# Filling nulls in PCS systems

Coverage extension and null fill in PCS systems can be accomplished with 8W CDMA bidirectional air-interface amplifiers.

PCS carriers are tasked with providing transparent access to the world of modern communications. Users only see the handsets and are oblivious to the system technology and vast infrastructure required to furnish cost-effective coverage throughout the network. They want complete freedom to move about without annoying communications disruptions when they encounter RF shielded areas like buildings, tunnels, parking garages or terrain obstructions.

During the early days of PCS, a disturbing “rule of thumb” crept into communications system design procedures. This rule said three or four PCS cells are necessary to provide the same coverage as one 850MHz cell, a requirement that hinders providing cost-effective PCS service.

Today, bidirectional amplifiers (or repeaters), particularly the higher power models, solve PCS coverage problems without increasing the basic cell count, thus tossing the old rule. Before addressing application solutions, some general considerations influencing bidirectional amplifier systems design will be discussed.

System considerations Bidirectional amplifiers (repeaters) in RF communications systems operate in much the same way as other transceiver elements. That is, they receive RF in one port and transmit RF on another port. Bidirectional amplifiers are really two amplifiers “turned” in opposite directions with their inputs and outputs combined and steered by directional elements, generally either circulators or diplexer filters. (See Figure 1 below.)

Range estimation The goal of a bidirectional amplifier is to adjust RF power toward a target area that is otherwise not served by the base station. Bidirectional, of course, means RF in both the transmit and the receive directions is processed by the amplifier. The two routes (really the same route) are typically known as the downlink and the uplink. Downlink signals move from the base station to a mobile (or portable), and uplink signals move from mobile to base. Propagation characteristics of the path in both directions are of interest. A bidirectional amplifier, or repeater, assists in shaping coverage to fit specific nulls within the service area of a base station.

Basic propagation is described by the free-space loss equation:

LossdB = 32.3 + 20logD + 20logF

where D = distance (in miles)

F = frequency (in megahertz).

This equation can be used to predict range under free-space conditions (that is, line-of-sight without multipathing). For example, how much signal could be expected from 10W effective radiated power (ERP) over a distance of five miles at a PCS frequency of 1,900MHz? Substituting these values into the free-space loss equation yields a free-space loss of 112 dB. The 10W ERP expressed in decibels above 1mW (dBm) is a transmit level of 140dBm. The 140dBm transmitted signal undergoes a 112dB loss over the path to the distant end. Determining receive level is then a matter of adding gains and losses over the path. Considering a receive antenna gain of 15dB with receive line and multicoupler losses of perhaps 5dB, the transmitted signal would reach the far end with a level of 262dBm. The arithmetic is:

+40dBm (ERP) – 112dB FSL) + 15dB (Ant. Gain) – 5dB (line) = -62dBm

Similarly, on the uplink side, assuming a portable transmit level of 600mW (127dBm), 6dB of portable antenna loss, the same path loss of 112dB, and line and multicoupler losses of 5dB, a signal of 280 dBm reaches the base station receiver. This implies the system is “talkback limited,” or unbalanced, from forward link to reverse link, by about 18dB. In this example, a bidirectional amplifier with adjustable gain would achieve parity between downlink and uplink. In general, null fill projects require bidirectional amplifiers.

By definition, “free space” assumes that there is a line-of-sight path between the transmitter and the receiver. But, because of tower height and terrain considerations, free-space path conditions may not exist. A test equation that can be used to estimate the differentiation between free space and other propagation models is:

D = (2.3 X 10^-6)F(HTHR)

where d = distance ( in miles)

F = frequency (in megahertz)

HT = transmitting antenna height (in feet)

HR 5 receiving antenna height (in feet).

When the path distance is less than d, free-space propagation is used. When the path distance is greater than d, another propagation model is used.

