Adaptive Envelope Shaping for Low and Medium Power Amplifiers with Dynamic Supply

This letter presents an adaptive envelope shaping (AES) method to linearize low and medium power amplifiers (PAs) with dynamic supply. This straightforward linearization solution results very useful for small cell or handset transmitters, where reducing power consumption and computational complexity of the digital part is crucial. With the AES method, there is no need of an a priori characterization of the PA to shape the supply voltage signal targeting maximum linearity. Excellent linearization results are obtained when the PA presents good AM-PM linearity, otherwise, additional phase distortion linearization has to be included to meet the ACLR specifications.

By using an envelope shaping function [1], the instantaneous 30 supply voltage can be chosen to either achieve optimum effi-31 ciency at the cost of having nonlinear distortion at the PA output 32 or, alternatively, to achieve certain levels of linearity at the cost of 33 a small loss of efficiency (e.g., Nujira-Wilson or N = 6 shaping in 34 [2]). To minimize the impact of the linearization subsystem (in P. L. Gilabert  method assumes the AM-PM distortion to be negligible, other-39 wise, additional phase distortion compensation (e.g., [3]) has to 40 be included in the in-phase (I) and quadrature-phase (Q) path. 41 To design the envelope shaping function, a previous charac-42 terization of the PA is necessary (e.g., gain versus output power 43 curves for different supply voltages). Normally, this characteri-44 zation is carried out through CW test signals. However, this 45 measurements are not always feasible or reliable, since thermal 46 and bias network equilibrium are different for CW versus mod-47 ulated signals. For example, PAs based on GaN HEMT tran-48 sistors experience a soft-compression effect when the AM-AM 49 measurement is made under static conditions [4]. Moreover, cer-50 tain topologies of the EA do not allow the use of CW excitation 51 due to its small PAPR and the need of stressing the PA with a high 52 mean output power in order to characterize the peaking range. As 53 a consequence, it is best if the extraction of the different gain 54 characteristic curves are done under a dynamic excitation (e.g., 55 LTE waveforms). This ultimately leads to a lack of precision of 56 the characteristic curves (i.e., blurring of the measured data) 57 that impacts the linearization performance of the envelope 58 shaping function (e.g., unbalanced ACLR compensation). 59 1531-1309 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
where ε[n] is the nonlinear distortion signal that, taking also 75 into account memory terms, can be modeled as where τ i (with τ ∈ Z and τ 0 = 0) are the most significant sparse 77 delays of the envelope. In matrix notation, w n = (w 0,0 , . . . , with Φ = (ϕ 0 , ϕ 1 , . . . , ϕ L ) T being the LxO data matrix, 87 where L is the number of data samples (n = 1, 2, . . . , L), and 88 μ (0 ≤ μ ≤ 1) being the weighting factor. Finally, e is the Lx1 89 vector of the error defined as where G 0 determines the desired linear gain of the PA, and 91 where y and E are the Lx1 vectors of the PA output and 92 baseband instantaneous envelope, respectively.

93
Targeting a future FPGA implementation, the AES can be 94 easily carried out using LUTs. Therefore, (1) and (2) can be 95 rewritten as the combination of N LUTs, (5) where w 0i are the offset coefficients that have a big impact on 97 the linearity vs. efficiency trade-off [5]. 98

