Abstract – Direct RF sampling receiver – a fully digital receiver architecture- undoubtedly becomes a favored choice for HF/VHF as this approach inherently bypasses the legacy nonlinearities caused by analog components. In DRF-RF and wideband multichannel in general, LNA is still an indispensable component to ensure the receiver’s sensitivity. However, with the presence of multiple channels, the total RF power often surpasses the linear threshold that LNA and the amplified signal become severely distorted. This paper proposed a method for mitigating the LNA distortion using the look-up table (LUT) approach. Specifically, our receiver is designed with two modes of operation. In training mode, a built-in signal circuit generates a training signal for extracting the LNA characteristic and eventually reconstructs the inverse LNA nonlinear model in the form of a LUT memory. During the receiving mode, a linearization circuit reverses the distortion impact by matching the RF power level with the inverse nonlinear model pre-stored in the LUT. The effectiveness of the proposed distortion compensation method first is evaluated by a MATLAB simulation with a multi-channel DRF-RF model. The simulation results show that the proposed approach significantly improved the SNDR for the channel of interest. Furthermore, the model has been practically verified, where the actual distorted signals are sampled from a commercial LNA (ZFL- 500LN+) by a customized FPGA board. Results from measurements show an improvement of ~7 dB for SNDR and 27% for EVM in a strong distortion scenario of QPSK modulation signal.
Keywords – Direct-sampling RF Receiver, DCR, LNA distortion, digital receiver, LMS algorithm, distortion inversion, multichannel receiver, software-defined radio, HF/VHF transceiver.
I. INTRODUCTION
HE direct RF sampling receiver (DRF-RX see Fig. 1) processes the signal fully in the digital domain and this architecture now has been widely adopted in many commercial devices [1]-[5]. By eliminating a number of analog sub-circuits, this structure (Fig. 1) allows the receiver
Manuscript received October 14, 2022.
Ngoc-Anh Vu, Hai-Nam Le and Quang-Kien Trinh is with Faculty of Radio-Electronics – Le Quy Don Technical University, Hanoi, Vietnam (e- mails: anhvn@lqdtu.edu.vn, kien.trinh@lqdtu.edu.vn, namlh@lqdtu.edu.vn).
Thi-Hong-Tham Tran is with Phystech School of Radio Engineering and Computer Technology, Moscow Institute of Physics and Technology, Russia (email: thamtth@ lqdtu.edu.vn)
to work with a wide band, simultaneous multiple-channel reception while maintaining a simple and cost-effective design. As can be seen in Fig. 1, in front of the LNA there is only a low pass filter (LPF) that phases out the unwanted signals with frequencies higher than the Nyquist Zone 1. Then the ADC digitizes the signal right after LNA, further processing is performed in the digital domain. Therefore, apart from the LNA and ADC, in this model, the receiver is not affected by other non-ideal analog components. Thus, factors such as DC offset and I/Q imbalance are no longer the problems in DRF-RXs [6], [7].
In conventional receiver structure, a variable attenuator is often inserted to adjust the overall gain to ensure that the LNA operates at the linear region [8]. However, in the direct RF sampling, the attenuator while lowering the overall RF signal level could completely dismiss some channels of interest when their power level is significantly smaller than the other.
Channel n
LO
Digital processing domain DEMOD 90o
0o ADC
Channel 2 Channel 1
LNA LPF
LPF
Fig. 1. The architecture of multichannel DRF-RX.
IP3
IP2
P1dB
Power input
Power output
Input Linearity IIP1
OIP1
Fig. 2. LNA Input-Output power characteristics
A LUT-based Scheme for LNA Linearization in Direct RF Sampling Receivers
Ngoc-Anh Vu, Hai-Nam Le, Thi-Hong-Tham Tran, Quang-Kien Trinh,
T
0 0.5 1 1.5 2 2.5 x 107 -120
-100 -80 -60 -40
Power Spectrum
Frequency (Hz)
Relative Amplitude (dBm)
Ch1 Ch2 Ch3
Ch4 (Interested )
Fig. 3. LNA nonlinearity distortion in multichannel direct sampling receiver
To maintain an adequate level of signal power for all signals and simultaneous reception of wideband multichannel, it is unavoidable that the total RF input energy often exceeds the LNA linear threshold IIP1 (see Fig. 2). In such situations, LNA enters the nonlinear region, harmonics and intermodulation generated from high power channels could severely interfere with low power channels, of which levels are close to the background noise [9–17], as shown in Fig 3. It is also worthwhile to note that, unlike the case of narrowband receivers, the nonlinear impact from ADC is not that severe as the impact caused by LNA. Indeed, according to the datasheets of the ADC [18] and LNA [19] [20], it can be seen that a moderate 14-bit ADC exhibits much lower nonlinear impacts1, compared to that of LNA in the DRF-RXs. Therefore, in this work, we mainly focus on techniques to tackle the impacts of LNA nonlinearity.
Many other research groups have also come up with different solutions to solve this LNA distortion problem [9, 10, 11]. Conventionally, the distortion is mitigated by subtracting the reconstructed/extracted distortion from the received signal [9], [10]. Bandpass filters (BPF) are used to separate the distortion or the component causing distortion as proposed in both the solutions [9], [10]. The method in [11] also uses a BPF at RF to extract a portion of the distortion information to find nonlinear parameters. A solution using linear reference receivers to obtain information for distortion handling is proposed in [12]. However, these solutions have some practical limitations, for example, the use of high-quality BPF filters in the RF domain is either too costly or impractical [11]. Further, the signal information to be filtered must be known in advance [9], [10]. In [13], [14], authors proposed another linearization method using a look-up table (LUT), which is applicable for power amplifier (PA) in transmitters, or narrow band, single- channel receivers. The reference [15] proposed a solution to reduce the noise of the LNA by reducing the temperature for the LNA, which helps to improve the received signal quality even at very low levels. However, the situation in the direct
1 For example., for ADS4249 [21] used in this work has SNR = 73.3 dBFS, SFDR = 100dB, i.e., has very low quantization noise and unwanted harmonics.
The LNA distortion, as we experimental show later, is much higher level of harmonics and intermodulation when operating in nonlinear region.
sampling receiver is the opposite, in which the levels of the input signals might be very high, and the total input signal level is higher than the upper threshold of the LNA. The solution in [16] uses the (adaptive) bandpass filter to mitigate the distortion components. This method could effectively remove the adjacent component but not the in-band distortion components. Another method using the multiband filter for extracting the harmonic and the intermodulation components is proposed in [17]. The main drawback of this method is the high complexity in designing FFT and the multiband filter in the RF domain.
