# Improved Signal Quality in Compressed Spectrum Sensing: A Novel LNA Design Approach for SDR boards

Hadj Abdelkader Benzater, Arab Azrar, Nacerredine Lassami, Djamal Teguig, Hamza Zeraoula

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Hadj Abdelkader Benzater, Arab Azrar, Nacerredine Lassami, Djamal Teguig, Hamza Zeraoula. Improved Signal Quality in Compressed Spectrum Sensing: A Novel LNA Design Approach for SDR boards. Circuits, Systems, and Signal Processing, 2025, 10.1007/s00034-025-03316-1. http://05291492

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# Circuits, Systems, and Signal Processing
## Improved Signal Quality in Compressed Spectrum Sensing: A Novel LNA Design Approach for SDR boards

Manuscript Draft

<table><tr><td>Manuscript Number:</td><td>CSSP-D-25-00761</td></tr><tr><td>Full Title:</td><td>Improved Signal Quality in Compressed Spectrum Sensing: A Novel LNA Design Approach for SDR boards</td></tr><tr><td>Article Type:</td><td>Original Research</td></tr><tr><td>Keywords:</td><td>LNA; SNR; CSS; SDR; GUI.</td></tr><tr><td>Corresponding Author:</td><td>Hadj Abdelkader Abdelkader BENZATER, Ph.D<br>Ecole Militaire Polytechnique<br>Algiers, ALGERIA</td></tr><tr><td>Corresponding Author Secondary Information:</td><td></td></tr><tr><td>Corresponding Author's Institution:</td><td>Ecole Militaire Polytechnique</td></tr><tr><td>Corresponding Author's Secondary Institution:</td><td></td></tr><tr><td>First Author:</td><td>Hadj Abdelkader BENZATER, Ph.D</td></tr><tr><td>First Author Secondary Information:</td><td></td></tr><tr><td>Order of Authors:</td><td>Hadj Abdelkader BENZATER, Ph.D<br>Arab AZRAR, Professor<br>Nacerredine LASSAMI, PhD<br>Djamal TEGUIG, PhD<br>Hamza ZERAOULA, Master of Sciences</td></tr><tr><td>Order of Authors Secondary Information:</td><td></td></tr><tr><td>Funding Information:</td><td></td></tr><tr><td>Abstract:</td><td>This paper introduces a novel methodology for optimizing low-noise amplifiers (LNAs) to enhance compressed spectrum sensing (CSS) performance in software-defined radio (SDR) systems. Leveraging the Agilent ATF-34143 PHEMT transistor, we develop a mathematical framework to maximize available gain while minimizing noise figure, addressing the critical tradeoff between amplification and signal quality degradation. Our approach analytically determines optimal source and load reflection coefficients using constant noise and gain circles, achieving a 7.24 dB reduction in global noise figure (from 8 dB to 0.76 dB) when cascaded with a USRP B210 SDR. Experimental validation demonstrates a 57.14 dB global gain, improving sensitivity by a factor of 5 compared to standalone SDR configurations. This work bridges theoretical LNA optimization with practical SDR applications, enabling robust CSS in low-SNR environments.</td></tr></table>
# Improved Signal Quality in Compressed Spectrum Sensing: A Novel LNA Design Approach for SDR boards

Hadj Abdelkader Benzater<fnref n="1" />*, Arab Azrar<fnref n="2" />, Nacerredine Lassami<fnref n="3" />, Djamal Teguig<fnref n="1" />, Hamza Zeraoula<fnref n="4" />

## Abstract

This paper introduces a novel methodology for optimizing low-noise amplifiers (LNAs) to enhance compressed spectrum sensing (CSS) performance in software-defined radio (SDR) systems. Leveraging the Agilent ATF-34143 PHEMT transistor, we develop a mathematical framework to maximize available gain while minimizing noise figure, addressing the critical trade-off between amplification and signal quality degradation. Our approach analytically determines optimal source and load reflection coefficients using constant noise and gain circles, achieving a 7.24 dB reduction in global noise figure (from 8 dB to 0.76 dB) when cascaded with a USRP B210 SDR. Experimental validation demonstrates a 57.14 dB global gain, improving sensitivity by a factor of 5 compared to standalone SDR configurations. This work bridges theoretical LNA optimization with practical SDR applications, enabling robust CSS in low-SNR environments.

**Keywords:** LNA, SNR, CSS, SDR, GUI.

<footnote n="1">¹Laboratoire Télécommunications, EMP, Algiers, Algeria.</footnote>

<footnote n="2">²Institute of Electrical and Electronic Engineering, University of M'hamed Bougara, Boumerdes, Algeria.</footnote>

<footnote n="3">³Laboratoire Traitement de Signal, EMP, Algiers, Algeria.</footnote>

<footnote n="4">⁴Laboratoire Systèmes Lasers, EMP, Algiers, Algeria.</footnote>

<footnote>*Corresponding author(s). E-mail(s): benzater.hadj@gmail.com;</footnote>

<footnote>Contributing authors: a.azrar@univ-boumerdes.dz;</footnote>
# 1 Introduction

Recent advances in RF circuit design and optimization techniques have enabled significant progress in two critical areas: enhancing compressed sensing (CS) implementations through analog front-end improvements, and developing mathematical frameworks for low-noise amplifier (LNA) optimization. These parallel developments address the growing demand for energy-efficient signal acquisition and high-performance analog processing in modern communication systems.

