# 1-bit Observation for Direct-Learning-Based Digital Predistortion of RF Power Amplifiers

TL;DR: A low-cost data-acquisition approach for model extraction of digital predistortion (DPD) of RF power amplifiers using only 1-bit-resolution analog-to-digital converters in the observation path to digitize the error signal between the input and output signals.

Abstract: In this paper, we propose a low-cost data-acquisition approach for model extraction of digital predistortion (DPD) of RF power amplifiers. The proposed approach utilizes only 1-bit-resolution analog-to-digital converters (ADCs) in the observation path to digitize the error signal between the input and output signals. The DPD coefficients are then estimated based on the direct learning architecture using the measured signs of the error signal. The proposed solution is proved feasible in theory, and the experimental results show that the proposed algorithm achieves the performance equivalent to that using the conventional method. Replacing high-resolution ADCs with 1-bit comparators in the feedback path can dramatically reduce the power consumption and cost of the DPD system. The 1-bit solution also makes DPD become practically implementable in future broadband systems since it is relatively straightforward to achieve an ultrahigh sampling speed in data conversion using only simple comparators.

## Summary (3 min read)

### Introduction

- One idea is to employ new algorithms to simplify the DPD model.
- One of the main concerns in DPD implementation is the bandwidth requirement of the feedback path that is used to capture the output signal from the PA for the purpose of model extraction.
- The band-limited method was proposed in [9] but it requires an extra bandpass filter in the RF transmit chain that is difficult and costly to design.
- Y. Liu et al. proposed a method in [18] to reduce the ADC dynamic range, but a minimum 8-bit ADC is required for achieving 2 comparable linearization performance with the conventional DPD.

### II. THEORETICAL DERIVATION

- The principle of DPD is that a digital block, called predistorter, is inserted into the transmitter chain to preprocess the input signal before it enters the RF PA.
- If the two nonlinear systems, i.e., the predistorter and the PA, exactly invert each other, a highly linear system can be achieved.
- Two architectures are generally employed for model extraction: direct learning and indirect learning architecture (IDLA).
- The IDLA estimates the postinverse of the PA first and then copies the coefficients of the post-inverse estimator to the pre-inverse one.
- While the DLA is usually used in closed-loop systems and it compares the PA output with the original input directly.

### A. Conventional Direct Learning Architecture

- The simplified conventional DLA block diagram is shown in Fig. 1 [21], [22], where the bold lower-case vectors x and y represents the input and output sequences, respectively.
- T ∈ CK×1, (1) where K is the length of the sequences used for training, x(n) and y(n), n ∈ Z are baseband input and output signals, respectively, and ( )T denotes the matrix transpose.
- Describe the input-output relationship of the DPD [1]–[3].
- Newtons method is one of the most popular candidates that solve this kind of nonlinear problem.

### B. Proposed 1-Bit Observation for Direct Learning Based Digital Predistortion

- In a DLA-based DPD system, the difference between the output and input signals, y(n) − x(n), should be properly 3 measured sample by sample, as demonstrated in (5).
- The magnitudes of the most error samples are relatively small, compared to the original input.
- Furthermore, although |∆I(n)| and |∆Q(n)| could hardly be strictly equal, they have the same statistical properties and during DPD training, the errors decrease with the number of iterations and they both approach zero when the training converges.
- Equation (10) is similar to that used in the simultaneous perturbation method [23], [24], where a Bernoulli process is carried out to estimate the gradient.

### A. System Description

- The block diagram of the proposed 1-bit observation DPD system is illustrated in Fig.
- The signs of the error signal are then sent to the DPD training block for model extraction.
- In the conventional system, time alignment is conducted in the digital domain by comparing the input and output data samples.
- In the proposed system, because only 1-bit comparators are used, the high resolution output samples are not available.
- In the proposed system, power alignment must be carried out in the analog domain, because only the input and output signal levels are aligned properly, the sign of the error signal then be obtained correctly.

### B. Time-Alignment Algorithm

- Calculating cross-correlation between the input and output signals in the time domain [28] for time alignment is a common approach in the conventional DPD training algorithms.
- If the authors transform it into the frequency domain, however, the signal power in in-band is still much higher than the noise floor, despite of high quantization noise.
- Power spectral density comparison of 20 MHz LTE signal with different resolutions.
- In the conventional system, time delay is only required to be calculated for aligning the captured input and output samples in the digital domain for model extraction purpose.