In our previous works [21]–[24], we have proposed several enhanced LNA linearization techniques based on reference receiver approaches specialized for DRF-RX. In this work, we for the first time present a LUT-based approach linearization that does not require the reference receiver. Specifically, our receiver supports two modes of operation. In training mode, we use a built-in signal circuit for generating training signals with different power levels for extracting the inverse LNA characteristic corresponding to those levels. The extracted information is stored in an internal LUT memory. During the receiving mode, a linearization circuit reverses the distortion effect using the pre-stored inverse characteristic. The major contributions of our work are listed in the following:
1) We proposed a novel reference-less linearization scheme using a built-in training and LUT memory for constructing the inverse characteristics of the LNA. Our approach does not use a reference receiver, hence, significantly reducing the complexity and the cost of the receiver in terms of hardware design and power consumption.
2) We proposed a design of DRF-RX that applied the LUT- based linearization technique. In this design, the training process is performed only when necessary and before the real receiving process, this relaxes the strict timing requirement for the receiver because there is no actual adaptive processing (e.g., LMS) needed during the normal receiving mode. This two-mode design feature brings twofold benefits in terms of processing power and processing latency in the receiving mode.
3) We developed a full MALAB model for a case study of a DRF-RX with QPSK and 16-QAM input channels. The model then has been partially ported to a customized FPGA implementation for proving the design concept on hardware. The real distorted signals from a commercial LNA (ZFL-500LN+) have been captured and evaluated accordingly for signal-to-noise and distortion ratio (SNDR) and error vector magnitude (EVM).
The following paper is organized as follows. Section II presents the solution to reduce distortion based on training in finding nonlinear inverse parameters of LNA. Simulation results on MATLAB and experimental measurements on the hardware implementation of the DRF-RX are presented in Sections III and IV. The conclusions are drawn in section V.
II. LINEARIZATION METHOD A. LNA nonlinear distortion and characteristics
The suitable LNA for multichannel DRF-RX receivers is required to have a small noise figure and work linearly with a large dynamic range. However, LNAs work linearly only within a limited input power range. The relationship between the power level of the input signal and the output signal of LNA is shown in Fig. 2. As can be seen from the figure, when the input signal power is higher than the linear threshold (IIP1), the amplifier becomes nonlinear, and the desired gain cannot be achieved [25]. As the result, the signal of a single channel can be distorted by harmonics and intermodulation generated from far-away channels since the frequency range of these receivers is typically large.
(a)
(b)
Fig. 4. Gain vs. Frequency of ZFL-500LN+ (a) and ZX60-P105LN+ (b)
Fig. 5. ZFL-500LN+ parameters with different input frequencies (5 MHz, 20 MHz, and 80 MHz)
In the following, we examine the characteristics of several commercial LNAs used in practical systems at HF/VHF bands.
Although in the proposed idea, we reserve the option for retraining the LNA when necessary, by integrating the training circuit in the receiver structure, it is important that the LNA exhibit relatively uniform and stable characteristics in the whole band to avoid multiple retraining processes for different frequencies, a training set is stable and can be used for a long time regardless of the input characteristics.
We have selected two available and popular LNA devices, ZFL-500LN+ [19] and ZX60-P105LN+ [20] from Mini- Circuits for our study. From the datasheet, the gain of ZFL- 500LN varies less than 0.7 dB with the frequency range from DC to 500 MHz; the gain of ZX60-P105LN+ varies less than 1 dB in the frequency range close to DC to 2.6 GHz (Fig. 4).
Furthermore, we examined in more detail the ZFL-500LN+
parameter with input frequency signals at 5.3 MHz, 50 MHz, and 125 MHz The results show that the parameters include the LNA gain, the nonlinearity of second and third-order at three tested frequencies almost the same (Fig. 5). Those results allow us confidently to confirm that the LNA characteristics are quite uniform throughout the working frequency range.
B. Structure of the DRF-RX receiver with proposed nonlinear distortion compensation
The structure of DRF-RX with the proposed LNA nonlinear distortion compensation method is shown in Fig. 6. The main receiver directly samples the signal of the entire frequency range using high-speed ADC. Multiple carrier channels with different modulation types can be simultaneously received. A dedicated signal generator is added to the receiver for generating the training input for extracting the LNA characteristic. A switch is used for selecting the input signal, which is the actual received RF signal in reception mode, or the training signal in the training mode. The distortion mitigation is performed in the digital RF domain (right after ADC) so that all channels within the working range of the receiver can be compensated simultaneously.
In the training mode, the RF signal is internally generated and converted into an analog signal by a digital-to-analog converter (DAC). This signal is fed to the training circuit via the switch. We use a 2-tone RF signal as a reference signal for the training process. The power level of the training signal is varied accordingly to the range of the input signal power with an adequate resolution. In the training period, the LMS circuit [26] will adjust the output signal of the nonlinear model to match the original 2-tone signal. As the LMS converges, the coefficients of the nonlinear model eventually characterize the inverse characteristic of LNA. The mathematical detail of this process is presented in Section II.2. For each input power level, the corresponding characteristic parameters are obtained and are then stored in the lookup table and will be accessed during the receiving mode.
-30 -25 -20 -15
-50 -40 -30 -20 -10 0 10
Power input (dBm)
Power output (dBm)
Linear 1st (5MHz) 2nd (5MHz) 3rd (5MHz) 1st (20MHz) 2nd (20MHz) 3rd (20MHz) 1st (80MHz) 2nd (80MHz) 3rd (80MHz)
1st 3rd
2nd
In the receiving mode, multiple carrier frequency channels with different types of signal modulation are fed both to a power estimation block and to the inverse nonlinear model. It is necessary to note that this is done entirely in the digital domain, so there is no issue with duplicating the signal as in the reference receiver approach using the signal analog coupler/splitter [9], [10], [12]. The same model used for training is now used to directly remove the distortion. The input signal level is continuously determined by an envelope detector during the reception process. The coefficients of the nonlinear model are updated from the LUT corresponding with the power level from the envelope detector. As the result, the model mitigates all the distortions caused by LNA nonlinearity by inverting them without affecting the receiver process. Only one compensation circuit can be used for all carriers and distortion is reduced at the RF domain. It is worthwhile to note that this distortion processing does not involve LMS convergence, i.e., the distortion components are removed in a direct manner. In contrast, the other approaches in [10], [12]), [21], [23], where the distortion components are reconstructed by an LMS algorithm, may cause additional timing issues and higher power consumption.
