Improving the Predictability of RF/DSP Transmitter Design
The use of OFDM modulation presents a challenge to communication systems engineers. The high peak-to-average ratio characteristics inherent in coded and uncoded OFDM dictates highly
accurate behavioral modeling during mixed RF/DSP circuit development.
By Cory Edelman
Orthogonal frequency division multiplexing (OFDM), a spread-spectrum technology, has become the transmission modulation scheme of choice for a number of emerging wireless communications applications. For example, a recommendation approved last year by the IEEE 802.11 working group specifies OFDM coding to support next-generation wireless LANs with transmission rates of 20 to 25 Mbps. Similarly, a
terrestrial digital video broadcasting standard, slated to deliver data rates up to 15 Mbps, is currently being developed through the auspices of the European Union.
The high peak-to-average ratio characteristics inherent in coded and uncoded OFDM dictates highly accurate behavioral modeling during mixed RF/DSP circuit development. The precise prediction of input backoff levels is essential to achieving sufficiently low adjacent channel interference (ACI) levels, a requirement for robust designs.
One approach to optimizing development efficiency combines careful modeling with a realistic stimulus using an integrated cosimulation method. A detailed circuit-level model of a power amplifier with the DSP simulation of a coded OFDM stimulus will be outlined as an example of this approach. The results of this example simulation will be compared to results using only behavioral simulation, and plotted against the measured performance of the power amplifier (PA).
Modeling the PA with OFDM
Unless special coding is performed, OFDM inherently produces a signal with a high crest factor (the ratio of peak power out to root mean square [rms] power out). Understanding and improving the accuracy of models used to simulate nonlinear PA behavior for ACI (more appropriately expressed here as adjacent channel power ratio [ACPR]) under an OFDM stimulus, is an ongoing effort. To date, the best representation is a simplified polynomial, similar to the behavioral model available in today’s
commercial simulation tools. Unfortunately, these tools are insufficient for simulating the actual behavior of an amplifier cascade.
In an effort to improve modeling accuracy, a unique approach has been employed that uses both a circuit simulator and a data-flow simulator. These simulators carry out mixed digital signal processing and circuit-level cosimulation of a monolithic microwave integrated circuit (MMIC) amplifier cascade, subjected to an OFDM stimulus. When compared with measured results from
the PA cascade, the results of this cosimulation approach revealed a significant improvement over the approximation obtained using a simplified polynomial behavioral model.
Two stages of upconversion were used in the test setup for ACPR measurement. A predriver amplifier combined with a variable attenuator provided the variable input signal power (simulated using an ideal linear behavioral model). To approximate a real-world amplifier cascade, two circuit models were used for the final amplification
stages.
A conventional Raytheon-Statz type model was used for the circuit model, and a simple resistive-bias network was employed to allow operation using a single +3-V supply. The MGA-8256 supplied a gain of approximately 9 dB, with an output 1-dB compression point around +18 dBm.
In the measurement set up, a 16-carrier OFDM modulation was generated using a frequency-agile arbitrary signal source, which requires approximately 16.8 MHz of bandwidth.
Figure 1
depicts the representative output spectrum of an OFDM signal using sixteen carriers and quadrature phase shift keying (QPSK) modulation.
For this endeavor, the OFDM modulator was constructed using models from a commercially-available library of DSP functions. This modulator was then applied to both behavioral and circuit-level models using a single, top-level schematic design.
Bits are mapped to a QPSK constellation, formatted, and then processed through an inverse fast Fourier
transform (IFFT). In this case, sixteen orthogonal carriers were created. Bandlimiting is accomplished by multiplying the beginning and end of each OFDM symbol (comprising the IFFT output plus guard symbols) by a raised-cosine function. This method is preferable to bandpass filtering, which would destroy the orthogonality of the carriers.
One way to reduce the crest factor found in OFDM is by using coded OFDM (COFDM). In the example described here, Reed-Muller encoding was implemented to reduce the
peak-to-average ratio from 11 to 3.7 dB. This encoding was included in the simulation by deactivating the standard four-state quadrature data mapper and substituting a subnetwork to implement the encoder.
To create a complex RF envelope, a sampling time step was assigned prior to modulating the signal onto a carrier. Depicting the signal by its complex envelope enabled a large reduction in the required sampling rate when representing the signal by its samples. Finally, the nonlinear performance of
the amplifier’s response to the modulated carrier was carried out using a circuit envelope simulator.
The conventional approach for optimizing efficiency uses a polynomial-based behavioral model of an amplifier to calculate its nonlinear response to a time-varying complex envelope. Possible input values include the 1-dB compression point, the third-order intercept point, or both. Other parameters that may be introduced include actual measured complex gain versus input power.
For this
example, the MMIC circuit model cascade was simulated using a harmonic-balance method to obtain the 1-dB compression point. The compression point and small-signal gain parameters were then specified for the model. Other than variations due to modeling, the observable difference in ACPR performance could not be attributed to any other variables. The 1-dB compression point of each model under OFDM stimulus was determined by finding the input power required to produced a 1-dB gain reduction, representing the
reference value for input backoff for that model.
