1. EE 6331, Spring, 2009 Advanced Telecommunication Zhu Han Department of Electrical and Computer Engineering Class 7 Feb. 10 th, 2009

2. ECE6331 Spring 2009 Outline Review –Stochastic large scale models: u Log-distance path loss model u log-normal shadowing –Outdoor propagation models –Indoor propagation models Small Scale Fading –Small-scale Multipath Propagation –Impulse Response Model of a Multipath Channel –Small-scale Multipath Measurements

3. ECE6331 Spring 2009 Free Space Path Loss Path Loss is a measure of attenuation based only on the distance to the transmitter Free space model only valid in far-field; –Path loss models typically define a “close-in” point d 0 and reference other points from there: Log-distance generalizes path loss to account for other environmental factors –Choose a d 0 in the far field. –Measure PL(d 0 ) or calculate Free Space Path Loss. –Take measurements and derive  empirically.

4. ECE6331 Spring 2009 Typical large-scale path loss

5. ECE6331 Spring 2009 Log-Normal Shadowing Model Shadowing occurs when objects block LOS between transmitter and receiver A simple statistical model can account for unpredictable “shadowing” –PL(d)(dB)=PL(d)+X0, –Add a 0-mean Gaussian RV to Log-Distance PLAdd –Variance  is usually from 3 to 12. –Reason for Gaussian

6. ECE6331 Spring 2009 Measured large-scale path loss Determine n and  by mean and variance Equ. 4.70 Equ. 4.72 Basic of Gaussian distribution

7. ECE6331 Spring 2009 Small-Scale Fading Rapid fluctuations of radio signal amplitude, phase, or delays Occurs or short time period or short travel distance Large-scale path loss effects can be ignored Caused by arrival of two or more waves from the source combining at the receiver Resultant detected signal varies widely in amplitudes and phase Bandwidth of transmitted signal is important factor

8. ECE6331 Spring 2009 Experimental record of received signal envelope in an urban area

9. ECE6331 Spring 2009 Multipathradio propagation in urban areas

10. ECE6331 Spring 2009 Determining the impulse response of a channel Transmit a narrowband pulse into the channel Measure replicas of the pulse that traverse different paths between transmitter and receiver

11. ECE6331 Spring 2009 Small-scale Multipath Propagation Fading: The rapid fluctuation of the amplitude of a radio signal over a short period of time or travel distance. Fading is caused by interference between two or more versions of the transmitted signal, which arrive at slightly different times. Multipath in the radio channel creates small-scale fading effects. Phenomenon : 1. Rapid changes in signal strength over a small travel distance or time interval. 2. Random frequency modulation due to varying Doppler shifts on different multipath signals. 3. Time dispersion caused by multipath propagation delays. If objects in the radio channel are static, and motion is considered to be only due to that of the mobile, then fading is purely a spatial phenomenon. Antenna space diversity can prevent deep fading nulls.

12. ECE6331 Spring 2009 Factors influencing Small-scale fading Multipath propagation: multipath propagation often lengthens the time required for the baseband portion of the signal to reach the receiver which can cause signal smearing due to inter-symbol interference. –Draw a figure to explain ISI Speed of the mobile: generate random Doppler shifts. –Train passing Speed of surrounding objects: if the surrounding objects move at a greater rate than the mobile, then this effect dominates the small- scale fading. The transmission bandwidth of the signal: if signal’s bandwidth  bandwidth of the multipath channel  received signal will be distorted. –The coherent bandwidth is a measure of the maximum frequency difference for which signals are still strongly correlated in amplitude.