C. LNA nonlinearity Training Circuit and Algorithm 1) Input power estimation circuit
The solution to handling distortion is based on the determination of the total power of the received signals.
Therefore, accurate power estimation of received signals at the RF domain is an important requirement of the solution.
In order to estimate the signal power level in the digital domain, many practical solutions are proposed in [27], [28]. In this work, to minimize complex calculations such as multipliers and filters at high sampling rates in the RF domain, we adopted the peak amplitude detector circuit in [28].
Specifically, the envelope is determined by taking the absolute value of the input samples to calculate positive and negative peaks. The envelope detector circuit in the same domain is a low pass filter circuit with a very low cutoff frequency [28].
The high-frequency components of the RF signal after passing through the filter circuit will be removed, the output signal has the envelope of the RF signal. The RF signal power of the receiving channels is determined based on the determination of the peak level of the signal after the envelope detector circuit as in formula (1).
𝑦𝐸[𝑛]
= 𝑦𝐸[𝑛 − 1] − 𝐾2𝑦𝐸[𝑛 − 1]
+ {𝐾1(y[𝑛 − 1] − 𝑦𝐸[𝑛 − 1]), y[𝑛 − 1] ≥ 𝑦𝐸[𝑛 − 1]
0, y[𝑛 − 1] < 𝑦𝐸[𝑛 − 1]
(1)
Where 𝑦[𝑛] is the input signal (𝑦𝑡𝑟𝑎𝑖𝑛[𝑛], 𝑦𝑅𝐹[𝑛]), 𝑦𝐸[𝑛] is the output signal of the detector. The detector is performed continuously, each output sample of 𝑦𝐸 is calculated from the previous two sample inputs 𝑦 and output 𝑦𝐸, so the delay of the
detector circuit is very small compared to the change in power of the RF input for LNA. In which, 𝐾1 and 𝐾2 coefficients determine the attack and release time of the detector circuit.
For simplicity of calculation, 𝐾1 and 𝐾2 are rounded to the power of 2 so that the actual processing will be only the bit shift operation. The input power estimation here is to determine the power of the antenna input signal over a relatively long period, the signal level is relatively stable. For signals with stable amplitude such as FSK or QPSK the selection of 𝐾1 and 𝐾2 coefficients is straightforward. For input RF signals with variable amplitude such as QAM, the detection should ensure that the maximum power level of the signal is determined over a period of the signal reception time.
2) The Training Algorithm
As already mentioned before, we use a conventional 2-tone reference RF signal consisting of two different frequency sine waves for extracting the inverse distortion characteristics. For each input power level, a set of LNA inverse model parameters are determined by an LMS circuit. The implementation diagram of the training process is shown in Fig. 6 and the inverse distortion coefficient calculating process is shown in Fig 7.
The sampled signal from the main receiver 𝑦𝑡𝑟𝑎𝑖𝑛[𝑛] is fed directly to the nonlinear compensation circuit while the sampled generated signal 𝑥𝑡𝑟𝑎𝑖𝑛(𝑛) is passed to the LMS circuit to adjust the coefficients w(n).
This circuit will adjust the inverse model to fit the function 𝑥̂𝑡𝑟𝑎𝑖𝑛(𝑛) = 𝐹𝐼𝑁𝑉(𝑦𝑡𝑟𝑎𝑖𝑛(𝑛))
= 𝐹𝐼𝑁𝑉(𝑥𝑡𝑟𝑎𝑖𝑛(𝑛) + 𝑒(𝑛)) (2) Where 𝐹𝐼𝑁𝑉 represents a mathematical model of the inverse model circuit. As 𝑥̂𝑡𝑟𝑎𝑖𝑛 is approaching the original 𝑥𝑡𝑟𝑎𝑖𝑛(𝑛), the 𝐹𝐼𝑁𝑉 is fit to the 𝐹𝐿𝑁𝐴−1, i.e., the inverse function of the LNA. As the result, the final output 𝑥̂𝑡𝑟𝑎𝑖𝑛[𝑛] is expected to have only the linear components as the non-distorted trained 𝑥𝑡𝑟𝑎𝑖𝑛(𝑛). The distorted component e(n) is removed by the inverse nonlinear model. This process is mathematically explained in the following.
Let’s denote 𝑔i(𝑥[𝑛]) is the i-th order of the main receiver input 𝑦𝑡𝑟𝑎𝑖𝑛[𝑛], thus
𝑔𝑖(𝑦𝑡𝑟𝑎𝑖𝑛[𝑛]) = 𝑦𝑡𝑟𝑎𝑖𝑛𝑖 [𝑛], i = 1,2… k (3) The current output of the compensation circuit expressed as
𝑥̂𝑡𝑟𝑎𝑖𝑛[𝑛] = ∑ 𝑤̂𝑖[𝑛]𝑔𝑖(𝑦𝑡𝑟𝑎𝑖𝑛[𝑛])
𝑘
𝑖=1
(4) This output is fed back to the LMS block, where it is subtracted from the reference input 𝑦𝑅𝐸𝐹(𝑛) for calculating the error.
g2[n] w2[n]
g1[n] w1[n] + +
LMS
DAC Signal
genarator
Estimated power level
Inverse nonlinear
ytrain[n] LUT
Level ωi
yE[n]
xtrain[n]
LNA
LPF ADC
LPF
Fig. 6. Reduced diagram of the DRF-RX in the training mode
g2[n] w2[n]
g1[n] w1[n] + +
Estimated power level
Inverse nonlinear
LUT
yRF[n] DDC
Level ωi
yE[n]
LPF ADC
LPF
LNA
Fig. 7. Reduced diagram of the DRF-RX in the receiving mode
Output Power
Nonlinear input Input Power
Linear input
Linear Outnput ...
...
DOPR
DIPR
LUT LUT
Fig. 8. Acquiring LNA characteristics by DIPR and DOPR
𝜀̂[𝑛] = 𝑥𝑡𝑟𝑎𝑖𝑛(𝑛) − ∑ 𝑤̂𝑖[𝑛]𝑔𝑖(𝑦𝑡𝑟𝑎𝑖𝑛[𝑛])
𝑘
𝑖=1
(5)
The LMS principally operates to minimize the square error 𝜀̂[𝑛]2 in (5), by taking the feedback error to dynamically adjust the nonlinear coefficient 𝑤̂𝑖[𝑛] as follows
𝑤̂𝑖[𝑛] = 𝑤̂𝑖[𝑛 − 1] + 𝜇𝑖𝑓𝑖(𝑦𝑡𝑟𝑎𝑖𝑛[𝑛])𝜀̂[𝑛] (6) This process continues until all coefficients 𝑤̂𝑖[𝑛] stabilize at a fixed value or varies under the desired threshold, at that time the square error reaches the minimum. During the approximation process, 𝑥̂𝑡𝑟𝑎𝑖𝑛[𝑛] is asymptotically approaching the linear reference input 𝑥𝑡𝑟𝑎𝑖𝑛(𝑛) After the
LMS converges, the generated output 𝑥̂𝑡𝑟𝑎𝑖𝑛[𝑛] ≈ 𝑥𝑡𝑟𝑎𝑖𝑛(𝑛).