Circuit envelope simulation vs. cosimulation
Traditional 2-tone tests (see
Figure 2
) do not correlate well with ACPR when measured using high peak factor modulated signals such as OFDM, CDMA, or wideband CDMA. In these cases, an alternative approach is required (see
Figures 3
and
4
).
While a circuit
simulator can generate several modulation formats, it is not practical to use one for long coded frames or sequences. In particular, DSPs and logic can’t be modeled in a voltage and current simulation environment. A better approach leverages two tools: a DSP behavioral simulator to create the signal, and a circuit simulator to model the PA cascade.
In the cosimulation effort, the stimulus signal was created using a model of a signal-processing algorithm. Thus, for a signal with a high peak-to-mean
ratio, a wide range of dynamic behaviors could be considered within the circuit, limited only by the model. For example, the changes in the bias voltage applied to active devices, resulting from an instantaneous signal amplitude change, could readily be examined.
This cosimulation effort involved connecting a model of the target circuit to the output of the signal processing and modulation components. An additional component was connected to the circuit’s output port to indicate the carrier output
frequency. This is a necessary step in defining the carrier about which the signal envelope is placed for subsequent measurement or additional simulation.
As with the behavioral model setup, the input power at the 1-dB compression point was identified by performing a harmonic-balance simulation. This result was used as the reference input power in the full OFDM simulation setup. The desired backoff could then be entered and the simulation input power could be controlled by an equation. The total input
power was verified by calculating the total power over sixteen carriers in W and then converting to dBm.
Simulation results
The simulation results can be viewed by placing a spectrum analyzer component at the circuit’s output.
Figure 5
shows typical simulation results of a behavioral model spectrum compared to the nonlinear amplifier spectrum obtained through circuit cosimulation. The difference in shape of the behavioral model’s
intermodulation spectrum fall-off compared to both the measured spectrum in
Figure 1
and the MMIC circuit model cosimulation results should be noted.
ACPR can be calculated using an integration-bandwidth method, similar to the approach used by spectrum analyzer hardware. Using this method, the total power in the desired channel is calculated and then compared to the power in the adjacent channel offset frequency using the same resolution bandwidth. In the
previously described example, when the same amplifier model was simulated using complementary Reed-Muller coded OFDM input, the ACPR with the coded stimulus improved by approximately 6 dB, from -55.5 to -61.5 dBc.
While dependent on the amount of input backoff, the simulation time required for cosimulation is longer than that required for the behavioral model approach. For example, in the 4-dB backoff case, the behavioral model simulated in 13 s, while cosimulation took 185 s. This data (shown in
Figure 6
) suggests the following:
Nonlinear, polynomial-type modeling based solely upon the 1-dB compression point provides minimal accuracy for predicting ACI performance, particularly at small backoffs (the most likely operating points). This approach predicts lower ACI levels (better performance) than those observed using real amplifiers. In addition, the observed output spectra do not resemble the fall-off shape of the measured spectra
in the out-of-band regions.
The nonlinear MMIC model implemented at the circuit level and cosimulated yields a higher ACI level (worse performance), particularly at small backoffs, yet is closer to what can be observed using real amplifiers. The cosimulated output spectra closely resemble the fall-off shape of the measured spectra in the out-of-band regions.
Accurate prediction
The cosimulation model is the recommended approach for accurate prediction of ACI
performance at small backoffs for mixed DSP/RF simulations. Combining a DSP behavioral simulator in a cosimulation environment with a time domain nonlinear circuit simulator in the complex envelope domain increases utility and improves accuracy. Complex signals such as OFDM and COFDM can be created and their effects on analog RF hardware performance can be observed, including the reduction in adjacent channel leakage power when coding is used.
Acknowledgements
The author wishes to
recognize the work and assistance of the following individuals in conducting the measurements cited in this article, and in the preparation of the OFDM and COFDM simulation models: Russell Perry, Robert Castle, Alan Jones, and Timothy Wilkinson from Hewlett-Packard Laboratories, Bristol, UK.
Cory Edelman is an applications engineer for Hewlett-Packard’s EEsof Division, specializing in communication systems applications. Edelman holds a BSEE from California State University,
Northridge. He can be contacted at
Lcory_edelman@hp.com
.
| Resources
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|---|
- Jones, A., Wilkinson, T., and Castle, R., ETSI BRAN Working Group 3 TD79, Adjacent Channel Interference Performance of Coded OFDM.
- Aldis, J., ETSI BRAN, Working Group 3 TD63, Physical layer options for HIPERLAN type 2.
- Edelman, C., Perry, R., Jones, A., Wilkinson, T., and Castle, R., ETSI BRAN, Working Group 3 BRAN #9 (Agenda Item), Modeling and Simulation of Power Amplifiers for OFDM Modulation.
|
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