RF Path Loss & Transmission Distance Calculations

RF Path Loss & Transmission Distance Calculations By Walter Debus Director of Engineering Axonn, LLC Technical Memorandum August 4, 2006

INTRODUCTION DOC# 8545-0003-01 For radio transmission systems that consist of at least one transmitter, plus trans/ceiver antennas and at least one receiver there are two questions that inevitably get asked. The questions are: how far apart can the transmitter and receiver be in distance while maintaining acceptable performance, and what can be changed to increase this separation distance? The simplistic answers to these questions are: use the Free Space Path Loss model in determining trans/ceiver separation, and change the transmitter power to increase separation distance. While these two assumptions work under restricted conditions, in general they are overly optimistic for most situations. This paper presents mathematical transmission models that represent more realistic transmission systems. Furthermore, a better understanding as to what can be changed in the system that result in greater transmission distance. In addition, measured field data is presented that supports the realistic math models. A typical RF transmission system is shown in Figure 1. The received signal strength (link budget) in Figure 1 is equal to: (1) R = P t + G tot L For a known receiver sensitivity value, the maximum path loss can be derived as shown in (2). (2) L = P t + G tot R Example: for P t = 39 dbm, G tot = 7.5 db, R = -95 dbm; the path loss can not exceed L 142 db without violating the receiver sensitivity. PATH LOSS AND DISTANCE CALCULATIONS Path Loss is the largest and most variable quantity in the link budget. It depends on frequency, antenna height, receive terminal location relative to obstacles and reflectors, and link distance, among many other factors. Usually a statistical path loss model or prediction program is used to estimate the median propagation loss in db. The estimate takes into account the situation - - line of sight (LOS) or non-los - -and general terrain and environment using more or less detail, depending on the particular model. For example, (3) is the Free Space loss model which only takes into consideration distance and frequency. Hence, this model is very limited in its ability to accurately predict path loss in most environments. (3) L fs = 32.45 + 20Log 10 (d km ) +20Log 10 (f MHz ) By rearranging terms in (3) the maximum distance can be calculated. For instance, using the example above with a Path Loss of 142 db and assuming f MHz = 2350, the maximum distance that can be achieved assuming free space path loss is: (4) d fs = antilog 10 [{142-32.45-20Log 10 (2350)}/20] 121 km. The distance of 121 km can only be achieved under the most optimistic case of LOS with absolutely no other types of distortion or reflections occurring. The National Institute of Standards and Technology (NIST) have done an excellent job in documenting and comparing several realistic empirical propagation loss models. Based on the NIST study, the remainder of this document examines the following loss models: Free Space Model CCIR Model Hata Models Walfisch-Ikegami Models (WIM) Figure 2 shows the numerous physical environment variables used to some degree by each of the above models in calculating path loss. Subsequently each loss model will be discussed more fully. FREE SPACE PATH LOSS MODEL (L fs ) - The L fs equation is shown in (3). Substituting (3) into (1) and then solving for distance yields the maximum distance equation for Free-space shown in (4). 1

