A New Two-Branch Amplification Architecture and its Application with Various Modulated Signals

W.Hamdane,A.B.Kouki,and F.Gagnon

(Department of Electrical Engineering,école de Technologie Supérieure,Montréal,Québec H3C 1K3,Canada)

Abstract:This paper proposes a new two-branch amplification architecture that combines baseband signal decomposition with RF front-end optimization.In the proposed architecture,the filtered modulated signals are separated into two components that are then amplified independently and combined to regenerate an amplified version of the original signal.A branch with an efficient amplifier transmits a low-varying envelope signal that contains the main part of the information.Another branch amplifies the residual portion of the signal.The baseband decomposition and parameters of the RFpart are optimized to find the configuration that gives the best power efficiency and linearity.For M-ary quadrature amplitude modulation(M-QAM)signals,this technique is limited in terms of power efficiency.However,for filtered continuous phase modulation(CPM)signals,especially for minimum shift keying(MSK)and Gaussian MSK(GMSK)signals,high power efficiency can be achieved with no significant impact on the overall linearity.The results show that this technique gives better performance than the single-ended class-B amplifier.

Keyw ords:CPM modulation;M-QAM;RFpower amplifiers;DC-RFefficiency;linearity;crest factor;shaping filters

1 Introduction

T he design of new wireless transmitters is becoming more complex as demand on spectral resources increases and available power for wireless terminals becomes limited.The amount of band occupied by the modulation scheme must be as small as possible in order to accommodate many channels in a given band.For this reason,complex modulation schemes such as M-ary quadrature amplitude modulation(M-QAM)(M up to 256)and M-ary phase shift keying(M-PSK)modulation have been proposed[1],[2].These modulations are spectrally efficient,especially with baseband filtering such as root raised cosine filtering(RRCF).

However,the resulting filtered signals have very high peaks,which are problematic for the power amplifier(PA)stage.To achieve linear amplification with acceptable power efficiency,many approaches have been proposed[3]-[10].In one approach,single branch amplification,typically a class-ABor class-B amplifier,is used to reduce power consumption.A linearization stage,such as digital predistortion[3]-[5],is generally needed with such topology to achieve good linearity and meet linearity requirements.Another approach is to use multibranch schemes[6]-[10],which are more complex but offer greater flexibility.The feed-forward technique[6]is very linear,especially for large-bandwidth signaling,but is not power efficient.Linear amplification with nonlinear components(LINC)[7]-[10],based on outphasing,is another solution.LINC is inefficient in terms of high crest factor signals,which measure the ratio of peak to average power.

Modulations with constant amplitude,such as continuous phase modulation(CPM)[2],[11]-[14]have also been developed.The information is carried in the signal's phase,which is shaped with different types of windows for smooth phase transitions.

These modulations have constant amplitude,and efficient non-linear amplifiers can be used,which makes CPM attractive.However,the spectral efficiency of this modulation depends on signal characteristics such as phase shaping and modulation index[2],[11]and is generally quantized in terms of out-of-band radiation,that is,at the side-lobe level.Unfortunately,spectrally efficient CPM signals,particularly those with low modulation index,have degraded bit error rate(BER)performance and require complex receiver architecture[2],[11].

Pulse-shaping CPM signals can therefore be considered.However,the constant envelope property is lost,and the design of a linear,power-efficient transmitter arises as a new issue.

▼Table 1.Impactof shaping filter on the crest factor

In this paper,we propose a new two-branch amplification architecture that combines digital signal processing and RFfront-end optimization.In section 2,we give a detailed description of the transmitter and the motivations for using a two-branch structure.The signal decomposition technique and overall power efficiency are also presented.In section 3,we investigate the use of this system with digitally modulated signals such as M-QAM and filtered CPM.In section 4,we discuss the performance of the proposed architecture and compare it with a single-ended class-B PA.Concluding remarks are given in section 5.

2 Proposed Two-Branch Amplification System

Using a baseband-shaping filter for digital modulations is unavoidable because it limits the amount of band occupied by the transmitted signal and eliminates inter-symbol interference(ISI)according to the Nyquist criteria[2].However,baseband-shaping filters increase the signal crest factor,which directly impacts efficiency in the amplification stage.For example,a quadrature phase-shift keying(QPSK)signal has a constant amplitude.When filtered with an RRCFfilter that has a roll-off(αrc)of 0.2,the crest factor of the signal can rise up to 5 d B.For a 16QAM signal,the crest factor increases from 2.5 d Bfor a non-filtered constellation to around 7 d B with the same RRCF(Table 1).