Many propagation models are in use today; most of them are parts of range-prediction programs. The Egli model is a straightforward manual method of predicting overall propagation loss over gently rolling terrain with average hill heights of about 50 feet. The Egli model is expressed as:

AE = 117 + 40logD + 20logF – 20log(HTHR)

where AE = path attenuation (in decibels)

D = distance (in miles)

F = frequency (in megahertz)

HT = transmitting antenna height (in feet)

HR = receiving antenna height (in feet).

A fill-estimation formula giving estimated RF coverage of dipole antennas can be derived from the free space loss equation. When antenna gain referenced to a dipole and line loss, amplifier gain, internal loss, available off-air signal strength and receiver sensitivity are taken in account, the derived formula becomes:

Dfeet = log^-1[(S+A+G-(-Sens.)-X-L-32.3-20logF)/20] X 5280

where D = distance between the dipole antenna and receiver

S = signal strength at the outside antenna (in dBm)

A = outside antenna gain (in decibels)

G = amplifier gain (in decibels)

Sens. = receiver sensitivity (in dBm)

X = line loss (in decibels)

L = inside absorption losses from walls, furniture, etc. (in dB)

F = frequency (in megahertz).

To obtain coverage in square feet, square the result and multiply by pi (p).

Figure 2 above left shows typical system gains and losses and how these values are used in the adapted free-space loss equation. In this example, an off-air pickup antenna and bidirectional amplifier feed a single-point antenna in a building’s parking garage within the sector coverage of a PCS cell site. The goal is to fill the parking garage null, which is beneath the building. Atop the building is in a 285 dBm signal strength contour. Substituting appropriate values into the formula, we have:

Dfeet = log^-1[(-85+15+70-(-95)-5-12-32.3-20log1900)/20] X 5280 = 536

where D = distance between inside dipole antenna and receiver

S = 285dBm outside signal strength on the roof

A = 15dB off-air antenna gain

=70dB bidirectional amplifier downlink gain

Sens. = 295 dBm receiver sensitivity of mobile unit

X = 5dB total line loss

L = 12dB interior absorption losses

F = 1,900MHz.

Figure 2 shows that estimated coverage is approximately 536 feet, or 903,000 square feet, around a dipole antenna in the interior of the null target area. (A dipole is shown for example purposes only. Radiating coaxial cable is recommended for efficient distribution of null-fill RF.) Variables in the “fill estimation” formula should be qualified as much as possible by measurement before using them to predict coverage. The formula considers only line-of-sight propagation and neglects multipath and other variants. Multipath can enhance or degrade performance, depending on conditions. Also, the absorption qualities of walls, furniture and other objects should be evaluated. The formula assigns a value of 12dB (L) as an estimated amount of absorption loss. Some texts assign an L value of 20dB or more, depending on the texture of the interior space to be filled. Preferably, absorption loss in a sample of the null target should be measured, giving a “dB/foot” density quantity for use in the formula.

The partial downlink budget shown in Figure 2 is built with some of the terms used in the coverage formula. A similar uplink budget can be calculated all the way back to the base station receiver. More link budgets will be included in the amplifier system design examples.

Composite power “RF power” generally refers to composite power, the total average power in the envelope. Assuming all carriers are of equal power in a RF envelope, composite power is described as:

CompositePowerdb = CarrierPower + (10log(n))

where n = number of carriers and power is in decibels.

For example, in the formula above, 16 carriers (or channels) of 8W (39dBm) each represents a composite power of 126W (51dBm). Or, a 10W (40dBm) amplifier is delivering its rated power out over eight channels if the power in each individual channel is 1.3W (31 dBm).

Isolation concerns Isolation between an air-interface antenna and a null-fill (repeating) antenna should be at least 10dB greater than system gain, as shown in Figure 3 on page 58. This 10dB of isolation is the minimum amount necessary to ensure system stability. Sufficient isolation is usually not a problem because isolation is an inherent quantity in a null-filling application. Thus, the same obstruction losses that must be overcome to “fill” the target area are usually more than enough to meet the 10dB isolation requirement. Antenna performance can provide additional isolation. The front-to-back ratio is a standard directional antenna term describing the ratio, in decibels, of forward-radiated power over power radiated off the back side of an antenna. Front-to-back ratios of 15dB-25dB are fairly common among directional antennas. Additional horizontal isolation can be obtained by taking advantage of structural or topographic features, such as penthouses or hills.

