EELE 6333: Wireless Commuications

Transcription

1 EELE 6333: Wireless Commuications Chapter # 2 : Path Loss and Shadowing (Part Two) Spring, 2012/2013 EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 1 / 23

2 Outline 1 Empirical Path Loss Models 2 Simplified Path Loss Model 3 Shadow Fading 4 Combined Path Loss and Shadowing 5 Outage Probability under Path Loss and Shadowing 6 Cell Coverage Area EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 2 / 23

3 Empirical Path Loss Models Introduction...1 Most mobile communication systems operate in complex propagation environments that cannot be accurately modeled by free-space path loss or ray tracing. Path loss models have been developed over the years to predict path loss in typical wireless environments such as large urban macrocells, urban microcells, and inside buildings. These models are mainly based on empirical measurements: Over a given distance. In a given frequency range. In a particular geographical area or building. Applications of these models are not always restricted to environments in which the empirical measurements were made the accuracy of such empirically-based models applied to more general environments is somewhat questionable. Many wireless systems use these models as a basis for performance analysis. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 3 / 23

4 Empirical Path Loss Models Introduction...2 Local mean attenuation (LMA) Defined as average of the path loss at a given distance over several wavelengths. The average is used to remove the effect of the multipath on the model. Measurements are typically taken throughout the environment, and possibly in multiple environments with similar characteristics. Empirical path loss The average of the LMA measurements at distance d, averaged over all available measurements in the given environment. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 4 / 23

5 Empirical Path Loss Models The Okumura Model... 1 One of the most common models for signal prediction in large urban macrocells. Applicable over distances of Km and frequency ranges of MHz. The empirical path loss formula of Okumura at distance d parameterized by the carrier frequency f c is given by: PL(d)dB = L(f c, d) + Amu(f c, d) G(h t ) G(h r ) G AREA where: L(f c, d) is free space path loss at distance d and carrier frequency f c. Amu(f c, d) is the median attenuation in addition to free space path loss across all environments. G(h t )/G(h r ) is the base station/mobile antenna height gain factor. G AREA is the gain due to the type of environment. The values of Amu(f c, d) and G AREA are obtained from Okumura s empirical plots. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 5 / 23

6 Empirical Path Loss Models The Okumura Model... 2 EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 6 / 23

7 Empirical Path Loss Models The Okumura Model... 3 Okumura derived empirical formulas for G(h t ) and G(h r ) as Main disadvantage of this model is its slow response to rapid change in the terrain. Okumura s model has a db empirical standard deviation between the predicted and the measured pathloss values. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 7 / 23

8 Empirical Path Loss Models Hata Model The Hata model is an empirical formulation of the graphical path loss data provided by Okumura. Valid over roughly the same range of frequencies, MHz. Simplifies calculation of path loss since it is a closed-form formula. The standard formula for empirical path loss in urban areas under the Hata model is P L,urban (d)db = log 10 (f c ) log 10 (h t ) a(h r ) + ( log 10 (h t )) log 10 (d) where a(h r ) is a correction factor for the mobile antenna height based on the size of the coverage area. The Hata model well-approximates the Okumura model for distances d > 1 Km Does not model propagation well in current cellular systems with smaller cell sizes and higher frequencies. Indoor environments are also not captured with the Hata model. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 8 / 23

9 Empirical Path Loss Models Piecewise Linear (Multi-Slope) Model... 1 A common empirical method for modeling path loss in outdoor microcells and indoor channels. This approximation relates db attenuation with the log-distance. Piecewise linear model represents an approximation to different measurements. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 9 / 23

10 Empirical Path Loss Models Piecewise Linear (Multi-Slope) Model... 2 A piecewise linear model with N segments must specify N 1 breakpoints d 1,, d N 1 and the slopes corresponding to each segment s 1,, s N. Different methods can be used to determine the number and location of breakpoints to be used in the model. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 10 / 23

11 Empirical Path Loss Models Indoor Attenuation Factors... 1 It is difficult to find generic models that can be accurately applied to determine empirical path loss in a specific indoor setting. WHY?!! Indoor path loss models must accurately capture the effects of attenuation across floors due to partitions, as well as between floors. The attenuation per floor is greatest for the first floor that is passed through and decreases with each subsequent floor passed through, WHY?!!! Because the number of attenuating floors increases due to the scattering up the side of the building and reflections from adjacent buildings. Ex. At 900 MHz, the attenuation when the transmitter and receiver are separated by a single floor ranges from db, while subsequent floor attenuation is 6-10 db per floor for the next three floors, and then a few db per floor for more than four floors. If the transmitter is located outside the building, the penetration loss decreases by about 1.4 db per floor at floors above the ground floor. WHY?!!! EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 11 / 23

12 Empirical Path Loss Models Indoor Attenuation Factors... 2 The experimental data for floor and partition loss can be added to an analytical or empirical db path loss model P L (d) as P r dbm = P t dbm P L (d) N f i=1 FAF i N p i=1 PAF i where FAF i represents the floor attenuation factor (FAF) for the ith floor traversed by the signal, and PAF i represents the partition attenuation factor (PAF) associated with the ith partition traversed by the signal. The number of floors and partitions traversed by the signal are N f and N p, respectively. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 12 / 23