In both cases,the amount of spectrum occupied by the transmitted signal is greatly reduced by filtering.But this comes at expense of a dramatic increase in envelope variation.Using single-ended amplifiers generally requires high back-off levels in order to maintain acceptable linearity,and these high back-off levels reduce power efficiency.Therefore,to improve efficiency while ensuring good linearity,we propose a new two-branch amplification system.This system is based on a special decomposition of the filtered input signal.First,the decomposition is applied in baseband,and then specifications of the RFfront-end are determined.This entails specifying the output combining structure and power handling capabilities(P1dBand gain)of the amplifiers that are needed in each branch.Therefore,the amplifiers and output combiner must be designed specifically to meet the established specifications.

2.1 Signal Decomposition

The filtered output of a digitally modulated signalis denoted by h(t).It is decomposed in baseband into two different signals,m(t)and r(t),which have desired power properties and are amplified by optimized amplifiers.m(t)is the main signal,has a constant or low-varying envelope,and carries the main part of the information.r(t)is the remaining part of h(t).Geometrically,this can be represented as a projection of the vector h(t)on the chosen region for m(t)followed by a calculation of r(t).The placement of the projection region is denoted byγ,the ratio of average power of m(t)to average power of r(t).γimpacts the power levels in both branches and the ratio between these power levels.This ratio,in turn,determines the characteristics and performance of the required amplifiers.The optimal choice ofγis a function of the probability density function(PDF)distribution of h(t)and should be such that the difference between the average powers in both paths is minimal.

2.2 RF Front-End Architecture

The decomposed signal must be amplified and combined using the RF transmitter front-end depicted in Fig 1.The RFtransmitter front-end consists of two PAs(main and auxiliary amplifiers)and a directional coupler.The main amplifier generates a high-power output signal and should be a highly efficient class-B,C or F amplifier[15]-[17].Because the input signalhas a low-varying envelope,a non-linear power-efficient amplifier can be used without introducing significant distortion into the main signal component.The auxiliary amplifier amplifies the low-power residual signal.This amplifier must be sufficiently linear to keep the overall system linear.Then,a directional coupler is used to sum the outputs of both amplifiers and generate an amplified version of the filtered signal.A directionalcoupler is a four-port device typically realized in microstrip or stripline technology by closely spaced transmission lines[6].

The parameters of this architecture are as follows:

Input parameters

m(t) inputsignalof the mainamplifier

r(t) inputsignalof the auxiliary amplifier

Pin_mainaveragepowerof the mainsignal

Pin_auxaveragepowerof the residualsignal

γ ratio of theaverage power of themain signalto the average power of the residualsignal

Δm(t) crestfactor of themain signal

Δr(t) crestfactor of theresidualsignal

Amplification stage parameters

α insertionloss of thecoupler

β power coupling coefficient

gmainmainamplifier's gain

gauxauxiliary amplifier's gain

PDC_mainDCpower of main amplifier

PDC_auxDCpower of auxiliaryamplifier

ηmainmainamplifier power efficiency

ηauxauxiliary amplifier power efficiency

Pout_mainaverageoutputpower of the main

amplifier

Pout_auxaverageoutputpower of the auxiliary

amplifier

P1dB(Amain)P1dBof themain amplifier P1dB(Ares)P1dBof theauxiliary amplifier

The input parameters for the amplification stage are obtained after optimization has been done in the signal decomposition stage.The amplification stage parameters are the parameters for both amplifiers and the directional coupler.Based on the architecture in Fig.1,we can write the following equations:

▲Figure 1.Amplification system model.