DOC# 8545-0003-01 CCIR PATH LOSS MODEL (L ccir ) - An empirical formula for the combined effects of free-space path loss and terraininduced path loss was published by the CCIR (Comite' Consultatif International des Radio-Communication, now ITU-R) and is given by: (5) L ccir = 69.55 + 26.16Log 10 (f MHz ) -13.82Log 10 (h b ) a(h m ) + [44.9-6.55Log 10 (h b )]Log 10 (d km ) B a(h m ) = [1.1Log 10 (f MHz )-0.7]h m [1.56Log 10 (f Mhz )-0.8] B = 30 25Log 10 (% of area covered by buildings) Substituting (5) into (1) and solving for distance yields the following CCIR maximum distance equation: (6) d ccir = antilog 10 {[P t + G tot - R - 69.55-26.16Log 10 (f MHz ) + 13.82Log 10 (h b ) + a(h m ) + B] / [44.9 6.55Log 10 (h b )]} Example: for P t = 39 dbm, G tot = 7.5 db, R = -95 dbm, f MHz = 2350, h b = 8 meters, h m = 1 meter and B = 25% area covered by buildings; yields a maximum CCIR distance of: (7) d ccir (meters) 550 HATA PATH LOSS MODELS (L hata ) based on the CCIR model and following extensive measurements of urban and suburban radio propagation losses, Okumura published many empirical curves useful for radio system planning. These empirical curves were subsequently reduced to a convenient set of formulas known as the Hata models that are widely used in the industry. The CCIR and Hata models differ only in the effects of the mobile antenna and area coverage. There are four Hata models: Open, Suburban, Small City, and Large City. The basic formula for Hata path loss is: (8) L hata = 69.55 + 26.16Log 10 (f MHz ) -13.82Log 10 (h b ) a(h m ) + [44.9-6.55Log 10 (h b )]Log 10 (d km ) K Type of Area a(h m ) K Open 4.78[Log 10 (f MHz )] 2 18.33Log 10 (f MHz ) + 40.94 [1.1Log Suburban 10 (f MHz )-0.7]h m 2[Log 10 (f MHz /28)] 2 + 5.4 [1.56Log Small City 10 (f Mhz )-0.8] 0 Large City 3.2[Log 10 (11.75h m )] 2 4.97 0 Substituting (8) into (1) and solving for distance yields the following Hata maximum distance equation: (9) d hata = antilog 10 {[P t + G tot - R - 69.55-26.16Log 10 (f MHz ) + 13.82Log 10 (h b ) + a(h m ) + K] / [44.9 6.55Log 10 (h b )]} 2

DOC# 8545-0003-01 Example: for P t = 39 dbm, G tot = 7.5 db, R = -95 dbm, f MHz = 2350, h b = 8 meters, h m = 1 meter; yields maximum Hata distances of: 5300, Open (10) d hata (meters) 1600, Suburban 740, Small City 740, Large City WALFISCH-IKEGAMI PATH LOSS MODELS (L wim ) the WIM has been shown to be a good fit to measured propagation data for frequencies in the range of 800 to 2000 MHz and path distances in the range up to 5 km. The WIM distinguishes between Line Of Sight (LOS) and NLOS propagation situations. In a LOS situation where the base antenna height is greater the 30 meters (h b 30) and there is no obstruction in the direct path between the transmitter and the receiver, the WIM path loss model for LOS is: (11) L wim-los = 42.64 + 26Log 10 (d km ) + 20Log 10 (f MHz ) Substituting (11) into (1) and solving for distance yields the following WIM LOS maximum distance equation: (12) d wim-los = antilog 10 {[P t + G tot - R - 42.64-20Log 10 (f MHz )] / 26} Example: for P t = 39 dbm, G tot = 7.5 db, R = -95 dbm, f MHz = 2350; yields maximum WIM LOS distance of: (13) d wim-los (meters) 16200 For NLOS situations the WIM model uses all the parameters listed in association with Figure 2. The model is the most complex but it has the ability to represent more environments. In the absence of data, building height in meters may be estimated by three times the number of floors, plus 3m if the roof is pitched instead of flat. The model works best for base antennas well above roof height. The NLOS path loss equation is best presented in sections due to its complexity. The high level NLOS path loss equation is: (14) L win-nlos = L fs + L rts + L msd, L rts + L msd 0 L fs, L rts + L msd < 0 L fs = Free-Space loss = 32.45 + 20Log 10 (d km ) + 20Log 10 (f MHz ) L rts = -16.9-10Log 10 (w) + 10Log 10 (f MHz ) + 20Log 10 (Δh m ) + L ori -10 + 0.354 Ø, 0 Ø 35º L ori = 2.5 + 0.075(Ø-35 ), 35 Ø 55º 4.0 0.114(Ø-55 ), 55 Ø 90º 3