When directional antennas are mounted collinearly (one directly above the other), isolation is greatly enhanced by vertical separation. Vertically polarized antennas have pattern nulls off their ends. Fortunately, at cellular and PCS frequencies, the deep end nulls of directional antennas can be used to achieve additional isolation.

The vertical antenna isolation graph in Figure 4, above right, is based on the equation:

IsolationDB = 28 + 40logSV/lambda

where SV = vertical separation between antenna radiating centers

lambda = wavelength (same units).

Output power and intermodulation The output power of a bidirectional amplifier is formally expressed in terms of its 1dB compression point, which is the output power at which gain has dropped 1dB from where it would have been in a totally linear system. Intermodulation (IM) worsens with increasing levels of overdrive. The projected amount of IM can be calculated by using the amplifier’s 1dB compression point and output signal power levels.

In general, bidirectional amplifiers are operated in a manner that keeps the composite power output well below the 1dB compression point. This is done to minimize IM products. Be careful to ensure that the input composite power is not capable of overdriving the amplifier. Input power levels must be accounted for in accordance with the “10log(# of carriers)” rule previously mentioned. In signal-dense urban areas, it is often necessary to filter the input of broadband amplifiers to prevent competing signals from driving an amplifier’s output to its 1dB compression point. An overdriven amplifier generates significant IM and, worse, it will totally saturate, resulting in desensitization to its intended signals.

Noise considerations c Noise factor and noise figure – System noise is another anomaly that affects RF propagation. Basically, there are two types of noise. One is inherent to the environment, and the other is generated within the equipment. One might argue these ultimately become the same thing. Here, consideration is given to noise in bidirectional amplifiers and “front-end” noise in typical communications receivers.

The ultimate sensitivity of an amplifier is set by the noise inherent to its input stage. A precise evaluation of an amplifier’s performance, as far as noise is concerned, is described by its noise factor-the specific numerical proportion of a device’s input signal-to-noise ratio (SNR) to its output SNR at a certain temperature and over a certain bandwidth. The logarithmic expression of noise factor is its noise figure, and, thus the output noise power generated in a device is given by:

PN = -174 + 10logBW + G+ N

where PN = noise power in dBm at 2908 Kelvin (room temperature)

BW = bandwidth (in hertz)

G = gain (in decibels)

N = noise figure.

Example: From the formula above, total noise power generated in a cellular amplifier with a gain of 40dB, a noise figure of 10dB, and across a 25kHz bandwidth would be 280dBm. This amplifier, if driven to its maximum output power of 1W (30dBm), would have an output SNR of [30 2 (280)], or 110dBm. This is a huge SNR, and it affords excellent operation in single-amplifier systems. However, as amplifiers and passive elements are added in cascade (as they are in large distribution systems), noise buildup must be addressed. As distance increases and amplifiers are added, noise performance becomes increasingly critical.

* Amplifiers in cascade – When several devices are cascaded to form a chain, the whole chain can be evaluated as a single element with a cascaded noise figure. The general formula for total system noise factor (Fs) is:

FS = F1 + [F2-1/G1] + F3-1/G1G2]+ … [Fn-1/G1G2G3 … G(n-1)]

where Fs = system noise factor

G1 … G(n-1) = numerical gain of individual elements:

G = log^-1[gain,dB/10]

where loss (in dB) is taken as negative gain

F1 … F(n-1), F=1/G for passive elements. F1 … F(n-1), F = log^-1[N/10] for active elements where N is noise figure.

Example: 110 feet of 7/8-inch, foam-dielectric coaxial cable, two bidirectional amplifiers, and a bandpass filter are cascaded as shown in Figure 5 above.

