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Design of a Wideband Adaptive Linear Amplifier with a DSB Pilot and Complex Coherent Detection Method

In this article, a novel adaptive linearization method, based on a double sideband (DSB) pilot in a feedforward power amplifier, is presented. The methods of generation and detection of the DSB pilot signal are described in detail. With this method, an...

April 5, 2006
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In third generation (3G) mobile communication systems, linear amplification is required for linear modulations. Nonlinear amplification yields inter-modulation distortion (IMD) products and results in unacceptable spectral regrowth in adjacent channels. To achieve linear amplification, linearization techniques are usually employed. Various techniques have been developed to reduce IMD products in high power amplifiers. Generally, three main linearization methods are used. They are the feedforward method, the feedback method and the predistortion method. Adaptive techniques are usually employed to improve the linearization performance.

Adaptive feedforward Method with DSB Pilot

The feedforward method is a commonly used approach, which provides a significant improvement in the linearity of power amplifiers.1–5 The mechanism used in a feedforward amplifier is to cancel the inter-modulation products produced by the main amplifier. The diagram of the feedforward amplifier with a DSB pilot is shown in Figure 1. The purpose of the DSB pilot is to obtain a better adaptive cancellation.

A feedforward amplifier consists of two loops. The first one, Loop 1, is the carrier cancellation loop that is used to cancel the carriers and obtain the IMD products of the main amplifier (denoted as error signal). The second loop, Loop 2, is the IMD cancellation loop, which is used to reduce the output IMD products with the error signal. For simplicity, assume that the amplifier is injected with a two-tone signal, as shown at node A. The output of the main amplifier will contain the IMD products in addition to the main amplified signals, as shown at node B. The DSB pilot signal is injected at the output of the main amplifier, as shown at node C. In Loop 1, an error signal that contains the IMD products generated in the PA and the DSB pilot signal is obtained, as shown at node D. This error signal is the result of the comparison of a sample of the PA output signal, appropriately attenuated, with a properly retarded sample of the input signal. This combination is usually carried out in a 180° combiner. In Loop 2, the error signal obtained in the previous circuit is appropriately amplified (as shown at node E) and injected in opposite-phase to the output in order to cancel the IMD introduced by the PA and the pilot signal, as shown at node F. Delay lines should be used in both loops for wideband operation. The amount of correction is limited by the ability of the two loops to match the gain and phase between the main signal and error path. In Loop 1, the main path consists of the main amplifier and Attenuator 2, while the error path consists of the Delay Line 1, Attenuator 1 and Phase Shifter 1. In Loop 2, the main path consists of the Delay Line 2, while the error path consists of the Delay Line 1, Attenuator 3, Phase Shifter 2 and the Error Amplifier.

The cancellation is very sensitive to the operating condition of the power amplifier, such as operating temperature, operating frequency and the power level of the input signal. Therefore, adaptive techniques are required in feedforward amplifiers. The purpose of the adaptive method is to achieve the best cancellation in both loops. The criterions for the optimal cancellation in the two loops are different. The purpose of the first loop is to cancel the main signal. As a result, the optimal cancellation of the first loop can be achieved by minimizing its output power. In the second loop, the situation is more complicated because it is very difficult to obtain an accurate power level of the distortion signals. Therefore, a pilot signal is generally injected at the output of the main amplifier to facilitate the adaptive cancellation of the second loop. With a pilot signal, the optimal cancellation of the second loop can be approximately achieved by minimizing the cancelled pilot signal power. The amount of correction of a feedforward amplifier is limited by the mismatch of the gain and phase between the main signal and the error signal. When only a small amount of gain and phase error is achieved, the correction is determined by1–3


?IMD = amount of IMD improvement in dB

?G = amplitude error between the main path and error path

?? = phase error between the main path and error path

Much research has been done on the analysis of the mismatches that affect the performance of feedforward amplifiers. This article focuses on the analysis of the second loop with a DSB pilot. It is known that the bandwidth of cancellation is mainly limited by the mismatch of the group delay, and the optimization of the phase error is more difficult than that of the amplitude error. To simplify the analysis, only the phase error and the group delay are considered, and the gain of the two paths is assumed to be perfectly matched. The selection of the pilot is very important for the feedforward amplifier. The chosen frequency of the pilot should be outside the operating frequency band so that it can be detected accurately without difficulties. Assuming that the center frequency of the amplifier is ?0, the pilot signals are located at ?0 – ?? and ?0 + ??, where ?? is the frequency of the offset source. The voltage of the output pilot signal after cancellation is


