To better understand the nonlinear mechanism, try approximating the amplifier with a low-degree polynomial like the approach taken in Equation 7⁵. 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 2ω₁−ω₂ and 2ω₂−ω₁.

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:

n₀ = −121 dBm

SNR = 9 dB

IP₃ = 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 2ω₁−ω₂ and 2ω₂−>ω₁ (co-channel interference).⁶

Solving these two equations results in the value: P_INT @ P₂ = −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 v₁, it causes an amplitude interference of:⁶

Now, consider the minimum power that can be allowed by the distortion nonlinearity at v₁ (P₁ = −>105 − 9 = −114 dBm). The interference power that is needed to generate this distortion is P_INT = P₂ = 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.