Coaxial cable loss is 1.4dB, amplifier #1 gain is 35dB, amplifier #2 gain is 38dB, noise figure of each amplifier is 10dB, and the insertion loss of the filter is 3.5 dB. The system noise factor is:

Fs = 1.38 + [10-1/0.72]+[2.24-1/(0.72)(3162.27)]+[10-1/(0.72)(3162.27)(0.45] = 13.89

therefore the system noise figure is:

N = 10log13.89 = 11.43

Thus, the noise figure of the cascaded string, 11.43dB, is greater than the noise figure of the first active element in the string, 10dB. This relationship is always true; how much greater the noise figure of the cascaded string is than the first active element depends on the “noise mass” of the string. (Because it makes little difference to the outcome, noise contributions of short jumper cables were not included in this example.) In more formal noise performance evaluations, all noise-contributing elements should be considered.

When a series of cascaded amplifiers, each of gain G, is interconnected, with each driving a load equal to its gain (loss 5 G), the system is said to be a “0dB system.” The system noise factor equation then simplifies to:

Fs = F1+(F2-1)+(F3-1)+ … (Fn-1)

Simplifying further and converting to noise figure, this becomes:

N = 10log[n(F-1)+1]

where N = noise figure

n = number of amplifiers

F = noise factor.

For example, in Figure 5, four sections of cascaded line amplifiers and radiating cable are operating in a “0dB” tunnel system. Each line amplifier of 20dB gain drives a section of radiating cable with 20dB loss.

The uplink noise figure of each line amplifier is 9dB. The noise factor is therefore:

F = log^-1[9/10] = 7.9

From the zero dB noise figure equation above, the cascaded noise figure of the amplifier string becomes:

N = 10log[4(7.9-1)+1] = 14.6

Noise power out of the string can be evaluated by applying the string noise figure to the last amplifier in the string as if it was operating alone. With a 25 kHz bandwidth this is:

PN = -174+10log25,000+20+14.6 = -95.4dBm

SNR at the string end is referenced relative to -95 dBm. If the amplifier signal output is +30 dBm, SNR would be

(30 – (-95) = 125dB

*Sensitivity – One definition of sensitivity is “the smallest signal that a network can reliably process.” This specifies the strength of the smallest signal at the input of a network that causes the output signal to be M times the output noise power. M also must be specified, and it is usually “1.” Some receiver sensitivity measurement procedures, such as 12dB sinad, use a slightly different value for M. With M = 1, PN (noise power) is also the noise floor. For a source temperature of 2908K and across a specified bandwidth, the relationship of sensitivity and noise figure is:

Sens.(dBm) = -174 + N + 10logBW + 10logM

Over a typical channel bandwidth of 25kHz, the basic sensitivity of a typical 1W bidirectional amplifier (N 5 10dB) is 2120dBm. This is much lower than the 2116dBm receiver sensitivity of an ordinary communications receiver.

In the first example above, with two of these amplifiers, cable and filter (N = 11.4), the basic sensitivity would be 2119dBm. Thus, noise builds up as component count increases. However, 2119dBm is still below typical radio receiver sensitivity, meaning that weak output signals at the threshold of receiver sensitivity would still be discernible above the noise floor. SNR, although not good in this case, would be expressed as (-116dBm – (-119dBm)) = 3dB. In other words, sensitivity is approaching the limit of usability with respect to -116dBm signals.

At any point in a system, or network, a sensitivity calculation indicates if the system is capable of processing signal levels that are expected at that point. In any application, it is vitally important to maintain a sufficient margin of signal power over noise power (SNR). Acceptable SNR is the result of adequate sensitivity.

*Noise and CDMA – Calculated total output noise power (PN) of a typical CDMA amplifier with 95dB gain, noise figure of 6dB and across a 1.25MHz bandwidth is 212dBm. At first, this seems like an alarming amount of noise power, especially compared with a typical base station receiver sensitivity of -116dBm (0.35mV). Seemingly, noise power of such amplitude would certainly “swamp” the front end of any sensitive receiver. Consider, though, that this noise power will be attenuated by the path loss from the repeater amplifier to the receiver.