A = amplitude of the pilot in both the main path and the error path

?t = delay error between the main and error paths

?? = phase error between the main and error paths

The total pilot signal power, after cancellation, is

For simplification, let ? = ?? + ?0?t and ?0 = ???t; Equation 3 can then be rewritten as

After calculating the derivative

and let it equal to zero, the solution is

For a wideband, feedforward amplifier, the delay error ?t should be as small as possible, generally less than 1 ns, and ?? is approximately several tens of megahertz. The value of ?0 is very small, normally approximately several degrees. Thus, the total power of the pilot signal is minimal when ? = 0. For a feedforward amplifier, the best cancellation performance is generally obtained when ? = 0. Therefore, when the power of the cancelled pilot is minimized, it means that the optimal cancellation of the second loop is obtained. It is very clear that the DSB pilot method is more accurate and efficient for wideband linearization than the single sideband (SSB) pilot method.

Generation and Detection of the DSB Pilot Signal

The generation of the DSB pilot signal can be accomplished with a high carrier-suppression analog modulator. Here, the detection of the DSB pilot signal is accomplished with a complex coherent method, as shown in Figure 2. The LO of the mixer is the same as that of the modulator; therefore, there is no frequency error in this system. The advantage of the complex detection method is that it can accurately determine the power of the DSB pilot signal by eliminating the phase error in the system. The pilot signal input to the detector can be written as


A1, ?1 = amplitude and phase of the low sideband pilot signal

A2, ?2 = amplitude and phase of the high sideband pilot signal

The LO for the mixers is VLO = cos?0t.

The IF output signals of the mixers are


G1 = cascaded gain of mixers, IF filters and IF amplifiers

The output voltages of the square-law detectors after the low pass filters are


G2 = conversion gain of the detectors

The output voltage of the complex detector is

It is obvious that the output voltage is proportional to the total power of the DSB pilot signal and is independent to the phase difference between the pilot and the LO signals. Therefore, the total power of the DSB pilot signal is accurately detected by the complex detector. The output voltage of a simple detector, however, is dependent to the phase of the pilot, as shown in Equations 8 or 9. The advantage of the complex detection is very clear for the DSB pilot.

The adaptive controller is used to minimize the voltage of the power detector and the complex detector by adjusting the Attenuator 1 and Phase Shifter 1 in the first loop, and Attenuator 3 and Phase Shifter 2 in the second loop. As stated above, optimal cancellation is obtained when these voltages are minimized.

Experimental Results

An adaptive feedforward amplifier was designed and fabricated for use in the WCDMA band. The output power of the amplifier is 10 W. Figure 3 gives the two-tone IMD results of the power amplifier. The spacing between the two-tone input frequencies is 20 MHz. The original IMD3, before linearization, is approximately –35 dB. After linearization, the levels of the IMD components are less than –62 dB. The improvement in IMD performance is better than 27 dB. Figure 4 gives the multi-carrier adjacent channel power ratio (ACPR) results for the power amplifier. The input of the amplifier is a four-carrier WCDMA downlink signal with 64 dedicated physical channels (DPCH) in each carrier. The multi-carrier ACPR performance before and after linearization is shown. The improvement in ACPR is better than 15 dB.


A wideband adaptive feedforward amplifier with high linearity is designed for a WCDMA base station using the DSB pilot method. The theoretical analysis and experimental results show that the DSB pilot method and the complex detection method are valid and effective for feedforward linearization.


1. J.K. Cavers, “Adaptation Behavior of a feedforward Amplifier Linearizer,” IEEE Transactions on Vehicular Technology, Vol. 44, No. 1, February 1995, pp. 31–40.

2. Y.K.G. Hau, V. Postoyalko and J.R. Richardson, “Sensitivity of Distortion Cancellation in feedforward Amplifiers to Loops Imbalances,” IEEE MTT-S 1997 International Microwave Symposium Digest, Vol. III, June 1997, pp. 1695–1698.

3. S.G. Kang, I.K. Lee and K.S. Yoo, “Analysis and Design of feedforward Power Amplifiers,” IEEE MTT-S 1997 International Microwave Symposium Digest, Vol. III, pp. 1519–1522.

4. J. Zhou, L. Feng, X. Zhu and W. Hong, “Design of an Ultra-linear Wideband feedforward Amplifier Using EDA Tools,” Microwave Journal, Vol. 43, No. 1, January 2000, pp. 124-130.

5. M.G. Choi, Y.C. Jeong and I.H. Park, “Method and Apparatus for Amplifying feedforward Linear Power Using Pilot Tone Hopping,” US Patent No. 081,156, 2000.

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