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A m systems amplifier imran

Nisoli, S. Stagira, D. Silvestri, S. Svelto, O. Sartania et al. DOI :


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Metrics details. An Erratum to this article was published on 24 April The high peak-to-average power ratio PAPR remains a major drawback of multicarrier modulations. Hence, the nonlinear characteristics of power amplifiers PA results in strong distortion and low power efficiency when multicarrier modulations are used.

In this paper, the impact of the nonlinearities on the amplified multicarrier signal is analyzed, considering both PAPR limitation using clipping and PA linearization.

We provide analytical EVM expressions that depend on the PA and predistortion characteristics, as well as the PAPR and the average power of both input and clipped signals. These expressions are general formulas which allow to measure in-band distortion at the PA output. The simulation results show that the proposed expressions present perfect accuracy.

Moreover, the trade-off between the PA linearity and efficiency is investigated considering the performance of the clipping and predistortion techniques.

Finally, the predistortion complexity is discussed aiming at reducing it with respect to an EVM constraint. Furthermore, multicarrier modulations may be a worthy candidate for the next generation 5G cellular systems.

All these techniques suffer from high peak-to-average power ratio PAPR of the transmitted signal which prevents to feed the power amplifier PA at its optimal point, hereby lowering its power efficiency. Considering the PA characteristics and the PA power efficiency, it is well-known that the closer the average power of the transmitted signal to the nonlinear zone of the PA characteristics, the higher the PA efficiency.

So, a trade-off between the linearity and the efficiency of the PA should be carefully considered. In the literature, one can find two main strategies to deal with this problem: PAPR reduction of the transmitted signal and linearization of the PA. The PAPR reduction approach aims at reducing the dynamic range of the transmitted signal.

The second approach is the linearization which tries to compensate for the nonlinearity of the PA. Among the large variety of linearization techniques, the most popular ones are digital predistortion DPD [ 6 ], linear amplification with nonlinear component LINC [ 7 ], and feedback [ 8 ].

In our study, we consider the clipping technique as a PAPR reduction technique and the predistortion as a linearization technique. Although PAPR reduction and linearization techniques work in a complementary way [ 9 , 10 ], it turns out that they are often designed separately and implemented independently in conventional systems [ 11 — 16 ].

Nevertheless, recent studies have investigated some joint design of these techniques in order to enhance their interoperability [ 17 — 20 ]. In this paper, we propose to go a step beyond this strategy by introducing a new adaptive approach which controls the clipping and predistortion functions in a flexible way.

Our aim is to maximize the PA efficiency and minimize the predistortion complexity with respect to the linearity constraint, as represented by the error vector magnitude EVM of the amplified signal, and according to some predefined parameters. The EVM is a common figure of merits used to evaluate the quality of communication systems. Indeed, most of wireless communication standards such as the IEEE Our objective is to derive a flexible transmitter model able to update its parameters according to incoming requirements and outside environment.

Hence, this work is a very important step in the analytical study of the global optimization approach of the transmitter efficiency and linearity. In this context, we are involved in this paper in the analytical derivation of the EVM of multicarrier signals. In [ 24 , 25 ], we already derived EVM expressions of clipped predistorted multicarrier signals amplified by Rapp PA model.

In this paper, we study the amplitude probability distribution of the signal after applying the clipping technique. After that, we derive the EVM expression of nonlinear amplified multicarrier signals using a memoryless polynomial PA model when clipping is activated or not. Then, we focus on the impact of the predistortion technique on the EVM expression.

Once again, we derive the EVM of multicarrier signals when the memoryless polynomial predistortion is activated. Therefore, our first contribution consists in providing EVM expressions as a function of the transmitted power, the clipping threshold, and the PA and predistortion characteristics, as well as the PAPR of the input and clipped signals. As far as theoretical EVM derivations are concerned, some upper-bounds can be found in [ 26 , 27 ], and other contributions, as [ 28 — 30 ], give closed-form EVM expressions but modeling the RF front end as a simple clipping.

To the best of our knowledge, despite numerous studies in the literature about PAPR, no analytical expression of the EVM, taking into account all the above mentioned parameters, exists in the literature.

Moreover, we investigate the theoretical analysis of the PA linearity-efficiency and the predistortion complexity. We first examine the PA linearity-efficiency trade-off. Thereby, we provide an analytical expression which gives the optimal input back-off IBO and clipping threshold which must be taken to maximize the PA efficiency for any EVM constraint. Secondly, we discuss the trade-off between the PA linearity and the predistortion complexity aiming at reducing the predistortion complexity with respect to an EVM constraint.

Therefore, we seek the optimal configuration of clipping and predistortion which maximizes the PA efficiency taking into account the predistortion complexity and satisfying the EVM constraint. The remainder of the paper is organized as follows. In Section 2 , we introduce our system model. Then, the theoretical derivations of the EVM with the simulation results in both cases without and with predistortion are presented in Section 3 and 4 , respectively.

Afterwards, the theoretical analysis of the trade-off between the PA linearity-efficiency and the complexity of the predistortion is presented in Section 5. Finally, a conclusion and perspectives are drawn in Section 6. Figure 1 represents a simplified block diagram of the transmission chain with clipping and predistortion stages preceding the PA. The multicarrier signal x 1 t , generated by the system, becomes x 2 t after clipping, and x 3 t after the predistortion operation.