Now PCS system designers, integrators, installers and service providers can extend PCS system performance with newer 8W, channelized, bidirectional amplifiers that provide signal level enhancement to the PCS spectrum. An 8W CDMA amplifier has the gain and output power range needed to boost RF signal levels sufficiently for use in a variety of in-building and outdoor null-fill applications and to extend PCS services into locations such as airports, metros, hospitals, parking garages, business parks, campuses or high-rise offices.

CDMA transmission Figure 6 on page 62 is a test plot of a CDMA 1900 amplifier showing spectral regrowth. The TIA/EIA standard for spectral regrowth requires that average intermodulation measured in a 30kHz bandwidth be 45dB below the average power measured in a 1.25MHz bandwidth. Therefore, the marker delta reading must be corrected by the bandwidth ratio of 1.25MHz/30kHz, or 16.2dB. The plot shown in Figure 6 demonstrates a -50.4dBc intermodulation to composite power ratio. CDMA signals come through unchanged other than having undergone a nominal 3.5ms (either link) throughput delay. The capacity enhancement and transmission advantages of CDMA are totally accounted for in the signal passage through these amplifiers, bringing a new definition to the term “transparent” in CDMA applications.

CDMA application examples *Buildings – A few examples will show how coverage can be extended into RF-shielded locations with the proper use of amplifiers. In most cases, line losses will not be shown separately. In a real system, line losses are “system-specific” and can be held to reasonably low values by proper cable selection. Thus, in these examples, when line losses are not shown, they can be assumed to be lumped in with other component losses.

Figure 7 on page 63 depicts a 10-story building of approximate dimensions 150 ft. X 120 ft. X 100 ft. located 1.4 miles from the base station (BTS). The building antenna height is 160 ft. and the BTS height is 40 ft. Calculated (Egli) path attenuation to the BTS is 112dB.

The building is constructed of concrete and steel with metallized, tinted windows, and as such is virtually RF-shielded from the PCS base station. The challenge of extending CDMA coverage into this building can be accomplished with a bidirectional amplifier and 150 ft. of radiating coaxial cable. Radiating cable is the null-fill antenna in this system.

In the link budgets and comments to follow, CDMA transmission and distribution is dealt with as if it were conventional modulation. The example in Figure 7 presumes the system is “uplink-limited” or “talkback-limited.” That is, the transmission in the building is poor both ways-but worse in the uplink direction. Therefore, the example will “design to” or tailor performance to the uplink direction, as shown in the budget in the box at the left.

The 292dBm signal into the receiver is 24dB above typical receiver sensitivity of 2116dBm. This is “good margin,” capable of offsetting other system unknowns or design oversights.

With the knowledge that a workable uplink budget can be achieved, the downlink budget is then considered. Because the system is uplink-limited, there are no critical downlink considerations. The downlink calculation does, however, provide a good “sanity check” for previous calculations and gives a strong starting point for installation gain adjustments. The downlink budget in the box on page 65 determines that +86dB of gain is needed to reach portable receivers with a signal level of -90dBm.

The -90dBm signal level into the portable receiver is about -6dB above receiver sensitivity. This, too, is “good margin.” A gain of only +6dB is required in the downlink, whereas the full amplifier gain of 95dB was necessary in the uplink budget. The required gain difference is attributable to the difference in BTS output power compared with mobile output power. The talkback limitation was a known concern at the outset, and it explains why it was “designed to the uplink” before considering the downlink.

*Highways – In a rural highway scenario, bidirectional amplifiers can reduce numbers and costs compared with a BTS-only approach. Typically, one BTS and four amplifiers can be used to obtain greater coverage distance than two base stations. The scheme of one base station and four amplifiers can be extended over long stretches of highway. Obviously, considering capital equipment, backhaul and yearly recurring costs, this can amount to significant savings in the service provider’s highway coverage budget. The BTS is the most likely place to start with in the description of a highway system.

In a highway coverage system, reasonable distances can be reached with 100-foot towers. As in most mobile systems, a highway coverage example will be severely limited in the “talkback” direction. Tall towers assure line-of-sight propagation between amplifiers, but the ultimate goal is to reach a mobile on the ground. Tower-to-mobile range is calculated by a range prediction model such as the Egli model. Figure 8 on page 66 shows the downlink range to a mobile that can be expected from a BTS transmitter output of 16W (42dBm). For this example, a 100-foot tower and a 22dB-gain antenna were chosen. Path loss is determined by adding gains, losses, and receiver sensitivity and solving for “X.” The downlink gain budget from BTS to mobile is:

42dBm+22-6=-95dBm

where -95dBm = mobile receive target level

-2dB = antenna gain

-6dB = portable antenna efficiency

Solving, X = -153dB.

With a 100-foot tower, a 22dB-gain antenna and 26dB of receive antenna “gain,” a 42dBm-ERP signal will be attenuated by 153dB over the path. Solving the Egli formula for path distance yields:

D = log^-1[153-117-20log1,900+20log(100X6)/40] = 4.46 miles

This establishes a BTS talkout range of 4.5 miles. Next, it must be determined if the mobile can talk back to the BTS receiver over the same path. Because the system is talkback-limited, a tower-mounted amplifier (TMA) is required in each uplink receiver. Uplink gain budget from mobile to BTS receiver is:

27dBm-6-153+22+X = -95dBm

where -7dBm = 600mW portable output

-6 = portable antenna efficiency

X = additional gain

Solving, X = 15dB, or the amount of additional gain in the uplink path necessary to establish parity between BTS talkout and mobile talkback.

So, it appears that a 15dB-gain TMA will offset the disparity between talkout and talkback. Unfortunately, because of noise considerations, a 15dB-gain TMA will not deliver a 15dB path improvement.

Path improvement through use of a TMA can be estimated by noise analysis of the receive path on a “before and after” basis, as shown in Figure 9 below. The noise between the antenna and the input to the receiver can be calculated on the “before” diagram. Each noise-contributing element is calculated separately before combining in the cascade noise factor formula, starting at the input jumper.

Input jumper:

G = log^-1[-0.3/10] = 0.93 and F = [1/0.93] = 1.07

100-foot, 7/8″ line:

G = log^-1[-2.0/10] = 0.63 and F = [1/0.63] = 1.58

Duplexer:

G = log^-1[-1.1/10] = 0.78 and F = [1/0.78] = 1.29

Receiver, with noise figure, N, of 5dB:

F = log^-1[5/10] = 3.16

Cascade noise factor:

FS = 1.07+[1.58-1/0.93]+[1.29-1/(0.93)(0.63)]+[3.16-1/(0.93)(0.63)(0.78)] = 6.92

Therefore, noise figure of the system without a TMA:

N = 10log6.92 = 8.40

Referring to the “after” diagram in figure 9, system noise figure with a TMA can be calculated. The path through the TMA has special support components including a different duplexer and a bias tee. It also uses a smaller, more economical 1/2″ feeder cable, starting at the jumper.

Input jumper, G = 0.93 and F = 1.07, same as above.

TMA, with 15dB gain and noise figure of 2.2dB:

G = log^-1[15/10] = 31.62, F=log^-1[2.2/10]

100-foot, 1/2″line:

G=log^-1[3.4/10] = 0.46 and F = [1/0.46] = 2.19

Bias tee:

G= log^-1[-0.2/10] = 0.95 and F = [1/0.95] = 1.05

Duplexer:

G = log^-1[-0.5/10] = 0.89 and F = [1/0.89] = 1.12

Receiver, with noise figure N, of 5dB:

F = log^-1[5/10] = 3.16

By the cascade noise factor equation: See the box at the top of page 67.

Therefore, noise figure of the system with a TMA:

N = 10log2.02 = 3.06

Noise figure improvement amounts to subtraction of the before and after noise figures, or 8.40 – 3.06 = 5.34dB. Five decibels of noise figure improvement translates to the same amount of improvement in talkback conditions. In essence, the addition of a 15dB TMA yields a 5.3dB improvement or enhancement in the talkback path.

Interestingly, the difference between the basic sensitivities is also 5.34dB. Path improvement depends heavily on ambient noise and component losses but is rarely more than 7dB without the use of cryogenic amplifiers. The BTS corrected receiver input calculation now becomes:

The BTS designed to deliver -95dBm to a mobile receiver at 4.5 miles will receive a talkback level of -105dBm from mobiles at the same distance. Even though total range is less than on the downlink side, good performance at 4.5 miles is assured because the BTS receive level of -105dBm is 11dB above minimum receiver sensitivity.

In summary, with the parameters set forth, the BTS to mobile range is 4.5 miles. Mobile talkback limitations cannot be completely overcome with tower-mounted amplifiers. The realizable talkback gain of 5dB in the TMA supports only partial parity between talkout and talkback. Some service providers reduce, or pad down, transmitter outputs to maintain exact parity with the best obtainable uplink. Ranging the repeater to mobile distance

Now that the base station to mobile range has been determined, the next step is to find the repeater to mobile ranges. Because the output power and height of each repeater is the same, the potential downlink range to mobiles from each repeater site will be the same. It stands to reason that the repeater sites should not be separated by any greater distance than their talk-out range, or range to mobiles. This range is determined by the output power of the repeaters. With a repeater power output of 139dBm (8W) and a mobile target receive level of 295dBm, path loss and repeater downlink range are calculated:

Path = 39+22-X-6=-95

and, solving,

X = 150dB path loss.

Distance via the Egli formula is:

D = log^-1[150-117-20log1900+20log(100X6)/40] = 3.8 miles

The downlink range of each repeater is 3.8 miles because they all have the same +39dBm (8W) output power. Essentially, for each repeater to reach a mobile at maximum range, the repeater towers must be spaced 3.8 miles apart. Compare this with the range of 2W (+33dBm) repeaters, which would be only 2.7 miles. With known intertower distances, the next step is to work out details pertaining to the “backbone” part of the system -the RF link between towers. Preliminary calculations indicate that line-of-sight propagation exists between towers at the 80-foot and 100-foot heights. Vertical antenna separation of 20 feet on each tower ensures adequate isolation between uplink and downlink. Calculated free space loss over 4.5 miles between the BTS and first repeater is 111dB and that between repeaters is 109dB. Link power levels can now be determined by adding gains and losses.

Backbone downlink signal from the base transmitter through the first repeater is calculated:

42dBm BTS out + 22dB base antenna gain -111dB path loss + X = 39dBm repeater output

where 39dBm = 8W CDMA output of the amplifier

X = total downlink gain at repeater 1.

Solving for X indicates 86dB total gain is needed to drive the repeater to its full rated output power of 39dBm, or 8W. Gain adjustments on the amplifier used in this example gives the option of choosing more economical, lower-gain antennas in the downlink. Opting for a 12dB-gain antenna, the balance of the required 86dB can be provided by the downlink amplifier. Gain of the amplifiers is adjustable from 65dB to 95dB. In this case, downlink gain would be set for (86 – 12), or 74dB.

The backbone link between the two repeaters is calculated in similar fashion:

39dBm repeater 1 output + 22dB antenna gain – 109dB path loss + X = 39dBm (repeater 2 output)

Solving for X, this works out to 87dB, and again the antenna can contribute 12dB, requiring a balance of 75dB from repeater 2, which is also driven to its full 8W or 139dBm output. As determined earlier, 39dBm plus 22dB antenna gain at each repeater site will deliver 295dBm into mobile receivers 3.8 miles away. As a check of the backbone downlink calculations, a “power flow” budget would be as shown in the box at the left.

All that remains is to calculate the uplink backbone gain values. Other elements in the uplink are now fixed.

To review, there are 22dB-gain, top-mounted antennas and tower-mounted amplifiers in each uplink location, including the BTS. Uplink antennas of 12dB gain are at the 80-foot level of each repeater tower. Before completing the uplink backbone calculations, it is necessary to determine the amount of path enhancement contributed by the tower-mounted amplifiers working into the repeaters. Previously, uplink path enhancement at the BTS receiver was found to be about 5dB. Tower-mounted amplifier enhancement should be evaluated again for the repeaters because the TMAs are working into different noise figures than in the receiver.

The amplifier noise figure is 6dB and its noise factor, F, is 3.98. The noise factor calculation will be the same as for the TMA/receiver, except for the last term, which now contains the amplifier noise factor of 3.98. Noise factor of an uplink repeater with a TMA and (repeater) amplifier is calculated as:

(See the box at the top of page 69.)

and, uplink noise figure with a TMA and amplifier is

N = 10log2.09=3.2dB

To find the amount of TMA enhancement in the uplink repeaters, it is necessary to calculate the noise figure with no TMA and subtract the noise figure with TMA, 3.2 dB above. Noise factor with no TMA is:

Fs = 1.07+[1.58-1/0.93]+[1.26-1/(0.93)(0.63)(0.78)] = 8.66

and N = 9.4dB.

Therefore, the amount of uplink repeater path improvement with TMAs is 9.4dB – 3.2dB = 6.2 dB. Backbone uplink signal level from the mobile into the first repeater is calculated:

27dBm, mobile out – 6 dB, antenna efficiency -150dB, path loss + 22dB, antenna gain 1 6dB, TMA = -101dBm into repeater 2 amplifier.

To determine the required amplifier gains in the two uplink repeaters, an equation of gains and losses from the input of repeater 2 all the way back to the input of the BTS receiver is set up:

Solving, 2X = 147dB total gain. Splitting the gain between the two uplink amplifiers gives 73.5dB gain in each amplifier. An uplink backbone “power flow” budget would be:

In summary, highway repeater tower locations are specified based on downlink transmit power from the base station and subsequent repeaters. Then, the ability of mobiles to talk back in the uplink to each location is verified. Because of inherent talkback limitations, it is usually necessary to use tower-top amplifiers in each uplink path. Next, the intertower or backbone portion of the repeater system is established. The wide range of gain adjustment available in the amplifiers used in this example leads to efficient level management in the backbone. Accordingly, it is possible to use lower gain, more economical antennas in parts of the backbone.

*Tunnels – A CDMA 1900 amplifier and radiating cable are a great combination for solving tunnel or other “shielded conduit” passageway coverage problems. The following example considers an 1,800-foot tunnel located about1.0 mile from the PCS cell site. Coverage in the tunnel is provided by 7/8″ radiating cable. Typical of most urban situations, this example assumes the remote antenna is not within line of sight of the BTS. Attenuation calculated with the Egli Model shows about 120 dB over the path. In actual design situations, path loss should be measured. Worst case link budgets look like this:

See original table.

No tower-top amplification was specified in the uplink, although the -105dBm talkback signal to the BTS receiver might warrant the use of a TMA. About 5dB of talkback improvement could be expected with TMA. It would assure better parity between talkout and talkback. However, the system designer must make a judgment call with respect to added cost vs. improvement in performance.

Creating a ubiquitous network As PCS systems are built out, designers will most certainly be confronted with the problem of null filling. Bidirectional CDMA amplifiers and tower-top amplifiers can help with the most challenging system designs.

Swinney is an applications engineer for the Andrew RF Amplifier Group in Dallas. He can be reached through email at [email protected] This article is a revised and updated version of an article that originally appeared in MRT’s companion publication, Site Management & Technology, in the Spring 1999 issue.