The sensitivity of modulation fidelity on PA envelope variation in OFDM transmitter systems
- Yiming Lei†^{1}Email author,
- Mingke Dong†^{1} and
- Ye Jin^{1}
https://doi.org/10.1186/1687-1499-2014-52
© Lei et al.; licensee Springer. 2014
Received: 9 January 2014
Accepted: 28 February 2014
Published: 3 April 2014
Abstract
Intermodulation distortion (IMD) caused by nonlinear power amplifier (PA) is a major weakness in orthogonal frequency-division multiplexing (OFDM) transmitter systems, and most behavioral studies of IMD are based on specific example PAs. In recent papers, PA percentage linearization (PL), a general measurement for PA envelope variation, is investigated for its influence on system performance. Meanwhile, PL still somehow depends on specific example PA, and it mostly considers the PA saturation point (SP) variation. In this paper, a comparison analysis is presented to investigate the system performance when both SP and nonlinearity onset point (NOP) variations are considered. The simulations show that how the PA envelope variation can be represented by the signal impairment over IBO and OBO domains, respectively. It is interesting to find that although SP attracts much concern in current studies, NOP actually has a clear influence on modulation fidelity of nonlinear OFDM transmitter systems. Moreover, it is observed that when input power gets close to saturation range, the PAs having relatively higher nonlinearity show relatively lower distortion level over the input power domain. These interesting simulation observations above are analytically explained based on a mixed time domain and statistical analysis of IMD mechanism. An example IEEE 802.11a OFDM signal is driving through five example solid state PAs, and the system performance is measured by error vector magnitude (EVM) and adjacent channel power ratio (ACPR).
Keywords
1 Introduction
Orthogonal frequency-division multiplexing (OFDM)-modulated signals are widely used in wireless communications systems for their advantage of high spectrum efficiency [1, 2]. However, OFDM signals have a nature of high peak to average power ration (PAPR), since they consist of lots of independent input subcarriers. This high PAPR nature makes OFDM transmitter systems very sensitive to the nonlinearity of RF power amplifiers (PAs) integrated within transmitters, and significant nonlinear distortion generated in the amplification process is a major weakness of OFDM signal systems [3, 4]. The nonlinear distortion can be evaluated by the modulation fidelity over wanted subcarriers and the out-of-band spectral regrowth, and they can be quantitatively expressed by error vector magnitude (EVM) and adjacent channel power ration (ACPR), respectively [5].
For the designers of OFDM transmitter systems, the influence of PA envelope character on system modulation fidelity is a fundamental concern, and it attracts lots of studies [6–9]. However, most relevant studies are based on a specific example PA, and the influence of PA envelope variation on system performance is not well explored yet. In recent papers [10, 11], the PA envelopes are characterized by percentage linearization (PL) determined by PA saturation point (SP), and the influence of PL on system modulation fidelity is investigated. Meanwhile, the influence of PA envelope is not investigated yet as both SP and nonlinear onset point (NOP) variations are considered. Thus, a couple of questions can be asked here. What is the influence of PA envelope on modulation fidelity performance of nonlinear OFDM transmitter systems when both NOP and SP variations are considered? Can the simulation observations be explained analytically? This paper presents our efforts to answer these questions.
In this paper, the characteristic of PAs is considered as some kind of degradations from that of the ideal PA, i.e., a fully linearized hard limiter. This degradation is characterized by both NOP and SP defined in [10, 11]. Totally, five solid-state PA (SSPAs) envelopes with various settings of NOP and SP are designed, where the AM/PM conversion of these PA envelopes are neglected as in [10, 12], and these example PAs are modeled by Bessel-Fourier (BF) behavioral model [13, 14]. A 16QAM-modulated IEEE 802.11a OFDM signal is driven through these designed PAs. The intermodulation distortion (IMD) of output signal of example PAs is measured by EVM and ACPR, and the obtained EVM and ACPR results are displayed over input backoff (IBO) and output backoff (OBO) domains, respectively. This allows us to see how the variations of PA envelopes are represented through their associated EVM/ACPR results. An interesting outcome is that when these example PAs are driven close to their saturation ranges, PAs having relatively higher nonlinearity show relatively lower distortion level over IBO domain. On the contrary, PAs having relatively higher nonlinearity show relatively higher distortion level over the whole OBO domain. Another interesting outcome observed from the comparative experiment is that NOP is not much concerned in the characterization of PA envelope in current studies, but the system performance actually is more sensitive to the variation of NOP than to that of SP. These simulation observations are analytically discussed by using a recent mixed time-domain and statistical analysis approach of IMD [15, 16]. It can be seen that when input power increases, the weights of high-order terms in PA Bessel-Fourier model become comparable with those of dominated low-order terms. Therefore, the IMD of a PA envelope becomes more sensitive to the input power as it has more high-order model terms. This finding explains the simulation observations.
Section 2 presents the designed example PA envelopes. Section 3 presents the BF PA envelope model and the mixed time-domain and statistical analysis approach of IMD. The simulation observations and associated discussions are presented in Section 4, and this is followed by the conclusion in Section 5.
2 PA envelopes having various NOPs and SPs
In simulation-based analysis of nonlinear OFDM transmitter systems, the single SSPA transfer characteristic used can vary from device to device. Without comparative analysis of multiple-PA-based simulation experiment, valuable outcomes can be missed. In this paper, several PA envelopes having various envelope characters are designed, and the design scheme is presented below.
where g[.] and Φ[.] denote PA AM/AM and AM/PM conversion, respectively; and A_{e}(t) is the envelope amplitude of input signal. Since AM/PM conversion of SSPAs does not have strong variation [13], Φ[.] of example PAs is set as zero.
Characters of five example PA envelopes
PA | Envelope characters | PL_{A}(%) |
---|---|---|
L _{0} | D_{NOP-CISP} = 0 dB = D_{SP-CISP} | 100 |
L _{1} | D_{NOP-CISP} = 3 dB = D_{SP-CISP} | 75 |
L _{2} | 3 dB = D_{NOP-CISP} < D_{SP-CISP} = 6 dB | 50 |
L _{3} | 6 dB = D_{NOP-CISP} > D_{SP-CISP} = 3 dB | 50 |
L _{4} | D_{NOP-CISP} = 6 dB = D_{SP-CISP} | 0 |
3 IMD analysis in nonlinear OFDM transmitter systems
where D_{mod} is the model dynamic range [18]; ${J}_{{n}_{l}}$ is the ${n}_{l}^{\text{th}}$ order Bessel function of the first kind; b_{ k } is the k th coefficient of an L th order Bessel-Fourier model. As in [13, 14], s_{o}(t) includes fundamental carriers and zonal band intermodulation products (IMPs), and each of them maps to a unique realization of the parameter set [ n_{1}, n_{2},…, n_{ N }]. The fundamental carriers IMPs can be distinguished by the condition of$\sum \left|{n}_{l}\right|=\lambda $, where λ=1 indicates fundamental carriers and other values of λ(λ≥3) indicates the λ th order IMPs.
where f denotes the frequency; δ[.] is the Dirac function; DDF_{3}(f) denotes the distribution density function of third-order IMPs as defined in [15], and it can be easily counted according to the number of subcarriers. Here, IMD is represented by the dominated third-order IMPs, and higher-order IMPs are omitted.
This indicates that the power of IMD increased as input power as σ^{2} increases, and the power of high-order IMD components are more sensitive to the variation of σ^{2} than that of the low-order ones.
4 Simulation observations and discussions
In this section, the modulation fidelity of an IEEE 802.11a OFDM signal driving through five example SSPAs are presented. The EVM and ACPR are two specific measures of system SNR, which focuses on the in-band distortion and out-band spectrum regrowth, respectively. The EVM and ACPR results shown in this section are simulated based on the classical statistical (Stat) approach in [14]. The simulation results reveal how the PA nonlinearity is represented by the signal impairment over IBO and OBO domains, respectively, and the associated simulation observations are discussed based on above analysis.
In Figure 6, the weights of Bessel-Fourier model terms of L_{0} and L_{4} example PAs are presented. It can be seen that as analyzed above, the weights of high-order terms of L_{0} PA are higher than those of L_{4}. This is because L_{0} has a relatively sharp variation at CISP. Thus, as observed in above figures, the modulation fidelity of L_{0} shows more significant degradation than L_{4} does when input power increased.
5 Conclusions
In this paper, a comparison analysis is presented to investigate the system performance when both SP and nonlinearity onset point (NOP) variations are considered. The simulations show that how the PA envelope variation can be represented by the signal impairment over IBO and OBO domains, respectively. It is interesting to find that although SP attracts much concern in current studies, NOP actually has the clear influence on modulation fidelity of nonlinear OFDM transmitter systems. Moreover, it is observed when input power gets close to saturation range, the PAs having relatively higher nonlinearity show relatively lower distortion level over the input power domain. These interesting simulation observations above are analytically explained based on a mixed time domain and statistical analysis of the IMD mechanism.
Authors’ information
YL, MD, and YJ are from State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronic Engineering and Computer Science, Peking University, Haidian District, Beijing, China.
Notes
Declarations
Acknowledgements
The authors wish to acknowledge the support from State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronic Engineering and Computer Science, Peking University. The authors also wish to acknowledge the suggestions from Prof. Máirtín O’Droma in the Telecommunications Research Centre, University of Limerick, Ireland.
Authors’ Affiliations
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