99
The experimental test-bench is depicted in Fig. 2. For testing 100 purposes, we used a broadband high efficiency continuous-mode 101 class-J power amplifier at 950 MHz, based on the CGH35030F 102 packaged GaN HEMT from Cree Inc. The signal generation 103 and measurement equipment consist of: Texas Instruments 104 boards (TSW1400EVM pattern generator + TSW30H84EVM 105 DACs and I-Q modulator), a Tabor WW2572A arbitrary wave 106 generator, and a Keysight Infinium DSO9404A oscilloscope 107 for capturing the RF signals. Another oscilloscope is used for 108 capturing the drain voltage and current, and this information 109 is used for calculating the drain power consumption. A PC 110 running Matlab controls all the instrumentation and does all the 111 required digital signal processing. We used as the EA the high-112 speed (35 MHz bandwidth and 900 V/μs slew-rate at Av = 2 113 and 10 Ω load) high-current (1.1 A) Linear Technology IC 114 LT1210. For the sake of simplicity we considered the linear but 115 slightly efficient IC LT1210 as the EA. Thus, the drain biasing 116 voltage could be lowered down to 0 V while the reported 117 PAE values take only into account the consumption at the RF 118 PA drain. The scope of this work is to prove the linearity 119 performance of the proposed AES method. The signal used was 120 an uplink LTE signal of 5 MHz bandwidth and 8.3 dB of PAPR. 121 The targeted ACLR levels to meet the specifications for the 122 LTE uplink channel were −38 dB. Table I shows the ACLR, 123 NMSE and PA's PAE when using the proposed AES method 124 for different mean output power levels and dynamic supply 125 strategies, namely, ET and EER. To detect the importance of 126 the AM-PM distortion, and thus determine the linearization 127    Table I) and operating close to a class-E switched-153 mode, the AM-PM distortion results less harmful (except for 154 the feedthrough effect at low drain voltage supply levels) and 155 with only AES, in 3 iterations (at least 25 are required in ET 156 mode) the linearization specifications were met. For handsets 157 or low/medium power equipment, the PA has to be carefully 158 designed to show a linear AM-PM characteristic and thus 159 avoiding additional DPD compensation in the I-Q path.  method assumes the AM-PM distortion to be negligible, other-39 wise, additional phase distortion compensation (e.g., [3]) has to 40 be included in the in-phase (I) and quadrature-phase (Q) path. 41 To design the envelope shaping function, a previous charac-42 terization of the PA is necessary (e.g., gain versus output power 43 curves for different supply voltages). Normally, this characteri-44 zation is carried out through CW test signals. However, this 45 measurements are not always feasible or reliable, since thermal 46 and bias network equilibrium are different for CW versus mod-47 ulated signals. For example, PAs based on GaN HEMT tran-48 sistors experience a soft-compression effect when the AM-AM 49 measurement is made under static conditions [4]. Moreover, cer-50 tain topologies of the EA do not allow the use of CW excitation 51 due to its small PAPR and the need of stressing the PA with a high 52 mean output power in order to characterize the peaking range. As 53 a consequence, it is best if the extraction of the different gain 54 characteristic curves are done under a dynamic excitation (e.g., 55 LTE waveforms). This ultimately leads to a lack of precision of 56 the characteristic curves (i.e., blurring of the measured data) 57 that impacts the linearization performance of the envelope 58 shaping function (e.g., unbalanced ACLR compensation).
where ε[n] is the nonlinear distortion signal that, taking also 75 into account memory terms, can be modeled as where τ i (with τ ∈ Z and τ 0 = 0) are the most significant sparse 77 delays of the envelope. In matrix notation, w n = (w 0,0 , . . . , where G 0 determines the desired linear gain of the PA, and 91 where y and E are the Lx1 vectors of the PA output and 92 baseband instantaneous envelope, respectively.

93
Targeting a future FPGA implementation, the AES can be 94 easily carried out using LUTs. Therefore, (1) and (2) can be 95 rewritten as the combination of N LUTs, (5) where w 0i are the offset coefficients that have a big impact on 97 the linearity vs. efficiency trade-off [5]. 98

99
The experimental test-bench is depicted in Fig. 2. For testing 100 purposes, we used a broadband high efficiency continuous-mode 101 class-J power amplifier at 950 MHz, based on the CGH35030F 102 packaged GaN HEMT from Cree Inc. The signal generation 103 and measurement equipment consist of: Texas Instruments 104 boards (TSW1400EVM pattern generator + TSW30H84EVM 105 DACs and I-Q modulator), a Tabor WW2572A arbitrary wave 106 generator, and a Keysight Infinium DSO9404A oscilloscope 107 for capturing the RF signals. Another oscilloscope is used for 108 capturing the drain voltage and current, and this information 109 is used for calculating the drain power consumption. A PC 110 running Matlab controls all the instrumentation and does all the 111 required digital signal processing. We used as the EA the high-112 speed (35 MHz bandwidth and 900 V/μs slew-rate at Av = 2 113 and 10 Ω load) high-current (1.1 A) Linear Technology IC 114 LT1210. For the sake of simplicity we considered the linear but 115 slightly efficient IC LT1210 as the EA. Thus, the drain biasing 116 voltage could be lowered down to 0 V while the reported 117 PAE values take only into account the consumption at the RF 118 PA drain. The scope of this work is to prove the linearity 119 performance of the proposed AES method. The signal used was 120 an uplink LTE signal of 5 MHz bandwidth and 8.3 dB of PAPR. 121 The targeted ACLR levels to meet the specifications for the 122 LTE uplink channel were −38 dB. Table I shows the ACLR, 123 NMSE and PA's PAE when using the proposed AES method 124 for different mean output power levels and dynamic supply 125 strategies, namely, ET and EER. To detect the importance of 126 the AM-PM distortion, and thus determine the linearization 127   additional phase distortion compensation was necessary to meet 150 the −38 dB ACLR specifications. Instead, in EER mode, with 151 the class-J PA driven deep into saturation (see the PA gain 152 column in Table I) and operating close to a class-E switched-153 mode, the AM-PM distortion results less harmful (except for 154 the feedthrough effect at low drain voltage supply levels) and 155 with only AES, in 3 iterations (at least 25 are required in ET 156 mode) the linearization specifications were met. For handsets 157 or low/medium power equipment, the PA has to be carefully 158 designed to show a linear AM-PM characteristic and thus 159 avoiding additional DPD compensation in the I-Q path. 160