DOC# 8545-0003-01 L msd = L bsh + K a + K d* Log 10 (d km ) + K f* Log 10 (f MHz ) 9Log 10 (b) -18Log 10 (1 + Δh b ), Δh b > 0 L bsh = 0, Δh b 0 54, Δh b > 0 K a = 54 + 0.8 Δh b, Δh b 0 and d km 0.5 54 + 0.8 Δh b (d km /0.5), Δh b 0 and d km < 0.5 18, Δh b > 0 K d = 18 + 15( Δh b /h B ), Δh b 0 0.7(f MHz /925 1), Small City K f = 1.5(f MHz /925 1), Large City Substituting (14) into (1) and solving for distance yields the following WIM NLOS maximum distance equation: (15) d wim-nlos = antilog 10 {[P t + G tot - R - 32.45 - (30 + K f )Log 10 (f MHz ) + 16.9 + 10Log 10 (w) - 20Log 10 (Δh m ) - L ori - L bsh - K a + 9Log 10 (b)]/ (20 + K d )} Example: for P t = 39 dbm, G tot = 7.5 db, R = -95 dbm, f MHz = 2350, Small City; yields maximum WIM NLOS distance of: (16) d wim-nlos (meters) 820 USE OF PATH LOSS MODELS A good question asked is, what is the best path loss model to use? For instance, from the common example used above in each model the calculated distance values range widely. Table (A) shows these calculated example values. What is the correct model? Table A Calculated Distance Values for Common Example Path Loss Model Calculated Distance Value in Meters Free-Space 121,000 WIM LOS 16,200 Hata Open 5,300 Hata Suburban 1,600 WIM NLOS 820 Hata Small/Large City 740 CCIR 550 The two extremes (Free-space and CCIR) in Table (A) are further clarified in Figure 3 which is a graph of the various model path losses as a function of distance. At a distance of 1 km the difference in the two extremes is approximately 50 db and at 10 km this difference grows to approximately 70 db. Hence, it is extremely important to pick a model that is representative of the environment the RF system is working into or gross errors in system performance will occur. 4

DOC# 8545-0003-01 Measured data offers a means to better understand what path loss model to use in calculating transmission distance. Field strength measurements were conducted on a COFDM 1 system. The transmitter was installed on the roof of a single story building and the receiver was mobile. The system configuration consisted of transmitter power of 39 dbm, antenna gain of 9 db, connection losses of 1.5 db, transmitter height of 8 meters, receiver height of 1 meter and transmission frequency of 2350 MHz. At various known GPS location points surrounding the building field strength measurements were made. Figure 4 shows the GPS map and the various signal strength measurements at various points. Also shown are 100 meter rings that are used to average the measurements. Figure 5 is a graph of both the calculated and measured receiver signal strength for the roof mounted system. Note in Figure 5 the good correlation between the Hata small/large city model and the measured data. Also, the WIM-NLOS model closely correlates with the measured data. The CCIR model seems overly pessimistic and the open LOS type models seem overly optimistic. Based on Figure 5, along with ease of use, the Hata small/large city model is recommended for most urban environment path loss calculations. RULE OF THUMB DOUBLE-THE-DISTANCE ESTIMATOR A common rule of thumb that is used in RF engineering is: 6 db increase in link budget results in doubling the transmission distance. This rule is correct for the Free-space path loss model but is overly optimistic and does not hold true for more realistic models. In some cases it may take in excess of 15 db increase in link budget to double the transmission distance. The increase value is a function of the variables shown in Figure 2 with the transmitter height being the most sensitive. Table (B) lists the db increase value needed to double the distance for the various path loss models and for the system variables used in the above distance calculation examples. Values are shown for two different transmitter antenna heights. Hence, based on Table (B), a good rule of thumb for urban environments is: 12 db increase in link budget results in doubling the transmission distance. Table B Link Budget Increase Values Needed to Double Transmission Distance Path Loss Model db Increase Value Needed To Double Distance T x Height = 1m T x Height = 15m Free-Space 6.0 6.0 WIM-LOS 7.8 7.8 Hata Models 13.5 11.2 CCIR 13.5 11.2 WIM-NLOS 15.3 11.4 SENSITIVITY ANALYSIS OF DISTANCE CALCULATIONS Equations 4, 6, 9, 12 and 15 calculate the maximum transmission distance for the various path loss models. Given these equations exist allows for a maximum distance sensitivity analysis to be performed. The method of analysis is to change a single variable in an equation by a fixed percentage and then calculate the resultant percentage change in maximum distance. Repeating this process for each variable provides the knowledge as to what variable is the most sensitive to change. With this knowledge, focus can be placed on the system elements that will afford the biggest payback in effort expended to increase transmission distance. The Hata model will be used for illustrative purposes. Referring back to (9), the variables that can be changed in the Hata distance equation are: transmit power, total gain, receiver sensitivity, frequency, transmitter height and receiver height. Each of these variables was changed one-at-a-time by ± 2% increments up to ± 10%. The percentage difference in distance was then calculated at each point. Figure 6 is a graph of the resultant Hata sensitivity analysis. As seen, the receiver sensitivity is the most sensitive variable to change that effects transmission distance. A 10% increase in receiver sensitivity results in a 75% increase in transmission distance. A sensitivity analysis was performed on all path loss models with similar results as found with the Hata model. That is, receiver sensitivity and transmit power are number one and two when it comes to distance sensitivity. SUMMARY 1 COFDM - Coded Orthogonal Frequency Division Multiplex 5