▼Table 2.QPSKand 16QAMdecomposed signaldynamics

and

The total output power of the amplification system,Pout,is given by:

The coupler's parameters satisfy the following equation[6]:

For perfect linearity,the two paths must be balanced and must have the same gain.This condition can be mathematically expressed as

With the system parameters established,it is possible to determine the ratio P1dB(Amain)to P1dB(Ares)and the globalpower efficiency of the proposed amplification architecture.After mathematical simplification(Appendix A),the final expression of the ratio P1dB(Amain)to P1dB(Ares),denoted asχ,is

Based onχ,it is possible to predict the potential use of this technique with a given signal.As shown in(7),this parameter depends only on the signal envelope statistics and the coupler parameters.The global efficiency is expressed as

The power efficiency of the amplification system is then a function of the power efficiency of the two amplifiers,the coupler parameters,and the ratio of the average powers of both signals.For a given set of amplifiers,fixedηmainandηaux,and a given signal,fixedγ,the optimal efficiency depends solely on the choice of the coupler.A very low coupling coefficient leads to a highly inefficient auxiliary PA.Too much coupling leads to considerable loss in the main path.

In the next section,we discuss the use of this amplification technique with different input signals.Based onχ,it is possible to determine whether the system willbe power efficient with a given signal or not.

3 Use of The Proposed Amplifier with Various Signals

3.1 The Case of M-QAM Signals

The first step in determining the suitability of this technique for the signals of interest is to decompose the signals and calculate all obtained parameters,particularlyγ,Δm(t),and Δm(t).Then,χfor different coupling coefficients is calculated,which allows us to determine whether there is a potential gain when using this technique.For M-QAM signals,we focus on the QPSK and 16QAM modulations.For the QPSK,the main signal corresponds to its mean value m(t).r(t)is the vectorial difference between m(t)and h(t).For the 16QAM signal,we project h(t)onto the region centered by its mean value and reduce the crest factor of m(t)to around 2.5 d B,the crest factor of the non-filtered 16QAM signal.Again,r(t)is the vectorial difference between m(t)and h(t).This operation is performed for differentαrc.The statistics for each signal component are given in Table 2.

The crest factor of r(t)is very high,and this increases the power requirements on the residual amplifier,particularly in QPSK modulation.

χcan be plotted using these component statistics for varying coupling factors,and Fig.2 confirms the above observations.Depending on the constellation and the value ofαrc,a highχis obtained for a coupling factor order of-3 d Bor less.This implies that around half the power generated by the main amplifier is used to compensate for the coupler loss.The high crest factor of r(t)imposes a high P1dBon the auxiliary amplifier,in the order of the main amplifier.This technique,accordingly,is not power efficient with such signals.

?Figure 2.χvs.coupling factorβ(QPSK and 16QAM).

3.2 CPM Modulation:The Impact of Filtering CPM Modulations on Spectral Efficiency and BER

CPM modulation is a class of phase modulation that has been widely used in wireless communication systems such as GSM[13],[14].The expression of the CPM signal is

where fcis the carrier frequency,φ0is the initial phase,Eis the symbol energy,T is the symbol duration,and φ(t,I)is the time-varying phase of the carrier.The time-varying is defined as

whereθnis the accumulation of all symbols up to time(n-1)T,h is the modulation index,and q(t)is the integration of some pulse g(τ),that is,

The modulation order M,the value of h,and the pulse type directly impact the spectralcharacteristics of the resulting signaland its detection performance[11].Small values of h result in CPM signals that occupy a small amount of bandwidth but have poor detection.Compared to rectangular pulses,smoother pulses,such as Gaussian pulses,improve spectral efficiency at the expense of receiver detection.In this paper,we consider binary CPM where h is 0.5.When g(τ)is rectangular,the corresponding modulation is called minimum shift keying(MSK).When g(τ)is Gaussian,the obtained signal corresponds to the Gaussian MSK(GMSK)modulation,which has a more compact spectrum with good error detection.

Both signals have constant amplitude according.This enables the use of highly efficient amplifiers such as class-C or Fand makes this type of modulation very attractive.However,the amount of bandwidth occupied is relatively high in terms of fractional out-of-band radiation(Fig.3).To reduce the amount of bandwidth occupied,we introduce RRC filtering withαrcset to 0.35.For both signals,the side lobes are dramatically attenuated,increasing spectral efficiency(Fig.3).The resulting change in signaldynamic,expressed in terms of crest factor,is relatively small:

Δh(t)=0.62 for MSK andΔh(t)=0.77 for GMSK.The phase transitions in time are too small.Thus,when these signals are filtered,the output signal trajectories stay close to the unity circle,resulting in a small added amplitude modulation.Afinite peak-to-peak variation is obtained and does not exceed 2.1 d B.