13 Simplified Path Loss Model... 1 The following simplified model for path loss as a function of distance is commonly used for system design [ ] γ P r = P t K d0 d where K is a unitless constant which depends on the antenna characteristics and the average channel attenuation, d 0 is a reference distance for the antenna far-field, and γ is the path loss exponent. P r dbm = P t dbm + KdB 10γ log 10 [ d d 0 ]. The values for K, d 0, and γ can be obtained to approximate either an analytical or empirical model. d 0 is typically assumed to be 1-10 m indoors and m outdoors. When the simplified model is used to approximate empirical λ measurements KdB = 20 log 10 4πd 0 (assuming omnidirectional antennas). EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 13 / 23

14 Simplified Path Loss Model... 2 K can be determined by measurement at d0 or optimized (alone or together with γ) to minimize the mean square error (MSE) between the model and the empirical measurements. The value of γ depends on the propagation environment. The value of γ for more complex environments can be obtained via a minimum mean square error (MMSE) fit to empirical measurements. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 14 / 23

15 Simplified Path Loss Model... 3 Ex. 2.3: Consider the set of empirical measurements of P r /P t given in the table below for an indoor system at 900 MHz. Find the path loss exponent γ that minimizes the MSE between the simplified model and the empirical db power measurements, assuming that d 0 = 1 m and K is determined from the free space path gain formula at this d 0. Find the received power at 100 m for the simplified path loss model with this path loss exponent and a transmit power of 1 mw (0 dbm). Distance from Transmitter 10m 20m 50m 100m 300m M = Pr P t -70 db -75 db -90 db -110 db -125 db EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 15 / 23

16 Simplified Path Loss Model... 4 Solution The MMSE error equation for the db power measurements is F (γ) = 5 i=1 [M measured(d i ) M model (d i )] 2 where M measured (d i ) is the path loss measurement at distance d i and M model (d i ) = K 10γ log 10 (d) is the path loss based on the simplified model at d i. Using the free space path loss formula, K = 20 log 10 (.3333/(4π)) = db. F (γ) = ( γ) 2 + ( γ) 2 + ( γ) 2 + ( γ) 2 + ( γ) 2 = γ γ 2 Differentiating F (γ) relative to γ and setting it to zero yields df (γ) dγ = γ = 0 γ = To find the received power at 100 m under the simplified path loss model P r = P t + K 10γ log 10 d d 0 ) = log 10 (100) = dBm EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 16 / 23

17 Shadow Fading A signal transmitted through a wireless channel will typically experience random variation due to blockage from objects in the signal path. This model has been confirmed empirically to accurately model the variation in received power in both outdoor and indoor radio propagation environments. In the log-normal shadowing model the ratio of transmit-to-receive power ψ = Pt P r is assumed random with a log-normal distribution. Models for path loss and shadowing can be superimposed to capture power falloff versus distance along with the random attenuation about this path loss from shadowing. P r d P t (db) = 10 log 10 K 10γ log 10 d 0 ψ db where ψ db is a Gauss-distributed random variable with mean zero and variance σψ 2 db. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 17 / 23

18 Combined Path Loss and Shadowing Ex. 2.4: In Ex 2.3 we found that the exponent for the simplified path loss model that best fits the measurements Table 2.3 was γ = Assuming the simplified path loss model with this exponent and the same K = db, find σψ 2 db db, the variance of log-normal shadowing about the mean path loss based on these empirical measurements. The sample variance relative to the simplified path loss model with γ = 3.71 is F (γ) = 5 i=1 [M measured(d i ) M model (d i )] 2 Thus σ 2 ψ db = 1 5 [( )2 + ( ) 2 + ( ) 2 + ( ) 2 + ( ) 2 ] = Thus, the standard deviation of shadow fading on this path is σ ψdb = 3.65 db. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 18 / 23

19 Outage Probability under Path Loss and Shadowing In wireless systems there is typically a target minimum received power level P min below which performance becomes unacceptable (e.g. the voice quality in a cellular system is too poor to understand). Outage probability p out (P min, d) The probability that the received power at a given distance d, P r (d), falls below P min : p out (P min, d) = p(p r (d) < P min ). See Ex. 2.5 page 46. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 19 / 23

20 Cell Coverage Area Cell Coverage Area The expected percentage of area within a cell that has received power above a given minimum. The transmit power at the base station is designed for an average received power at the cell boundary. Shadowing will cause some locations within the cell to have received power below and above the average. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 20 / 23

21 Cell Coverage Area... 2 EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 21 / 23

22 Cell Coverage Area... 3 The coverage area is given by: where See Ex. 2.6 and 2.7 pages EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 22 / 23

23 Next Lecture The homework assignment will be available tomorrow s night on the course webpage. The homework is due in one week. In Next Lecture Chapter 3: Statistical Multipath Channel Models. EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 23 / 23