Fading •over large distances, due to gross changes in path •also called shadowing, log-normal fading Fast Fading •over distances on the order of a wavelength •also called Rayleigh fading Assumptions for above types: •many waves of roughly equal amplitude arrive •Rayleigh distributed amplitude •uniformly distributed phase •spatial angle of arrival •azimuth is uniformly distributed •elevation: PDF has mean of 0o, biased towards small angles, does not extend to infinity, and has no discontinuities Rician Fading •there is a LOS or dominant path, producing fewer deep fades occurs in small cells Chapter 5 –Small-scale multipath propagation 2 Dr. Sheng-Chou Lin Wireless Communication Multipath Fading: Duration and Frequency AT LEAST 18 dB C/I 10 0 -10 THRESHOLD FOR dB ESTIMATING n and t time or wavelength for a Rayleigh signal 95% of the amplitude is above -10 dB V = vehicle speed, = carrier wavelength n = average number of level crossings at 10 dB below average power t = average fade duration at 10 dB below RMS power n = 0.75V crossings/second and t = 0.132 seconds V e.g. at 850 mHz and 15 miles per hour, n = 16 crossings/second, and t = 6 msec Chapter 5 –Small-scale multipath propagation 3 Dr. Sheng-Chou Lin Page 2 Wireless Communication Multi-path Propagation Effects Multi-path Propagation Signal levels vary as user moves Slow variations come from blockage and shadowing by large objects such as hills and buildings Rapid Fading comes as signals received from many paths drift into and out of phase •phase cancellation occurs, causing rapid fades that are occasionally deep Rayleigh Fading •the fades are roughly /2 apart: A 7 inches apart at 800 MHz. 10-15 dB 3 inches apart at 1900 MHz •called Rayleigh fading, after the statistical model that describes it t Chapter 5 –Small-scale multipath propagation 4 Dr. Sheng-Chou Lin Wireless Communication Selective Diversity . maximum amplitude A . ... .. .. ... .. ..... path 1 ... ... .. ... ... path 2 t Use a diversity scheme to take advantage of uncorrelated fading Use the dominant instantaneous amplitude This eliminates most of the deep nulls Chapter 5 –Small-scale multipath propagation 5 Dr. Sheng-Chou Lin Page 3 Wireless Communication Space Diversity A Method for Combating Rayleigh Fading D Fortunately, Rayleigh fades are very short and last a small percentage of the time Two antennas separated by several wavelengths will not generally experience fades at the same time “Space Diversity”can be obtained by using two receiving antennas Signal received by Antenna 1 and switching instant-by-instant to whichever is best Signal received by Required separation D for good Antenna 2 decorrelation is 10-20(BS) •12-24 ft. @ 800 MHz. Combined Signal •5-10 ft. @ 1900 MHz. Required separation D is (MS) Chapter 5 –Small-scale multipath propagation 6 Dr. Sheng-Chou Lin Wireless Communication Space Diversity D Application Limitations Space Diversity can be applied only on the receiving end of a link. Transmitting on two antennas would: •fail to produce diversity, since the two signals combine to produce only one value of signal level at a given Signal received point -- no diversity results. by Antenna 1 •produce objectionable nulls in the radiation at some angles Signal received Therefore, space diversity is by Antenna 2 applied only on the “uplink”, i.e., reverse path Combined •there isn’t room for two sufficiently Signal separated antennas on a mobile or handheld Chapter 5 –Small-scale multipath propagation 7 Dr. Sheng-Chou Lin Page 4 Wireless Communication Doppler Shift Doppler spreading increases the signal bandwidth •fd : moving toward, –moving away •fd = cos() (v/ ) Example: fc 1850 MHz, 60mile/hour (mph) •= c / fc = 3 × 108 / 1850 × 106 = 0.162 m •v = 60 mph = 26.82 m/s •The mobile is moving toward the transmitter, fd = 26.82 / 0.162 = 1850.0 Hz •The mobile is moving away the transmitter, fd = - 1850.0 Hz •fd = 0, as = 90 cos() = 0 v D Chapter 5 –Small-scale multipath propagation 8 Dr. Sheng-Chou Lin Wireless Communication Impulse Response Model of a multipath Channel The small-scale variations