The output of the PA is z t. One of the major drawbacks of multicarrier waveforms is the high PAPR of the signals obtained in the time domain. The PAPR of a signal is defined as the ratio between the maximum and the average power of the signal over a time interval T , and is given by. There are many PAPR reduction techniques that aim at reducing the dynamic range of the signal amplitude.

Clipping is one of the most used techniques for PAPR reduction due to its simplicity and its straightforward reduction gain. Thus, the clipped signal, x 2 t , is represented as.

This technique results in both in-band and out-of-band distortions because of its nonlinear operation. Additionally, it changes the amplitude probability distribution function of the signal which is discussed in the next subsection. We assume that the multicarrier signal is characterized by a complex stationary Gaussian process [ 31 ]. Therefore, its amplitude converges to a Rayleigh distribution whose probability density function PDF can be written as.

However, after clipping, the PDF of the signal amplitude changes and is stated in the following lemma.

Please note that for a given number of subcarriers and a type of modulation, there is a maximum value that PAPR can reach. Therefore, we obtain.

Thus, we can write. Hence, calculating the integral in Eq. Note that the signal amplitude in practice does not tend to infinity and is limited to a maximum value R max which depends on the system parameters as the number of subcarriers.

The amplitude distribution of the input signal x 1 t , and the clipped signal x 2 t , are presented in Fig. The former, because of its small size, can be used in mobile transmitters, whereas the latter is mostly employed for high-power satellite transponders. In this paper, we consider the SSPA type for a mobile transmitter and assume that it is memoryless and does not present any phase distortion.

Predistortion is based on the following simple idea: the signal is applied to H PD r which is exactly the inverse of the PA transfer function. Thus, the concatenation of these two functions will ideally be equivalent to a linear function.

Since the PA model is a polynomial function, the inverse predistortion function can also be expressed as a polynomial. Therefore, the predistortion function is expressed as follows. The error vector magnitude EVM is a metric which measures the distortion level of a signal. A signal sent by an ideal transmitter would have all constellation points precisely at their ideal locations. However, various imperfections in the implementation such as the nonlinearity of the PA function and the PAPR reduction stage cause the actual constellation points to deviate from the ideal locations.

Figure 3 represents X k and Z k the k th complex symbols of the signal before clipping and after amplification, x 1 t and z t , respectively. In this figure, a unitary amplification gain is assumed for the clarity of the representation. The EVM is defined as the ratio of the root mean square RMS of the difference between a collection of measured symbols and ideal symbols to the root of the mean signal power.

Therefore, the EVM of the amplified signal z t is expressed as follows. Then, Eq. In this section, we present the results of the EVM derivations when predistortion is not activated, in both cases with and without clipping, as a function of the PA characteristics, the average power and the PAPR of both input and clipped signals. Firstly, we start by deriving the EVM expression when clipping and predistortion are deactivated.

Using Eqs. Our main result is presented in the following theorem. This theorem provides an analytical EVM expression in the form of a series expansion involving gamma functions and depending on different parameters. Note that this expression will be useful in the following analytical derivations of the EVM with clipping.

We now lead the EVM calculation considering that the clipping is activated. In this case, using Lemma 1, Lemma 2, Eq. Eventually, as in the case without clipping, Theorem 2 gives an EVM expression in the form of a series expansion composed of Gamma functions and depending on several parameters. In this subsection, we present a comparison between the theoretical EVM, given by Theorem 1 and Theorem 2, and the simulated EVM when clipping is activated or not.

Note that each simulation considers 10 5 randomly generated OFDM symbols with subcarriers associated to QAM modulation symbols. From the curves in Figs. This is due to the nonlinear characteristics of the DVB-T PA even within the expected linear region, which results in additional distortion. Finally, from the comparison between the theoretical and simulated curves, we conclude that our analytical results in Theorem 1 and Theorem 2 perfectly match the simulated EVM for both PAs.

This proves the accuracy of our proposed analytical EVM derivations with and without clipping. In this section, we assume that the predistortion technique is activated. Hence, we investigate the EVM calculation, in both cases with and without clipping, based on the PA characteristics, the predistortion characteristics, and the clipping threshold, as well as the average power and the PAPR of both input and clipped signals.

Thus, the equivalent transfer function of the predistortion and amplification stages will be denoted by H EQ ,. In this case, using Eqs. As in the case without predistortion, this theorem provides an EVM expression in the form of a series expansion based on gamma functions.


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IEEE Transactions on Circuits and Systems II: Express Briefs, Volume 67

a m systems amplifier imran

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Autonomous predistortion calibration of an RF power amplifier


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Metrics details. An Erratum to this article was published on 24 April The high peak-to-average power ratio PAPR remains a major drawback of multicarrier modulations. Hence, the nonlinear characteristics of power amplifiers PA results in strong distortion and low power efficiency when multicarrier modulations are used. In this paper, the impact of the nonlinearities on the amplified multicarrier signal is analyzed, considering both PAPR limitation using clipping and PA linearization. We provide analytical EVM expressions that depend on the PA and predistortion characteristics, as well as the PAPR and the average power of both input and clipped signals.

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