Thus, the transfer function of the compensation circuit at the LMS convergence is the inverse of the LNA’s transfer function. As a result, all distortion impacts caused by LNA are rolled back at this stage. The set of converged parameters are stored along with the input power level, which is taken from the power estimation circuit, into the memory. These parameters are used for recovering the original signal from the distorted one during the working phase.
D. The discretization model for LUT
The number of the LUT data points or the resolution of the data set tightly related to the performance of the compensation circuit, the time spent on the training phase, and the memory utilization. The training time is not that crucial because this process is performed only when necessary, for instance, during the device initialization or when there is a need for model calibration as the result of a change in hardware components or performance degradation due to aging. The trade-off between the memory utilization and the performance is very clear and this would need practical implementations for determining the most optimized configuration. Theoretically, the resolution is good enough when the characteristic parameters are relatively constant within a divided unit.
The data points can be selected with respect to the input power division (DIPR) or output power division (DOPR). In the former method, we divide the input power range into equal distance points while in the latter, by equal distance of the output power range. These methods are illustrated in Fig.8.
Adoption of DIPR essentially exhibits faster training time because the training signal will only need to change the level according to the predefined number of divisions. However, this solution relies precisely on specific LNA characteristics, i.e., the nonlinear domain has to be known in advance. With DOPR, the training signal power level is swept continuously from the linear region to the saturation domain. Therefore, the training duration will be longer than DIPR but there is no need to identify the LNA nonlinear characteristic in advance. In other words, the training process in DOPR is the same for different LNAs, and hence, significantly reduces the circuit complexity. Both of these dividing methods are simulated to evaluate the distortion correction effect in Section III below.
III. EVALUATIONOFTHEPROPOSED
COMPENSATIONTECHNIQUES
A. Training DRF-RX receiver
The coefficients for the nonlinear model for inverse distortion were calculated using a 2-tone training signal and the LMS algorithm, as presented in Section II.B. For the simplicity of the hardware implementation with the processing at the RF domain, the general model in use is the polynomial model (7) [25], [29].
𝑦[𝑛] = ∑ ∑ 𝑎𝑘𝑞𝑥(𝑛 − 𝑞) ∙ |𝑥(𝑛 − 𝑞)|𝑘−1
𝑄
𝑞=0 𝐾
𝑘=1
(7)
where K is the nonlinearity order and Q represents the memory length of the amplifier. In practice, we consider up to only the third-order nonlinear components. The higher distortion components (from 4th onward) are considered too small compared to the received signal and can be safely excluded.
Otherwise, the signal of interest is over-distorted and could not be recovered [25]. In the simulation for the training process, thermal noise and ADC quantization noise were added to the signals 𝑥̂𝑡𝑟𝑎𝑖𝑛[𝑛] and 𝑦𝑡𝑟𝑎𝑖𝑛[𝑛] in equation (3), (4). With this model, the nonlinear distortion is composed of all order components, including even and odd orders, which represent harmonic and intermodulation components.
In the experiment, the value of step size µ was chosen in the range [0.001-0.1]. Fig. 9 shows an example of the convergence of the second-order (𝑤2) and the third-order parameters (𝑤3) in the nonlinear model. The results show that the greater the value of µ, the faster the time of convergence but the less accuracy. Also, the model coefficients typically converge after 105 samples for both second-order and third-order parameters.
Nonetheless, in this work, the choice of time training with the LMS algorithm is not an important design criterion because the training process is performed only once before the receiving mode, or when a device calibration is required, as discussed before. In contrast, with the reference receiver technique in [9]
[10], the adaptive LMS and the compensation circuit have to work in real-time mode, so their response times could be crucial.
As the LNA parameters are uniform in the frequency domain, the choice of frequency for training can be arbitrary.
We hence design a case study that a maximum number of distortion components generated by LNA are captured. The major simulation parameters as presented in TABLE I. In this setup, 16-QAM signal has the double bit rate as that of QPSK so that the symbol rate of two cases are the same. Other than that, the other parameters, including filter coefficients, carrier frequency, and power level of each channel are the same for 16-QAM and QPSK. In this setup Ch4 is the channel of interest with very low power level (-51 dBm) and Ch1-Ch3 plays the role of the high power (-21 dBm) “causing distortion”
channels. We intentionally set the channel frequencies for an extreme case study so that Ch4 is most affected by all type of LNA distortions (i.e., second-order harmonic from Ch1 and third-order intermodulation from Ch2 and Ch3). These parameters are also used afterward for the experimental test.
In the simulation model, LNA parameters are referenced from the measurement data for ZLF-500LN+ using 2-tone reference signals of 5.3 MHz and 5.8 MHz are given to the DAC and the receiver's LNA input, these two frequencies are also on to the modulated RF signal range used for simulations.
With the input signal level changing from -35 dBm to -14 dBm, the LNA output signal will be distorted. We conducted the training process by DPIR method with 2-tone signal’s power ranging from -35 dBm to -14 dBm into 16, 32 and 64 intervals.
An example of the training curve is shown in Fig. 10. In this figure, the solid-black and red-dashed lines represent the direct and inverse LNA characteristics, respectively. Similarly, the training results for 16 points, selected based on the DOPR is represented in Fig. 11. The parameters received after training are stored in a LUT memory and will be used for compensating LNA nonlinearity in the receiving mode.