One issue with the filtered CPM modulations is the impact of RRC filtering on system-level performance.

To study this impact,we constructed a complete MATLAB/Simulink model of a wireless link using filtered modulation over an additive white Gaussian noise(AWGN)channel.On the receiver side,we used a matched RRC filter combined with coherent demodulators available in the Simulink library.There is no differential pre-coding,and we use a coherent direct demodulator with maximum likelihood detector.We conducted several simulations of the constructed model to evaluate BERvs.Eb/N0of the filtered MSK/GMSK signal over an AWGN channel.The results of these simulations with GMSK modulation are shown in Fig.4.

There is no significant degradation because a matched RRCFfilter is used at the receiver side.ISIis then largely reduced,and the signal is correctly demodulated.Similar results are obtained with the MSK signal.Given the better occupation of spectrum,good BER,and low signal dynamic,the filtered MSK-based modulated signal is worth considering.

Figure 3.?Power spectraldensity(PSD)of MSKand filtered MSKsignals.

?Figure 4.BERvs.Eb/N0 for GMSKand filtered GMSKin an AWGN channel.

▼Table 3.Signal decomposition

3.3 Application of the Proposed Amplifier to the Filtered CPM Modulation

To determine the performance of the proposed amplification architecture,we use the MATALB/Simulink model previously developed and add a baseband model for the RFfront-end.

We decompose the filtered MSK-based signals.Table 3 shows the dynamics for the residual signal as well as the difference in average power between both branches.

The very highγcan be explained by the level of side lobes for each modulation.As a result,the overall efficiency is expected to be higher in this case.Although the crest factor of the residual signals is considerably high,it is much lower than in QPSK.χis then plotted against the coupling factor for both considered signals(Fig.5).For a coupling level of-8 d B,χis around 15 for GMSK and around 10 d Bfor MSK.In comparison purpose,for the same coupling level with QPSK signal,χwas-7.This implies that this architecture is perfectly suitable for this type of signals.In the next section,we study the power efficiency of the system fed with these signals.

4 Architecture Performance with Filtered CPM Signals

In this section,we consider the amplification of filtered MSK-based signals and its impact on transmitter power efficiency and linearity.We have considered several amplifiers for the residual signal r(t),each corresponding to an amplification class.The main amplifier is assumed to be a 100%efficient class-C or class-F amplifier.For each secondary amplifier,

we compute power efficiency,optimal coupler coefficients,overall efficiency,and the system linearity.

4.1 Single Branch Class-B Amplification

The first intuitive amplification architecture proposed is a single-branch system.Because the input signal has a varying envelope,a class-C amplifier with low conduction angle and high power efficiency causes clipping and is therefore inappropriate.

By contrast,a class-Bamplifier has a conduction angle of 180°,allowing the entire signal to be amplified.Such an amplifier can be used for the filtered MSK signal.In this paper,we consider a realistic class-B amplifier designed with MRF9060—a 900 MHz Freescale laterally diffused metaloxide semiconductor(LDMOS)transistor.Fig.6 shows the simulated output power and efficiency of the class-B amplifier versus input power.

This PAhas a peak output power of 49 d Bm and DC-RFefficiency of 65%.A model of this amplifier is implemented in Simulink for the three MSKfiltered signals.For each signal,we compute the average power efficiency,and linearity expressed in terms of adjacent channel power ratio(ACPR)for different back-off levels.The results of these simulations are summarized in Table 4.When the PAis operated at its saturation point,it is highly efficient but has poor linearity.Higher efficiency is obtained for GMSKbecause the PARis lower than in MSK.As the input back-off is increased,linearity isimproved at the cost of power efficiency.Very low ACPRis obtained at a back-off level of 3 d B.These results give a realistic idea of the performance that can be expected from a single-ended PA and will be used as a reference for a subsequent comparison with the proposed two-branch amplification system.

Figure 5.?χvs.coupling factorβ(MSKand GMSK).

?Figure 6.Output power and power efficiency vs.input power for a single-ended class-B amplifier using the MRF9060 transistor.