DOC# 8545-0003-01 Care must be taken when choosing the path loss model for predicting RF system performance. Serious errors can occur by using the Free-space path loss model for all but the most restricted cases. A more realistic model to use for urban environments is the Hata small/large city model. The Hata model is easy to use and has demonstrated its ability to predict path loss with a good degree of accuracy. For urban environments, the use of 12 db is a good rule of thumb for predicting the needed increase in link budget in order to double the transmission distance. Receiver sensitivity is the first variable in a system that should be optimized in order to increase transmission distance. Other variables in a system also effect distance but must be changed by a greater percentage to equal the effects offered by changing the receiver sensitivity. Walter Debus Director of Engineering Axonn, L.L.C. 6

DOC# 8545-0003-01 Figure 1 Typical RF Transmission System A g /2 A g /2 Transmit Power (P t ) Path Loss (L) @ Distance (d) Receiver Sensitivity (R) P t = Transmitter power in dbm A g = Total antenna gain in db C l = Total connection loss in db G tot = (A g - C l ) Total gain in db L = Transmission path loss in db R = Receiver sensitivity in dbm d = Distance between transmitter and receiver in meters 7

Figure 2 DOC# 8545-0003-01 Physical Environment Path Loss Variables base antenna d buildings h b h B w b street level!h b = h b " h B!h m = h B " h m h m mobile antenna mobile station incident wave # direction of travel d = Distance in meters h b = Base antenna height over street level in meters h m = Mobile station antenna height in meters h B = Nominal height of building roofs in meters Δh b = hb-h B = Height of base antenna above rooftops in meters Δh m = h B -h m = Height of mobile antenna below rooftops in meters b = Building separation in meters (20 to 50m if no data given) w = Width of street (b/2 if no data given) Ø = Angle of incident wave with respect to street (use 90º if no data) 8

Figure 3 DOC# 8545-0003-01 Calculated Path Loss For Different Models (f MHz = 2350, h b = 8m, h m = 1m, 25% Buildings) 200 190 Path Loss in db 180 170 160 150 140 130 120 110 CCIR Hata Large City Hata Small City WI NLOS Hata Suburb Hata Open WI LOS Free Space 100 90 1 2 3 4 5 6 7 8 9 10 Distance in Km 9

DOC# 8545-0003-01 Figure 4 10

Figure 5 DOC# 8545-0003-01 Received Signal Level @ 2350 Mhz (P t = +39 dbm, Gain total = 7.5 db, h b = 8m, h m = 1m) Receive Level in -dbm 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CCIR Hata Large City Hata Small City WI NLOS Measured Hata Suburb Hata Open WI LOS Free Space Distance in Km 11

Figure 6 DOC# 8545-0003-01 Hata Sensitivities (F=2350Mhz, Pt=39dBm, R=-95dBm, G to t =7.5dB, TxH=8m, RxH=1m) 150% Percent Change in Distance 100% 50% 0% -50% Rcvr Sen. Tx Pwr Ant. Gain Freq Tx Height Rx Height -100% -10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10% Percent Change in Variable 12