Fig. 9. The convergence process of the nonlinear coefficients
Fig. 10. AM-AM characteristics of ZFL-500LN+ and linearization lines (DIPR)
Fig. 11. AM-AM characteristics of ZFL-500LN+ and linearization lines (DOPR)
0 2 4 6 8 10
x 105 -0.4
-0.3 -0.2 -0.1 0 0.1
Sample
2rd-order 3rd-order w1(u=0.002) w2(u=0.002) w2(u=0.01) w3(u=0.01) w2(u=0.05) w3(u=0.05)
-30 -25 -20 -15
-5 0 5 10
Power input (dBm)
Power output (dBm)
Linear ZFL-500LN+
Linearization
-30 -25 -20 -15
-5 0 5 10
Power input (dBm)
Power output (dBm)
Linear ZFL-500LN+
Linearization
B. Evaluating DRF-RX Performance in Receiving Mode As we have discussed earlier in Section II. A, the characteristic of the LNA is relatively uniform. Therefore, without losing the generality we evaluate the effectiveness of the compensation circuits for a wideband multichannel HF DRF-RX for a case study, whose specifications are listed as shown in Table I. This configuration is also will exactly matched the configuration that will be implemented in the experimental Session for comparison.
In this setup, the total RF input level is about -17 dBm, in which the channel Ch4 at carrier frequency 15.6 MHz is the low-power channel with the received power is about 30 dB lower than the other three channels. With the selected frequencies, the RF signal of Ch4 at the output of LNA will be severely affected by the second harmonic of the Ch1 and the third-order intermodulation of the two channels Ch2-Ch3. As described in II.B, during the receiving mode, the RF signal in the digital domain is split into two paths as shown in Fig. 7.
The path to the inverse model is carried out up to the third- order distortion. The other path is taken to the power detector circuit. The level of the RF signal power is continuously estimated by the envelope detector during the reception.
Depending on the defined power level, a set of corresponding nonlinear coefficients is extracted from the LUT.
(a)
(b)
Fig. 12. Spectra of the RF signals before and after compensation with LUT using (a) DOPR and (b) DIPR with total input power of -17 dBm
TABLE I.CONFIGURATION OF QPSK CHANNELS IN EXPERIMENTAL AND SIMULATED
Chanel Type Symbol rate/Power RF Carry Frequencies Ch1 QPSK/16-QAM 500 k/-21 dBm 𝑓1= 7.8 MHz Ch2 QPSK/16-QAM 500 k/-21 dBm 𝑓2= 13.6 MHz Ch3 QPSK/16-QAM 500 k/-21 dBm 𝑓3= 14.6 MHz Ch4 QPSK/16-QAM 500 k/-51 dBm 𝑓4= 15.6 MHz TABLE II.SNDR OF CHANNEL CH4BEFORE AND AFTER DISTORTION
PROCESSING WITH DIPR AND DOPRMETHOD Input
Power (dBm)
No compensation
(dB)
LUT16 (dB)
LUT32 (dB)
LUT 64 (dB) DOPR DIPR DOPR DIPR DOPR DIPR -35 20.54 29.65 27.43 31.63 28.84 31.67 28.9 -29 16.94 24.86 24.04 30.34 28.11 30.84 28.81 -23 15.16 22.49 22.3 29.79 28.54 31.24 29.33 -17 13.13 21.73 21.9 29.13 27.57 31.56 28.04
We quantified the linearization impact by evaluating the SNDR of Ch4, i.e., the lowest power and the most distorted channel. The improvement in SNDR of Ch4 will be evaluated with the two division methods DIPR and DOPR. The performance of the proposed method is simulated with different sizes of LUT from 16 to 64. The spectra of the signals before and after mitigation of the two division methods, DIPR and DOPR with the input power equals -17dBm, are presented in Fig. 12 (a)-(b)2. As can be seen from the spectra, with the LUT resolution of 64, the distortion is reduced close to the spurious background, the signal spectrum is almost equivalent to the signal without distortion, and further subdivision is unnecessary.
The summary of SNDR of Ch4 using DIPR and DOPR with different input levels and LUT sizes are listed in TABLE IV.
With total input power ranging from -35 dBm ÷ 17 dBm, the SNDR without applying compensation is about 20.55 dB ÷ 13.13 dB. After applying the compensation, the SNDR substantially increases for both DIPR and DOPR methods. And as expected with the increase of the LUT size the SNDR gradually improved from 9 dB÷11 dB (7 dB ÷ 8 dB) for DOPR and DIPR. Overall, from the result, it could be observed that the increase in LUT size to a certain value (32) has a weak impact on the SNDR. These results also indicate that DOPR is slightly superior to DIPR at iso LUT sizes. This comes with the cost in the complexity in training methodology as discussed in Session D.
IV. EXPERIMENTALVERIFICATIONOFTHE PROPOSEDDISTORTIONCOMPENSATION
SCHEME
In this section, we experimentally verify the effectiveness of the proposed distortion compensation method and the DRF-RX architecture with the actual distorted input samples from LNA.
2 The spectra of QPSK, QAM signal are the same, we present here only QPSK spectra for the sake of brevity.
0.5 1 1.5 2 2.5
x 107 -120
-100 -80 -60 -40
Frequency (Hz)
Relative Amplitude (dBm) Before Mitigation After Mitigation (/16) After Mitigation(/32) After Mitigation(/64) Ch1
Ch4 Ch2Ch3
0.5 1 1.5 2 2.5
x 107 -120
-100 -80 -60 -40
Frequency (Hz)
Relative Amplitude (dBm) Before Mitigation After Mitigation (/16) After Mitigation(/32) After Mitigation(/64)
Ch1 Ch3
Ch2
Ch4
We use a customized chip FPGA [30] with a high-speed 14-bit ADC ADS4229 and a 14-bit DAC DAC5672 [31] frontends (shown in Fig 13) to generate and capture signal samples3. These ADC and DAC have high resolution and SFDR > 85 dBc, so their non-ideal impacts are considered small compared to that of LNA. The ADC sample rate is 200 Msps so the band in this implementation is limited to HF and lower part of VHF ranges. To have a clear comparison with simulation results in Section III.B, the channel parameters for experiment are set exactly as those in the simulation setup as shown in Table I.
To build the lookup table, we have practically examined module ZFL-500LN+, the measurement results show that when the level is less than -35 dBm, the LNA works in the linear domain. With signal levels higher than -14 dBm, i.e., the LNA approaches the saturation region, resulting in extremely severe distortions, and even the accuracy of the power estimation circuit can be strongly affected. Therefore, for this particular LNA device, we limit our measurement with the input power ranging from -35 dBm to -14 dBm, and this range is divided into 16 equal intervals for training.