▼Table 4.Drain efficiency and ACPRfor a single-ended class-Bamplifier

4.2 Amplification of the Residual Signal:Class-AB

Class-ABis an intermediate class between classes A and B.It has better linearity than class-B but lower efficiency.We use a measurements-based modelof a 45 W peak Motorola MRF21045 base station amplifier[18].The amplifier's DC-RF conversion efficiency and power gain are shown in Fig.7.

Gain varies rapidly around the point of maximum efficiency,and this affects the linearity of the system.Therefore,when assessing the system's efficiency,linearity also needs to be considered.We use three input power levels(30 d Bm,32 d Bm,and 35 d Bm)and compute the average efficiency of the class-ABamplifier,assuming that the main amplifier is 100%efficient.We then evaluate the overallefficiency for each signal as a function of the coupling factorβ.For a givenγand ηaux(8),optimizing the overallefficiency is equivalent to optimizing the coupler coefficients.For both signals,we calculate the auxiliary amplifier efficiency,the optimal coupler,and the corresponding optimaloverall efficiency.To evaluate linearity,we calculate the resulting ACPR.Table 5 summarizes the optimal configuration performance and gives the output signal linearity expressed as ACPR.

For both signals,we have comparable second amplifier efficiency.However,because GMSK has a higherγ,it also has a higher overall efficiency.Efficiency can reach around 87%when the class-AB amplifier is in deep saturation.Overall efficiency of 79.5%can be achieved with the MSK signal.In terms of linearity,this architecture ensures high performance.Distortions are lower than-52 d Bc below the carrier level for MSKand-62 d Bc below the carrier levelfor GMSK.Therefore,using a class-AB amplifier substantially increases efficiency without significantly affecting linearity.

4.3 Amplification of the Residual Signal:Class-B

Given the excellent linearity of the class-AB amplifier,further efficiency within an acceptable margin of linearity can be achieved using a more efficient amplification class,such as class-B.

Taking the same amplifier used in the single-ended case,we carried out the same simulations as in the previous study.With full power and three back-off levels(1 d B,2 d B,and 3 d B),the power efficiency,optimal coupler,and linearity(expressed as ACPR)are as shown in Table 6.When power efficiency of the class-Bamplifier is higher than that of the class-AB,optimal global efficiency is improved.Maximum power efficiency is around 89%for filtered GMSK and 82%for filtered MSK when the class-B amplifier is at full power.An average increase in power efficiency of 2.5%is then obtained compared to the same architecture with a class-ABamplifier.

Figure 7.?DC-RFconversion efficiency and power gain of the MRF21045 amplifier.

There is almost no impact on linearity.At worst,ACPRdoes not exceed-51 d Bc,compared to-52 d Bc with a class-AB amplifier.These excellent linearity levels can be explained as follows:The nonlinearity of the auxiliary amplifier affects only a small portion of the residualsignal,which has a gain variation close to saturation.This distortion occurs at-γd B(γ＞25 d B)below the main branch that carries the most important part of the information.Consequently,even when a class-B amplifier(more non-linear than class-AB)is used,linearity is maintained at a high level.

▼Table 5.Architecture performance after optimization with a class-ABamplifier in the residual branch

▼Table 6.Architecture performance after optimization with a class-Bamplifier in the residualbranch

▼Table 7.ACPR(dBc)vs.phase and gain variation

4.4 Considerations for Practical Implementation:Impact of Branch Imbalance on System Linearity

In this paragraph,we discuss the practical implementation issues that arise from non-ideal components in the proposed amplification architecture.In two-branch amplification systems,such as LINC and Feed-forward,non-ideal components cause imbalance between the two branches.