13. ECE6331 Spring 2009 Comparison of the BER for a fading and non-fading channel

14. ECE6331 Spring 2009 Doppler Shift

15. ECE6331 Spring 2009 Illustration of Doppler effect

16. ECE6331 Spring 2009 Doppler Shift Distance difference Phase difference Doppler frequency shift Frequency shift is positive when mobile moves toward source In a multipath environment, frequency shift for each ray may be different, leading to a spread of received frequencies. For example, for pure sinusoid, the signal blurred in frequency. Example 5.1

17. ECE6331 Spring 2009 Impulse Response Model of a Multipath Channel Model radio channel as a linear filter with a time-varying impulse response Time variation due to motion of receiver and/or objects in the environment “Filtering” is caused by the summation of the amplitudes and delays of multiple arriving waves at an instant in time d=vt

18. ECE6331 Spring 2009 Fading due to two incoming signals combine with different phases

19. ECE6331 Spring 2009 Impulse Response Model of a Multipath Channel The impulse response is a wideband channel characterization and contains all information necessary to simulate or analyze any type of radio transmission through the channel. Impulse response model actually is a linear filter with a time varying impulse response. The variable t represents the time variations due to motion, whereas  represents the channel multipath delay for a fixed value of t. It is useful to discretize the multipath delay axis  of the impulse response into equal time delay segments called excess delay bins. The unit of excess delay is , and the maximum excess delay of the channel is N . The useful frequency span of the model is

20. ECE6331 Spring 2009 Impulse Response Baseband Model

21. ECE6331 Spring 2009 Impulse Response Model of a Multipath Channel That means the impulse response models may be used to analyze transmitted signals having bandwidth less than The baseband impulse response of a multipath channel can be expressed as If the channel impulse response is assumed to be time invariant over a small-scale time or distance interval, then the channel impulse response may be simplified as

22. ECE6331 Spring 2009 Impulse Response Model of a Multipath Channel

23. ECE6331 Spring 2009 Delay profile of a multipath channel

24. ECE6331 Spring 2009 Relationship between bandwidth and received power j2pfct j2pfct Transmitted signal x(t)=Re{p(t) e } Transmitted signal x(t)=Re{p(t) e } N-1 j  i N-1 j  i Received signal r(t) =  a i e p[t–ti] Received signal r(t) =  a i e p[t–ti] i = 0 i = 0 p(t) is a pulse train. p(t) is a pulse train. tmax tmax |r(t)|^2 =(1/tmax) ∫r(t) r *(t) dt 0 N-1 N-1 =  |a k |^2 =  |a k |^2 k = 0 k = 0 =>Total received power = sum of the power of individual multipath components.

25. ECE6331 Spring 2009 Average small-scale received power

26. ECE6331 Spring 2009 Impulse Response Model of a Multipath Channel

27. ECE6331 Spring 2009 5.20-5.25 Example 5.2, 5.3

28. ECE6331 Spring 2009 Small-scale Multipath Measurements Three methods of wideband channel sounding techniques  Direct RF Pulse System  Spread Spectrum Sliding Correlator Channel Sounding  Frequency Domain Channel Sounding Direct RF Pulse System  Determine the power delay profile of any channel by using pulse signal with pulse width  bb. The main problem with this system is that it is subject to interference and noise.  Another disadvantage is that the phases of the individual multipath components are not received.

29. ECE6331 Spring 2009 Small-scale Multipath Measurements

30. ECE6331 Spring 2009 Small-scale Multipath Measurements Spread Spectrum Sliding Correlator Channel Sounding Spread spectrum, processing gain Time resolution: 2Tc=2/Rc The advantage of a spread spectrum system is that, while the probing signal may be wideband, it is possible to detect the transmitted signal using a narrow band receiver, thus improving the dynamic range of the system as compared to the direct RF pulse system. The transmitter chip clock is run at a slightly faster rate than the receiver chip clock. This implementation is called a sliding correlator. A disadvantage of the spread spectrum system is that measurements are not made in real time, but they are compiled as the PN codes slide past one another

31. ECE6331 Spring 2009 Small-scale Multipath Measurements

32. ECE6331 Spring 2009 Small-scale Multipath Measurements Frequency Domain Channel Sounding 1. Measure the frequency response of the channel first then convert it to time response. 2. It is useful only for very close measurements (indoor channel sounding). 3. It is a non-real time measurement.

33. ECE6331 Spring 2009 Small-scale Multipath Measurements

34. ECE6331 Spring 2009 Questions?