CS enhances efficiency in detecting spectrum availability. However, reliable signal detection with CSS requires a high Signal-to-Noise Ratio (SNR). This study aims to improve the performance of CS on SDR platforms through optimized LNA design. By focusing on the trade-off between gain and noise figure, we aim to enhance the SNR and improve the detection capabilities of CSS algorithms.

Our recent research incorporates SDR-based validation of various compressed sensing approaches, as demonstrated in [1, 2]. This study aims to further improve the performance of the framework under challenging noise conditions. The SDR platform utilized consists of USRP B210 boards from Ettus Research.

# 2 Related works

Novel analog CS implementations leverage in-memory computing architectures to achieve sub-µs latency in signal recovery tasks. Recent work demonstrates resistive memory arrays that perform matrix vector multiplication (MVM) operations at 5.8 µs/convergence with $1.7 \times 10^{-3}$ normalized mean squared error (NMSE), allowing direct analog implementation of iterative CS algorithms [3]. This approach eliminates digital-analog conversion overhead through continuous-time closed-loop circuits, achieving $12.5 \times$ reduction in digitization rates compared to Nyquist sampling while maintaining $< 5.1 \times 10^{-3}$ NMSE in signal reconstruction [4]. RF front-end optimizations now integrate switched-capacitor networks with CS encoding, particularly in biomedical sensor arrays where compression ratios of 8 : 1 reduce transmission energy by 68% [4].

Modern LNA optimization employs multi-objective mathematical models balancing noise figure (NF), gain, and linearity. A 2023 implementation achieved 14.3 dB gain with 1.8 dB NF across 820–980 MHz using Grey Wolf optimization for impedance matching networks [5]. Advanced methodologies parameterize the scattering matrices through transistor ratios $g_m/I_D$, enabling the simultaneous optimization of the sizing and bias conditions of the device. Recent studies demonstrate Pareto-optimal solutions achieving 15.6 dB gain with 2.1 dB NF in 65nm CMOS through automated trade-off analysis between minimum noise and maximum gain conditions [6]. These techniques reduce design cycles by 40% compared to traditional iterative approaches while maintaining < 15 dB return loss [7].

The synergy between CS-optimized RF interfaces and mathematically refined LNAs creates new possibilities for wideband cognitive radios and IoT sensors, particularly in applications requiring simultaneous wide dynamic range (> 54 dB) and ultra-low power operation (< 1 mW) [3, 7]. Ongoing research focuses on co-optimizing

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these subsystems through joint noise-power-compression metrics to address 5G/6G front-end challenges.

Authors in introduced Invertible Diffusion Models (IDM) for CS, improving signal reconstruction quality while reducing memory usage [8]. Furthermore, a self-supervised, scalable deep compressed sensing method that, once trained in partial measurements, effectively manages various sampling ratios and matrices, demonstrat-ing improved performance and adaptability [9].

The performance of CSS detection is strongly influenced by the signal-to-noise ratio (SNR), as illustrated in Equation (1). A critical element affecting the output SNR is the noise figure F of the LNA, which plays a vital role in signal amplification. The noise figure quantifies the deterioration in signal quality caused by noise introduced during the amplification process [10]:

$$F = 10 \log_{10} \left( \frac{SNR_i}{SNR_o} \right) \qquad (1)$$

Among the various RF components on an SDR board, the LNA plays a critical role due to its substantial impact on the overall system noise figure. This relationship is mathematically expressed by Friis' formula [10], as illustrated below:

$$F_{\text{total}} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \cdots + \frac{F_n - 1}{G_1 G_2 \cdots G_{n-1}} \qquad (2)$$

where $F_{\text{total}}$ represents the overall noise factor, $F_i$ denotes the noise factor of the i-th stage, and $G_i$ is the corresponding gain of that stage. The noise figure, expressed in decibels (dB), is calculated as $F = 10 \log_{10}(F_{\text{total}})$. Equation 2 underscores the importance of using an LNA with both high gain and a low noise figure as the first component after the antenna to ensure optimal system performance.

The application note from Ettus Research explains the necessity of integrating an external LNA with SDRs to enhance receiver sensitivity by reducing the overall noise figure [11]. It provides guidelines on LNA selection, power distribution, and integration methods, including the use of Bias-T circuits.

While individual boards provide essential features for test and measurement applications, they have limitations that prevent them from functioning as complete subassemblies for **coherent, multichannel, high dynamic range data acquisition** with **high channel-to-channel isolation** [12].

Key issues include:

* **Insufficient gain:** The VGA and A/D board offer high dynamic range, but the minimum detectable signal is constrained by the A/D converter's discretization limit rather than the receiver's noise floor.