This imbalance,in turn,leads to a non-ideal combination of both signal components and results in deteriorated linearity.Imbalances can be caused by transistor aging,temperature,dissimilarity in the up-conversion blocs,and combiner imperfections.To determine the impact of branch imbalance on linearity in the proposed architecture,we use the filtered MSK signal,which is more sensitive to non-linearities.The class-B amplifier without back-off is used in the second branch.We successively introduce phase imbalance,denoted byΔΦ{0°,2.5°,5°},and/or gain imbalance,denoted byΔΦ{0 d B,0.25 d B,0.5 d B},and calculate the ACPRfor each scenario.A positiveΔΦmeans that the phase of the main branch is larger than that of the second branch and vice versa.Similarly,positiveΔG means that the gain of the main branch is larger than that of the second branch and vice versa.For negativeΔG,the auxiliary class-B amplifier is used in a deeper compression,and lower overall linearity is expected.The results of these simulations are given in Table 7.An ideal case whereΔG=0 andΔΦ=0 is the reference.The results show the impact of branch imbalance on system linearity.ACPRis degraded in all cases,and the threshold of-45 d Bc is exceeded only whenΔG=-0.5 d B for allΔΦvalues(highlighted).The effect of phase variation is the same whether ΔΦis positive or negative,whereas the positivity or negativity ofΔG directly impacts the amount of linearity degradation.This behavior is due to dissymmetry in gain between the branches.For positiveΔG,the signal of the main branch is uniformly amplified by that amount of gain.Uniform distortion is introduced into the system's output signal,leading to low ACPR degradation.However,for negativeΔG,the auxiliary amplifier is excited at its compression region,and an increase in gain in the second branch amplifies both the linearly amplified portion of the residual signal(exciting the PA at its linear region)and the distorted portion of the residualsignal(exciting the PA at its linear region)causing additional distortion.The resulting ACPRfor that case is higher.The problem of branch imbalance is wellknown,and digital predistortion techniques[4],[5]can be used to correct it,as in LINC amplifiers[19],[20].

?Figure 8.System efficiency vs.main amplifier efficiency.

4.5 Comparison of Architectures

Here,we summarize the results obtained with the single ended class-B amplifier and the new two-branch technique.We previously supposed that the main amplifier was 100%efficient.However,in reality such efficiency cannot be achieved.To determine the efficiency of the proposed architecture with realistic amplifiers in the main branch,we evaluate the sensitivity of the system's global efficiency to the efficiency of the main amplifier.We compute the global efficiency for different efficiencies of the main PA using a class-B auxiliary amplifier.In Fig.8,we present these results and include the efficiency of the single-branch class-B.Compared to the reference(a single-ended class-B amplifier),the new architecture performs better even when the efficiency of the main amplifier is not 100%.For GMSK,the main amplifier only needs to be about 72%efficient to outperform the single-ended class-B amplifier with excellent linearity.The main amplifier needs to be 77%efficient for the filtered MSK.In recent literature,drain efficiencies of up to 83%have been reached with class-F amplifiers[16],[17].With such amplifiers,the proposed architecture outperforms the class-B single-ended amplifier by almost 10%for GMSK signals and 7%for MSK signals.When linearity is taken into account,the proposed architecture becomes even more attractive.Highest efficiency with the single-ended class-B amplifier is reached when the amplifier is operated at full power,but linearity is poor,and ACPRis around-34 d Bc for the MSK signal.To meet more stringent ACPR specifications,the PA must operate with sufficient back-off,which lowers power efficiency.

5 Conclusion

This paper presents a new two-branch amplification system combined with appropriate baseband signaldecomposition.Amain amplifier is fed with a signal that has a crest factor lower than the original filtered signaland an auxiliary amplifier with a low power signal that carries the rest of the information.Asignaldecomposition technique and RFfront-end optimization have been presented.For M-QAM signals,this technique is,at best,similar to a balanced structure.However,with filtered CPM modulations,the newly obtained transmitter offers improved power efficiency of up to 10%compared to a single-ended class-Bamplifier using realistic amplifier models.Amore compact CPM spectrum is also obtained,with no significant reduction in BERperformance.Linearity was also shown to be excellent and largely outperforms the class-Bamplifier,and branch imbalance does not significantly impact system linearity.This technique is currently being trialed with filtered CPM signals.Acomparison of this technique for M-QAM signals with balanced amplifiers such as LINC has also been given.

Appendix

P1dBfor each amplifier can be written as

and

The latter can be expressed using(6)

Therefore,χcan be expressed simply as

The power efficiency of the system can be written as

DCconsumption of each amplifier can then be expressed as

and

which can be rewritten as

which relates the auxiliary amplifier's DC power consumption to thatof the main amplifier.Finally,using(A.9)and(A.6),the total consumed DCpower is given by

With the DCpower known,the totaloutput power of the architecture can be determined.Using(4)and(A.10),we can write

Replacing PDC_auxwith its expression in equation(A.10)yields

which can be put in the following form: