Network planning in GSM systems is moving toward re-engineering. This trend points to the fact that developed countries are facing problems due to overloaded networks and hot spots. Before attempting to implement any re-engineered solution, however, it's essential to consider the reduction of costs in that solution's implementation. For this reason and numerous others, tower-mounted amplifiers (TMAs) are proliferating in today's wireless systems.

In both Global System for Mobile Communications (GSM) and Universal Mobile Telecommunications System (UMTS), TMAs are used to provide a balanced system design. They allow mobile operators to place an equal amount of receiving and transmitting sites.^{1} TMAs also enable base stations to receive mobile signals more clearly and in a wider coverage area than they could otherwise achieve.^{2} Mobile network operators can therefore achieve the greatest possible coverage with less base stations, which limits their costs.

Clearly, TMAs are hailed as a benefit-filled solution. Yet the presence of interference must be taken into account. This article focuses on the nonlinear distortion in TMAs as well as that distortion's impact on the overall performance of GSM systems.

When any radio engineer decides to use a TMA, his or her goal is to improve the overall sensitivity of the system. Sensitivity gives the engineer an indication of a receiver's robustness. To do so, it captures a weak signal that directly affects the range of the system.

Sensitivity also reveals the receiver's level of noise immunity. According to Equation 1, sensitivity can be understood as the minimum input power needed to get a suitable signal-to-noise ratio (SNR) at the output of the receiver. For this reason, sensitivity is based on the following: the receiver noise figure, the minimum required signal-to-noise ratio for detection, and the thermal noise of the system.^{3}

S_{i,min} = NF + n_{0} + SNR (dBM)

S_{i,min} = sensitivity

NF = noise figure of the receiver

SNR = required output signal-to-noise ratio (usually related to the acceptable bit error rate)

n_{0} = thermal noise power of the receiver, n_{0 }= KTB, where K is the Boltzman constant, T stands for temperature, and B is the bandwidth of the system

In Equation 1, the temperature is defined by the environment in which the TMA will be installed. As a result, B is the GSM bandwidth, 200 KHz. K is a constant. SNR is imposed by the modulation technique. Hence, the only free parameter is NF. In a sense, that noise figure provides an idea of the SNR degradation that will occur when the signal traverses the receiver. One possible mathematical definition is expressed in Equation 2:

In a cascade of noisy blocks, the overall equivalent NF is given by Equation 3. By looking closely at Equation 3, one can gather some important information. For instance, the noise figure of the first block will impose the minimum noise figure of the system. (Remember that by definition, the noise figure is always either positive and higher or equal to 1.) In addition, an important conclusion can be made about the gain of the first components: The higher the gain, the higher the desensitization of the next blocks.

The sensitivity of tower-mounted amplifiers can be determined in different ways. FIGURE 1, for example, presents a basic receiving implementation that will be used to see the different effects of each subsystem. As can be seen in Equation 4, cable losses are the dominant factor in the system's noise figure. As a result, these losses are the major limiting factor for a receiver's sensitivity. To compensate for this problem, the idea is to desensitize the cable noise figure. To achieve that goal, manufacturers began providing TMAs.

A schematic TMA system is presented in FIGURE 2. The TMA subsystem is placed near the antenna. That subsystem is somewhat similar to the well-known low-noise block (LNB), which was used for several years in television satellite receivers. The main difference between them is that now, no frequency translation is needed.

To evaluate the effects of introducing a TMA, make some simple calculations. A GSM scenario typically has:

n_{0} = −>121 dBm

S_{i,min} = −105 dBm

SNR = 9 dB (typical value)

Using Equation 1, NF is calculated to be 7 dB (F = 10^{(7/10) }= 5).

Say the system was designed to have a noise figure of 7 dB. In that instance, a cable will severely degrade the overall system. Taking into account a cable of 3-dB losses, the result will be Equation 5:

The resulting sensitivity will be: S = −102 dBm.

Now, imagine that a typical tower-mounted amplifier is added with NF = 1.7 dB and G = 12 dB. By applying Equation 3, the result will be Equation 6. From Equation 1, it's now possible to calculate the new sensitivity:

S_{i} = 3 − 121 + 9 = −109 dBm

This new sensitivity value allows better signal reception. Such improved reception can be translated into the maximum coverage area. Using the Friis equation and the Hata-Okumura propagation model, the distances depicted in FIGURE 3 are attained for an urban environment (assuming an emitter with 30 dBm of transmitted power).^{4} Simply by adding a TMA, coverage was improved by 63%.

Clearly, tower-mounted amplifiers provide important sensitivity-improvement benefits. If one does not account for the presence of interference, however, adding a tower-mounted amplifier can become a very bad design decision.^{3} For example, look at the nonlinear distortion that is generated at the TMA itself.

Because a TMA is an active device, it will generate some form of distortion.^{6} Such distortion is mainly due to the finite amount of energy that can be used from the power supply. For this reason, any amplifier will somehow saturate at a certain amount of input power.

If a designer takes the previous approach, in which the sensitivity of a TMA was studied, no problem will appear. In that scenario, he or she is only dealing with small signal-excursion input signals. When referring to a high-power interferer, however, the scenario changes. The power of that interferer is simply not known.

To better understand the nonlinear mechanism, try approximating the amplifier with a low-degree polynomial like the approach taken in Equation 7^{5}. Next, consider what would happen if a two-tone signal was introduced at the input of this device by looking at Equation 8.

It becomes obvious that different spectral components will appear at the output. Nonlinearity generates spectral components all over the band. But the most important components are the ones that fall inside the bandwidth. Hence, only two types of output spectral components will be studied. The first is the third-order IMD (FIG. 4).

The second component to be studied will be the co-channel distortion, which is usually called desensitization (FIG. 5). The IMD distortion is responsible for the well-known spectral-regrowth effect. In a two-tone excitation, it will appear at 2ω_{1}−ω_{2} and 2ω_{2}−ω_{1}.

Remember that in GSM, there are several operators. Due to capacity problems, each operator can have several emitting and receiving channels. So it is quite obvious that this kind of distortion could at least partially impact the system's performance. Two different carriers will generate two interference signals that can fall exactly over the desired signals.

In the second case, the result is even more disastrous. An interferer can be so strong that the signal will be destroyed.^{6 }In both cases, the signal could be blocked if the interfering signal is strong enough to degrade it to that extent. In World War II, such "jamming" was actually one of the electronic war technologies.

To further examine TMA performance degradation, look again at Figure 2. Here, the TMA internal configuration was presented. The isolation between the Tx and Rx is high in the duplexer, thereby preventing the Tx signal passes from throwing the Rx filter and causing any nonlinear distortion. Now, study the impact upon the system when it receives two different Rx signals: a desired signal and an interference signal (FIG. 6). This interference can be from either the same or another operator. Here, consider it to be from a different operator. (Otherwise, it would be possible to minimize the interference by using some form of power control.)

First, calculate the values of the out-of-band power that is needed to degrade the useful signal. Remember that a 9-dB SNR has to be achieved. Use the following typical TMA values:

n_{0} = −121 dBm

SNR = 9 dB

IP_{3} = 25 dBm (typical value of a TMA amplifier)

The system is only useful when the nonlinear distortion generated by the interference is 9 dB below the sensitivity or higher. For the worst-case scenario, the minimum interferer signal power at the amplifier's input should be:

P_{INT} = S_{i }− SNR

where P_{INT} is the interferer power.

For a case of two-channel interference of equal amplitude, the third-order IMD value will be:

at 2ω_{1}−ω_{2} and 2ω_{2}−>ω_{1} (co-channel interference).^{6}

Solving these two equations results in the value: P_{INT} @ P_{2 }= −29 dBm. If a signal at the TMA's input reaches this value, one should expect an intermodulation power that degrades the system in a neighbor channel (FIG. 7).

If the desensitization is then calculated at v_{1}, it causes an amplitude interference of:^{6}

Now, consider the minimum power that can be allowed by the distortion nonlinearity at v_{1} (P_{1} = −>105 − 9 = −114 dBm). The interference power that is needed to generate this distortion is P_{INT }= P_{2 }= 6 dBm (FIG. 8).

The previous case assumed that the TMA had a full uplink bandwidth. In other words, it receives and amplifies all of the GSM operators. The current scenario assumes access to a sub-banded TMA for only one operator with a typical out-of-band attenuation of 80 dB. This interferer power thereby increases to the value of 51 dBm (126 W) for intermodulation and 86 dBm (398 kW) for desensitization. Of course, it is unrealistic to consider any interference for the sources in this case.

Although these values seem quite high, it's critical to not forget that bit-error-rate degradation might occur for lower interferer powers than sensitivity. Also, don't forget that these calculations were made assuming a two-tone input. A real signal would be better modulated by a multi-tone or real signal.^{6}

To evaluate the real impact of TMA nonlinear distortion, a computer simulation was performed using a system simulator.^{7} Consider two different operators at frequencies of 897.4 MHz (Operator 1) and 900 MHz (Operator 2). The output power of the desired signal (Operator 1) is fixed at 105 dBm. Meanwhile, the output power of the interference signal (Operator 2) will be raised from −105 dBm to 30 dBm—the maximum output power of a mobile station (FIG. 9).

From FIGURE 10, one can see that the curve will quickly move toward 100% BER. In the GSM example, a maximum BER of 0.2% was typically allowed in order to guarantee receiver quality.^{8} So the maximum interferer power allowed would be approximately −14 dBm at the input of the TMA. This kind of power can easily be found in urban environments, where a high density of BTSs and TMAs is available (mainly in hot-spot situations like commercial malls or garages).

In conclusion, a TMA will boost the system performance. But in the presence of strong interferer signals, it can be easily blocked. In these situations, it's better to opt for sub-banded tower-mounted amplifiers. Such TMAs allow the designer to attenuate the interferer power and therefore the impact of nonlinear distortions.

**REFERENCES:**

\[1\] Ira Wiesenfeld, "Testing tower top amplifiers," Mobile Radio Technology, May 1, 2003.

\[2\] LGP Telecom, "Tower Mounted Amplifier System" Application Note.

\[3\] Maxim, "Improving Receiver Sensitivity with External LNA," APP 1836, December 27, 2002.

\[4\] Rappaport, Theodore S., "Wireless Communications: Principles and Practice," Prentice Hall, N.J., 1996.

\[5\] Carvalho, N. B., and Madureira, R. C., "Intermodulation Interference in the GSM/UMTS Bands," III Conferência de Telecomunicações, Figueira da Foz, p. 396-399, April 2001.

\[6\] Pedro, José Carlos, and Borges de Carvalho, Nuno, "Intermodulation Distortion in Microwave and Wireless Circuits," Artech House Publishers, Norwood, Mass., August 2003.

\[7\] Advanced Design System, 2002, Agilent Technologies

\[8\] ETSI TS 100 910 v8.9.0 (2001-04), "Digital Cellular Telecommunications System (Phase 2+); Radio Transmission and Reception," ETSI.