### C. Estimation of the Step Size

- Another important issue in the proposed model extraction, i.e., (10), is the choice of the step size ĉk, which is critical to the linearization performance as well as the convergence speed.
- Lets define P peakin as the peak input power under a given average input power level and the peak-to-average power ratio (PAPR) of the original signal.
- Here the authors propose a novel algorithm using the characteristic of PA, the RMS of the input sequence x defined in (1) and signal bandwidth to predict c0.
- The damping factor λ is to fine tune the step size.
- A general criterion for choosing a reasonable γ is that the ratio between the two adjacent step sizes satisfies ĉk−1 ĉk ≈ std(y − x)k−1 std(y − x)k , (15) where std( ) denotes the standard deviation of a sequence.

### D. Overall Complexity Comparison

- The proposed 1-bit observation method uses only two simple comparators to quantize the error signal, as shown in Fig.
- Removing high resolution ADCs from the system can drastically reduce the power consumption as well as the cost of the feedback loop, since the ADC is the one of the most expensive and power consuming components in the RF front-end [12].
- Assuming the DPD correction bandwidth is 500 MHz, the total power consumption of the proposed method is 1.26 W, which is much less than that of the conventional one.
- In terms of computational complexity, the proposed algorithm in (10) also outperforms the conventional method in (5).
- This is because the low resolution values require less storage and exhibit faster read and write operations than the high resolution samples.

### IV. EXPERIMENTAL RESULTS

- Various experimental tests were conducted to evaluate the proposed method.
- Fully implementing the proposed 1-bit data observation based DPD in hardware shown in Fig. 3 is difficult because the two data acquisition paths must be realized in an analog circuit chip which will take considerable time and efforts to accomplish.
- The baseband board was designed to configure the RF board, generate and digitize the input and output signals, respectively.
- The quadrature modulation and demodulation were performed in the RF board and DPD signal generation was conducted in MATLAB.

### A. Proposed Method versus Conventional Method

- To validate the feasibility of the proposed method, the authors first assume the input and output signals are perfectly time aligned, and the output signal is normalized so that the average power of the output is the same as that of input signal.
- Again from the input-output power curve, the peak output power is P peakout = 39.36 dBm.
- (b) AM-AM and AM-PM characteristics without DPD and with proposed 1-bit DPD.
- Measured results for 60 MHz UMTS signal.

### B. Performance Evaluation with Proposed Time Alignment Algorithm

- The power alignment is implemented in the analog domain in the proposed 1-bit DPD system, which is different from the conventional normalization in the digital domain.
- Contrarily, when ρ > 1, although the power is not perfectly matched, the DPD is capable of dealing with all the samples falling in the region [0, 1], and 10 thus less error appears in this case.

### V. CONCLUSION

- This paper proposes a low-complexity 1-bit observation method for estimation of DPD coefficients.
- The feasibility of the proposed algorithm is proved in theory and validated in experimental tests.
- With the existing ADC technology, it is possible to achieve either high sampling speed with low resolution or high resolution with low sampling speed, but hardly to have both high sampling speed and high resolution at the same time.
- The 1-bit observation solution eases the requirement of ADC in DPD system, and thus reduces both the power consumption and the cost of the feedback path, compared to the conventional algorithms with high resolution data.
- 1) Applying DPD in small cells becomes a reality due to the ultra-low complexity;.

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##### Citations

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### Cites background from "1-bit Observation for Direct-Learni..."

...followed different approach in their papers [8], [9] and presented a DPD with the feedback ADCs replaced by high-speed digital-to-analogue converters (DACs) accompanied with high-speed comparators which allowed them to reduce system power consumption....

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3 citations

3 citations

### Cites background or methods from "1-bit Observation for Direct-Learni..."

...In this article, contrary to the earlier closed-loop works in [20]–[23], we adopt the so-called injection-based DPD structure [7], [27], as illustrated in Fig....

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...In [20], in a more traditional single-antenna DPD context, the use of 1-bit observations in closed-loop learning is...

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...The reader can find an implementation of the sign algorithm in combination with GN learning rule in [20]....

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...than polynomial-type ones used in the reference works [7], [20], [21], allowing large reductions in terms of the processing and learning complexities....

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3 citations

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