The 2-tone signals of 5.3 MHz and 5.8 MHz are transmitted in 16 defined levels for training (-35 dBm ÷ -14 dBm) respectively. These power levels are tuned by a circuit implemented on a customized DSP board. Those training signals are converted by DAC and fed to LNA. The output signal from LNA is directly sampled by ADC and the captured samples are transmitted to the computer in a real-time mode via Gigabit Ethernet. Subsequently, the output signal of the LNA is used to determine the signal level and the distortion coefficients of the inversion model are then calculated by the LMS algorithm. The after-training results are 16 parameter sets, corresponding to the energy levels of the LNA nonlinear region. Fig. 14 shows the post-LNA output spectrum on the spectrum analyzer when changing the training signal level. The results showed that the distortion components produced after LNA varies with the change of the input signal level. The higher is the input level, the more severe is the distortion.
ADS4249 DAC5672
ZFL-500LN+.
XC7A100T LPF
ATT
LNA
Fig 13. Experimental setup and diagram of solution evaluation.
3 Currently, the sampling rate ADC converters can reach up to Gsps [33] which makes the DRF-RX design suitable for RF signals up to the GHz but in this work due we demonstrated with only mid-range available ADC.
To evaluate the LUTs methods during the working mode, we use 4 signal channels with QPSK and 16-QAM modulation with the parameters are given in Table I. The total power of the RF signal varies with 4 levels: -35 dBm, -29 dBm, -23 dBm, and -17 dBm, which are in the power range for mentioned above DIPR. In this implementation, channel Ch4 in the four cases has a power level of about 30 dB lower than total input powers After DAC, the RF signal is fed to the LNA input before being digitalized by ADC. Finally, the entire modulated samples are captured and transmitted to the computer for further processing using inverse nonlinear algorithm4. The pre- trained LNA characteristic obtained from the training process is then used to perform the distortion removal. Overall, after applying the proposed linearization, the signal quality has shown a clear improvement. The detailed measured results are presented in the following.
To examine the LNA non-linearity, the received signals of four RF channels after the LNA are measured and analyzed using Aeroflex Broadband signal analyzer Aeroflex CS9000 with different total input power levels without applying the proposed linearization method. With this particular setup, the distortion including both the harmonic and intermodulation components presents at different frequencies in the band as the result of LNA nonlinearity. Among them, channel Ch4 is the most severely affected by the LNA's nonlinear distortion since its frequency is intentionally set at the position of harmonic and intermodulation caused by itself and other channels.
Specifically, the interfering components on channel Ch4 include both the second harmonic of channel Ch1 and the intermodulation of channel Ch2 and channel Ch3. Therefore, here we also take channel Ch4 to evaluate the quality before and after distortion.
Fig. 15 (a)-(b) show the eye and constellation diagrams of the QPSK signals. Here, for the sake of brevity, we present the results of only two representative power levels: -35 dBm (the smallest) and -17 dBm (the largest), while in the implementation four power levels were measured. From Figs.
15 (a)-(b), the eye height is 25% smaller than the amplitude of the signal and the expand constellation points. When the input signal level is -35 dBm, the distortions affecting Ch4 channel can already be observed. Though the constellation points enlarged, the distinction between symbols is still quite clear.
Especially when the input RF power level is -17 dBm, the constellation of the signal extended to the decision domain of another symbol, the eye diagram loses the usual shape and the signal is difficult to be decoded successfully. Similarly, it is shown in Fig. 16(a)-(b) that with the QAM signal the eye diagram shows a very low noise margin and the symbol constellation is widely spread. For both energy levels, the distortion impact on 16-QAM is visibly worse than that of
4 We have distortion compensation and demodulation implemented on the MATLAB model with fixed point representation. Nonetheless, since the processing is all digital, this essentially produces the same trustable results as those implemented on fully embedded digital receiver on hardware.
QPSK modulation as the trade-off of the higher bit-rate.
Especially, when the total input signal is at -17 dBm, the received symbols’ constellation is mostly evenly distributed on the IQ plane. This experiment results imply that the influence of the distortion is proportional to the input signal level and it can be extremely severe when the input level is close to the nonlinear upper threshold.
The results after distortion processing for RF signals with different levels are shown by the eye and constellation diagrams in Fig. 15 (c)-(d)) and Fig. 16 (c)-(d). The results show that the post-distortion processing eye height is nearly doubled compared to the pre-processing eye height of modulation signals QPSK and 16-QAM, respectively. The constellation points are clearly distinguished, and the radius is reduced to about half of the value before distortion correction.
Furthermore, the effectiveness of the proposed linearization method is quantified by the EVM and SNDR indexes. The EVM improvement is consolidated in TABLE VI. According to the table, EVM of QPSK has been improved by 6.5% when the amplifier input signal level is -35 dBm and clearly improved by up to 27.6 % at more severe test case with higher input power of -17 dBm. It is also notable that the improvement of the signal with 16-QAM modulation is not as
good as QPSK. The data on the TABLE IV shows that QPSK improvement is around 6.5 % ÷ 27.6 %, while it only reaches 3.5 % ÷ 7.0 % for 16-QAM. This can be explained by the fact that with the same SNR, the EVM of 16-QAM is lower than that of QPSK.
Regarding SNDR, the practical measurement shows that the distortion compensation also improves the SNDR of Ch4 by 4.10 dB to 7.10 dB (total input power from -35 dBm ÷-17 dBm). These improvements are slightly lower than the simulated results. This difference is essentially due to some idealization in the system model. Indeed, the LNA model is simplified with considering up to only the third-order components. In addition, the factors such as DAC accuracy, ADC nonlinearity, signal level determination, jitter and clock error, power quality etc. can all affect the model correctness.
Therefore, taking into account these nonidealities in the model, it is a logical fact that our experimental results are not as good as the simulation result. However, as can be seen from TABLE III and TABLE IV, the experimental results still confirm the effectiveness of the proposed solution, as with different levels of distortion and modulation type, both simulation and experiment results clearly show the improvement of the received channel after the linearization process.
(a) RF power level to the amplifier is -35 dBm, (b) RF power level to the amplifier is -29 dBm,
(c) RF power level to the amplifier is -23 dBm, (d) RF power level to the amplifier is-17 dBm,
Fig 14. The dependence of distortion level on the total input power measured with the training signal spectrum at LNA output, measured by Keysight Signal Analyzer N9010B
(a) Ch4 channel before processing (total RF power to the amplifier is -35
dBm, QPSK modulation), (b) Ch4 channel before processing (total RF power to the amplifier is –17 dBm, QPSK modulation),
(c) Ch4 channel after processing (total RF power to the amplifier is -35 dBm, QPSK modulation),
(d) Ch4 channel after processing (total RF power to the amplifier is -17 dBm, QPSK modulation),
Fig 15. Constellation and eye diagram of the Ch4 channel when total RF input power = [-35 dBm and -17 dBm], Ch4 power is 30 dB lower than total RF input power, QPSK modulation, measured by Aeroflex Broadband signal analyzer CS9000.