of a mobile radio signal ; assumptions •The velocity may be assumed constant over a short time (or distance) interval. •The multipath channel is a band-limited band-pass channel •The high frequency variations caused by carrier is removed. (baseband). N-1 hb (t, ) = ai ( t, ) exp [ j2fc i ( t ) + i (t, )] (-i ( t )] I = 0 i (t, ) ai ( t, ) : real amp. and excess delay of A time-varying discrete-time impulse response for a multipath radio channel Ith multipath component at time t. i (t, ) = 2fc I ( t ) + i (t, ) : the phase shift due to free space propagations of the Ith multipath component + additional phase shifts i (t, ) : lumps together all the mechanisms for phase shifts of a single multipath component within the ith excess delay bin. Chapter 5 –Small-scale multipath propagation 9 Dr. Sheng-Chou Lin Page 5 Wireless Communication Impulse Reponses Model (time invariant) If the channel impulse response is assumed to be time invariant or is at WSS over a small-scale time or distance interval, then N-1 hb () = ai exp [ ji ] (- i ) i = 0 x + i y 2 Power delay profile: the spatial of | hb (t, ) | over a local area. 2 P ( t ; ) = k | hb (t, ) | base band ,K relates the transmitted power • average over a local area to provide a single time -invariant multipath power make several local area measurement in different location P () Measurement : hb ( ) can be predicted by a probing pulse p( t ) p( t ) ( t - ) x2(t) = 1/2c(t)2 Chapter 5 –Small-scale multipath propagation 10 Dr. Sheng-Chou Lin Wireless Communication Bandwidth and Received power Wideband signal : a very narrow pulse, p( t ), does not fluctuate when a receiver is moved about a local area The received power varies very little Narrowband signal : the CW signal strength will vary at a rate governed by the fluctuations of ai and i large signal fluctuations (fading) occur • ai varies little over local area Narrowband • I varies greatly due to changes in propagation distance • When the path amplitudes are uncorrelated, multipath phases Wideband are I.I.d over [ 0 , 2] • multipath is not resolved • fading due to the phase shifts of the many unresolved multipath components – Ex: Tb = 10ns wideband signal and CW signal, fc = 4GHz Chapter 5 –Small-scale multipath propagation 11 Dr. Sheng-Chou Lin Page 6 Wireless Communication Bandpass and Baseband channel impulse response Mobile radio channel as a function of time and space. • Channel impulse response = h(d, t), x(t) = transmitted signal • the received signal y(d,t) = x(t) h(d,t), d: position of the receiver • d = vt, v : assumed constant over a short time interval. • h(d, t) h( t, ) , t : time due to motion, : multipath delay for a fixed t. Bandpass channel Complex baseband impulse response Bandpass channel factor of 1/2 are due to the properties of the complex envelope y(t) 1 f -f f c c f Complex Baseband 2 ~y(t) f f ~ ~ ~ ~ ~ ~ y(t) = 1/2 x(t ) h(t ), x(t ) = c(t ), h(t ) = hb(t ), y(t ) = r(t ) Chapter 5 –Small-scale multipath propagation 12 Dr. Sheng-Chou Lin Wireless Communication Complex Envelop of Bandpass System 1 x(t) htReh tej2fct , h th tjh t b b R I f Immediate complex -fc fc 1 j2fct 2 ht hb te c.c term 2 c(t) 1 f xt ctej2fct c.c 2 1 ytxththxt d h(t) f -fc f 2 c 1 h (t) h c t de j2fct c.c b b 4 Cos(2fct )+ j sin(2fct ) f 0 2 1 r(t)= ½ (c(t) h (t) h ct e j2fcdej2fct c.c b 4 b f 1 j2f t 1 c 1 ytRe hbtcte rt hbtct y(t) 2 2 f Chapter 5 –Small-scale multipath propagation 13 Dr. Sheng-Chou Lin Page 7 Wireless Communication Channel Baseband Complex Envelope Baseand impulse of a multipath channel N-1 Initial phase hb ( t, ) = ai ( t, ) exp [ j2fc i ( t ) + i (t, ) ] (- i ( t )) I = 0 i (t, ) Time invariant baseand impulse h(t) Re[hb N-1 hb ( ) = ai exp [ ji ] (- i ) i = 0 x + i y • Power delay profile : the spatial 2 average of hb (t, ) over a local area ~ d ~ t. • To provide a single time-invariant multipath power delay profile P () d(t) • Maximum bandwidth that this model can accurately represent is equal to 1 / 2 t Chapter 5 –Small-scale multipath propagation 14 Dr.
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