(a) Ch4 channel before processing when the total RF power to the amplifier
is -35 dBm (16-QAM modulation), (b) Ch4 channel before processing when the total RF power to the amplifier is - 17dBm (16-QAM modulation),
(c) Ch4 channel after processing when the total RF power to the amplifier is - 35 dBm (16-QAM modulation),
(d) Ch4 channel after processing when the total RF power to the amplifier is - 17 dBm (16-QAM modulation),
Fig 16. Constellation and eye diagram of the Ch4 channel when total RF input power = [-35 dBm and -17 dBm], Ch4 power is 30 dB lower than total RF input power, 16-QAM modulation, measured by Aeroflex Broadband signal analyzer CS9000.
TABLEIII.EVMIMPROVEMENTOFCHANNELCH4IN EXPERIMENTAL.
RF input power (dBm) -35 -29 -23 -17 EVM before processing (QPSK) 21.9% 24.0% 38.4% 51.6%
EVMafter processing (QPSK) 15.4% 15.9% 20.7% 24.0%
EVM before processing (16-QAM) 12.1% 12.2% 13.9% 16.5%
EVMafter processing(16-QAM) 8.6% 8.6% 8.5% 9.5%
TABLE IV.SNDRIMPROVEMENTOFCHANNELCH4
RF input power (dBm) -35 -29 -23 -17 SIMULATION (dB) 6.92 7.09 7.33 8.57 PRACTICAL IMPLEMENTATION (dB) 4.10 4.30 5.70 7.10
V. CONCLUSIONS
In this paper, we proposed a novel reference-less linearization scheme to tackle the LNA nonlinearity issues encountered in the direct RF sampling receiver in particular, and wideband RF receivers in general. Being a reference-less approach, the proposed design exhibits clear advantages in reducing the design complexity and performance as compared to the reference receiver approach, where a sub-channel is required for extracting the additional information. Unlike most of the prior approaches where the adaptive compensation circuit requires a certain amount of time for the convergence process, our LUT-based compensator circuit responds virtually without delay and could be used even in the scenarios that the RF signal is changing quickly.
The effectiveness of the proposed solution was evaluated by both MALAB simulation and hardware implementation with realistic scenarios. The model then has been partially implemented on FPGA. The real distorted signals from a commercial ZFL-500LN+ amplifier have been captured and evaluated for EVM and SNDR. The practical measurements using professional broadband signal analyzers show that our proposed linearization scheme could recover the signal quality even in extremely distorted scenarios.
We aspire that our proposed linearization technique with some modification could be applied for removing the distortion in the 5G baseband signal, which is considered a wideband one (5-100 MHz [32]), especially when available devices and similar structures have been recently debuted [33] [34]. The digital linearization approach essentially exhibits several benefits such as simple structure, easy calibration, and synchronization when working with MIMO. This direction could be one of the extensions of this work.
REFERENCES
[1] SDR-IQ™ Software Defined Radio, Spectrum Analyzer and Panoramic Adapter, [Online], Available:
http://www.rfspace.com/RFSPACE/SDR-IQ.html.
[Accessed 2nd Sep 2021].
[2] A. A. Abidi, “Direct-conversion radio transceivers for digital communications,” IEEE J. Solid-State Circuits, vol.
30, no. 12, pp. 1399–1410, Dec. 1995.
[3] O. Jamin, V. Rambeau, F. Goussin, and G. Lebailly, “An rf frontend for multi-channel direct rf sampling cable receivers,” in the Proc. of ESSCIRC (ESSCIRC) 2011, Sept 2011, pp. 347–350.
[4] B. Razavi, “Design considerations for direct-conversion receivers,” IEEE Trans. Circuits Syst. II, Analog Digit.
Signal Process., vol. 44, no. 6, pp. 428–435, Jun. 1997.
[5] The Perseus Direct-Sampling SDR Receiver, [Online], Available: https://www.ab4oj.com/sdr/perseus/main.html.
[Accessed 2nd Sep 2021].
[6] O. Jamin, Broadband Direct RF Digitization Receivers, Analog Circuits and Signal Processing 121, DOI 10.1007/978-3-319-01150-9_2, Springer International Publishing Switzerland 2014
[7] L. Anttila, M. Valkama, and M. Renfors, “Circularity- based I/Q imbalance compensation in wideband direct- conversion receivers,” IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2099–2113, Jul. 2008.
[8] IC-7300 – The Innovative HF Transceiver with High Performance Real-Time Spectrum Scope., [Online], Available:
https://www.icomamerica.com/en/products/amateur/hf/73 00/default.aspx. [Accessed 2nd Sep 2021].
[9] R. Vansebrouck, O. Jamin, P. Desgreys, and V.-T. Nguyen,
“Digital distortion compensation for wideband direct digitization RF receiver,” in Proc. IEEE 13th Int. New Circuits Syst. Conf. (NEWCAS), Jun. 2015, pp. 1–4.
[10] M. Grimm, M. Allen, J. Marttila, M. Valkama, and R.
Thoma, “Joint mitigation of nonlinear rf and baseband distortions in wideband direct-conversion receivers,”
Microwave Theory and Techniques, IEEE Transactions on, vol. 62, no. 1, pp. 166–182, Jan 2014.
[11] Raphaël Vansebrouck, Chadi Jabbour, Olivier Jamin, and Patricia Desgreys, “Fully-Digital Blind Compensation of Non-Linear Distortions in Wideband Receivers” IEEE Transactions on circuits And Systems-I: Regular Papers, vol. 64, no. 8, pp. 2112-2123, August 2017.
[12] Jaakko Marttila, Markus Allénand Marko Kosunen,
“Reference Receiver Enhanced Digital Linearization of Wideband Direct-Conversion Receivers” IEEE Transactions On Microwave Theory And Techniques, vol.65, no. 2, pp. 607-620, February 2017.
[13] K. J. Muhonen, M. Kavehrad and R. Krishnamoorthy,
"Look-up table techniques for adaptive digital predistortion: a development and comparison," in IEEE
Transactions on Vehicular Technology, vol. 49, no. 5, pp.
1995-2002, Sept. 2000.
[14] P. Jardin and G. Baudoin, "Filter Lookup Table Method for Power Amplifier Linearization," in IEEE Transactions on Vehicular Technology, vol. 56, no. 3, pp. 1076-1087, May 2007.
[15] A. Çağlar and M. B. Yelten, "Design of Cryogenic LNAs for High Linearity in Space Applications," in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 66, no. 12, pp. 4619-4627, Dec. 2019, doi:
10.1109/TCSI.2019.2936506.
[16] Y. Ma, Y. Yamao, K. Ishibashi and Y. Akaiwa, "Adaptive Compensation of Inter-Band Modulation Distortion for Tunable Concurrent Dual-Band Receivers," in IEEE Transactions on Microwave Theory and Techniques, vol.
61, no. 12, pp. 4209-4219, Dec. 2013, doi:
10.1109/TMTT.2013.2288088.
[17] L. Peng and H. Ma, "Design and Implementation of Software-Defined Radio Receiver Based on Blind Nonlinear System Identification and Compensation,"
in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, no. 11, pp. 2776-2789, Nov. 2011, doi:
10.1109/TCSI.2011.2151050.
[18] ADS4249 Dual-Channel, 14-Bit, 250-MSPS Ultralow-
Power ADC, [Online], Available:
https://www.ti.com/product/ADS4249. [Accessed 2nd Sep 2021]
[19] ZFL-500LN+, Low Noise Amplifier, 0.1 - 500 MHz, 50Ω, [Online], Available: http://www.minicircuits.com.
[Accessed 2nd Sep 2021]
[20] ZX60-P105LN+ Low Noise Amplifier, 40 - 2600 MHz,
50Ω, [Online], Available:
https://www.minicircuits.com/WebStore/dashboard.html?
model=ZX60-P105LN%2B. [Accessed 2nd Sep 2021]
[21] N. Vu, H. Le, T. Tran and Q. Trinh, "Novel Distortion Compensation Scheme for Multichannel Direct RF Digitization Receiver," 2019 19th International Symposium on Communications and Information Technologies (ISCIT), 2019, pp. 156-161, doi:
10.1109/ISCIT.2019.8905213.
[22] Ngoc-Anh Vu, Thi-Hong-Tham Tran, Quang Kien Trinh and Hai-Nam Le, “LNA Nonlinear Distortion Impacts In Multichannel Direct RF Digitization Receivers And Linearization Techniques,” Research in Intelligent and Computing in Engineering 2019, Sep 2019
[23] N. Vu, H. Le, T. Tran, V. Hoang and Q. Trinh, "Adaptive Distortion Inversion Technique for LNA's Nonlinearity Compensation in Direct RF Digitization Receivers," 2019 International Conference on Advanced Technologies for Communications (ATC), 2019, pp. 117-122, doi:
10.1109/ATC.2019.8924528.
[24] N. -A. Vu, H. -N. Le, T. -H. -T. Tran, V. -P. Hoang and Q.
-K. Trinh, "A LUT-based LNA Nonlinear Distortion Compensation Scheme in Direct-Sampling Receivers," 2020 IEEE Eighth International Conference on Communications and Electronics (ICCE), 2021, pp. 24- 29, doi: 10.1109/ICCE48956.2021.9352138.
[25] Gharaibeh, Khaled M, Nonlinear distortion in wireless systems: modeling and simulation with MATLAB, John Wiley & Sons Ltd, 2012.
[26] S. Haykin, Adaptive Filter Theory, 4th ed. Upper Saddle River, NJ, USA: Prentice-Hall, 2002.
[27] R. Lyons, "Digital Envelope Detection: The Good, the Bad, and the Ugly [Tips and Tricks]," in IEEE Signal Processing Magazine, vol. 34, no. 4, pp. 183-187, July 2017.
[28] M. Vucic and M. Butorac, "All-digital high-dynamic automatic gain control," 2009 IEEE International Symposium on Circuits and Systems, Taipei, 2009, pp.
1032-1035.
[29] N. Lashkarian and C. Dick, ‘‘FPGA implementation of digital predistortion linearizers for wideband power amplifiers,’’ in Proc. SDR Tech. Conf. Product Expo., 2004, pp. 1–6
[30] Xilinx Artix®-7 FPGA, [Online], Available:
https://www.xilinx.com/products/silicon-
devices/fpga/artix-7.html. [Accessed 2nd Sep 2021]
[31] DAC5672, Dual-Channel, 14-Bit, 275-MSPS Digital-to- Analog Converter (DAC), [Online], Available:
https://www.ti.com/product/DAC5672. [Accessed 2nd Sep 2021]
[32] What frequency spectrum will 5G technology use and how does this compare to 4G?, 15 Feb 2019 [Online], Available: https://www.arrow.com/en/research-and- events/articles/what-frequency-spectrum-will-5g-
technology-use-and-how-does-this-compare-to-4g.
[Accessed 2nd Sep 2021]
[33] Zynq UltraScale+ RFSoC, [Online], Available:
https://www.xilinx.com/products/silicon- devices/soc/rfsoc.html. [Accessed 2nd Sep 2021]
[34] ADC12J4000, 12-Bit, 4.0-GSPS, RF Sampling Analog-to- Digital Converter (ADC), Available at https://www.ti.com/product/ADC12J4000. [Accessed 2nd Sep 2021]
Ngoc-Anh Vu received his Engineering and Master Degrees in Electronic Engineering respectively in 2008 and 2014 from the Military Technical Academy in Hanoi.
Currently, he is a PhD student in Electronic Engineering at the Military Technical Academy university. His research interests
include the design of direct frequency converter radio transceivers, wideband multichannel transmitters, improving transceiver quality.
Dr. Hai-Nam Le received his Engineering and Master Degrees in Electronic Engineering respectively in 1996 and 2001 from the Military Technical Academy university in Hanoi; he received PhD (2006) in Communication Theory from Moscow Institute of Physics and Technology. His research area includes the design of SDR, digital signal processing. He has authored or co-authored more than 20 publications on journals and conference proceedings
Thi-Hong-Tham Tran received her Engineering and Master Degrees in Electronic Engineering respectively in 2008 and 2011 from Le Quy Don Technical University in Hanoi; she received PhD (2021) in Radio Engineering from Moscow Institute of Physics and Technology (MIPT). Her research interests include the design of direct frequency converter radio transceivers, wideband multichannel transceiver.
Dr. Quang-Kien Trinh (M’15) received BS (2007) and MS (2009) Degrees of Applied Mathematics and Physics respectively from Institute of Physics and Technologies (State University) in Moscow, Russia; he received PhD (2018) in Computer Engineering from National University of Singapore. Currently, he is the deputy head of the Department of Microprocessor Engineering, Faculty of Radio-Electronics, Le Quy Don Technical University. He has authored or co-authored more than 30 publications on journals (mostly IEEE) and conference proceedings and several patents.