* **Synchronization challenges:** In multi-unit setups using OctoClock-G, board-to-board coherence is unreliable, which is critical in applications like microwave tomography.
Thus, external microwave circuitry is necessary to enhance dynamic range and ensure signal coherence when using B210 SDRs. While innovations in Low Noise Amplifier (LNA) design have significantly enhanced the efficiency and effectiveness of CS, there remain gaps in the literature, particularly concerning the integration of LNA optimization within SDR platforms. This study aims to address these gaps by proposing an innovative LNA design solution tailored for CSS in SDR environments, focusing on maximizing available gain while mathematically minimizing the noise figure.

## 3 Mathematical Modeling

The amplifier design makes use of a transistor, characterized by its S-parameter matrix at the operating frequency, and must ensure unconditional stability. The schematic of the amplifier is presented in Figure 1. The design process focuses on determining the correct source and load reflection coefficients, denoted as $Γ_S$ and $Γ_L$, respectively. These terminations are selected not only to meet the noise figure requirements but also to maximize the available power gain, $G_a$.

To optimize the design, we tolerate a little rise in noise figure and maximize the available power gain. To stay within the low noise design the difference between $F_{min}$ and $F$ should be small to satisfy the system requirement. The values of the source reflection coefficient $Γ_S$ for which the noise figure $F$ lies on a circle known as constant noise circle defined by [13]:

$$Center \qquad C_F = \frac{\Gamma_{opt}}{N + 1} \qquad (3)$$

and

$$Radius \qquad R_F = \frac{\sqrt{N \cdot (N + 1 - |\Gamma_{opt}|^2)}}{N + 1} \qquad (4)$$

$$Where N = \frac{|\Gamma_S - \Gamma_{opt}|^2}{1 - |\Gamma_S|^2} = \frac{F - F_{min}}{4R_N/Z_0} |1 + \Gamma_{opt}|^2$$

$$We set r_n = \frac{R_N}{Z_0}.$$

By adjusting $Γ_S$, $G_a$ changes accordingly. Moreover, for a fixed value of the available power gain, there exists a range of $Γ_S$ values that result in a constant one. These values form what is known as the constant available gain circle, which is mathematically defined by the following equation [13]:

<figure><img src="image_2.png" /><figcaption>Fig. 1 Typical LNA circuit.</figcaption></figure>
$$Center C_a = \frac{g_a \cdot C_1^*}{1 + g_a \cdot (|S_{11}|^2 - |\Delta|^2)} \quad (5)$$

and

$$Radius R_a = \frac{\sqrt{g_a^2 \cdot |S_{12}S_{21}|^2 - 2g_a \cdot |S_{12} \cdot S_{21}| \cdot k + 1}}{1 + g_a \cdot (|S_{11}|^2 - |\Delta|^2)} \quad (6)$$

Where $g_a = \frac{G_a}{|S_{21}|^2}$, $C_1 = S_{11} - \Delta \cdot S_{22}^*$, $k = \frac{1-|S_{11}|^2-|S_{22}|^2+|\Delta|^2}{2 \cdot |S_{12}S_{21}|}$ and $\Delta = S_{11} \cdot S_{22} - S_{21} \cdot S_{12}$.

The constant noise figure and available gain circles provide a useful framework for achieving a balanced amplifier design. By plotting the constant noise figure circles for different values of $F$, it becomes evident that as it increases, the radius of its corresponding circle also grows. However, with an increase in $F$, the available gain also increases. Interestingly, as the available gain rises, the radius of its associated gain circle shrinks. Therefore, for a given noise figure $F$, the maximum available gain occurs when the gain circle with the smallest radius becomes tangent to the noise figure circle. To address this analytically, the normalized available power gain circle is defined as follows [14]:

$$g_a = \frac{1 - |\Gamma_S|^2}{2(1 - |S_{22}|^2) + |\Gamma_S|^2 \cdot D_1 - 2 \operatorname{Re}(C_1 \cdot \Gamma_S)} \quad (7)$$

With $D_1 = |S_{11}|^2 - |\Delta|^2$, where **Re**(.) denotes the real part of the argument, the source reflection coefficient $\Gamma_S$ must satisfy the required $F$, meaning it lies on the previously defined constant gain circle. The points around this circle can be parameterized as:

$$\Gamma_S = C_F + R_F e^{j\phi} \quad (8)$$

with $0 \le \phi \le 2\pi$. The magnitude of the source reflection coefficient is given by:

$$|\Gamma_S|^2 = |C_F|^2 + R_F^2 + 2R_F \cdot \operatorname{Re}(C_F e^{-j\phi}) \quad (9)$$

where

$$\operatorname{Re}(C_F e^{-j\phi}) = \operatorname{Re}(C_F) \cos(\phi) + \operatorname{Im}(C_F) \sin(\phi) \quad (10)$$

**Im**(.) denotes the imaginary part of the argument. Additionally, we have:

$$\operatorname{Re}(C_1 \Gamma_S) = \operatorname{Re}(C_F C_1) + R_F \cdot \operatorname{Re}(C_1 e^{j\phi}) \quad (11)$$

From Equations (10) and (11), we obtain:

$$\operatorname{Re}(C_1 \Gamma_S) = R_F [\operatorname{Re}(C_1) \cos(\phi) - \operatorname{Im}(C_1) \sin(\phi)] + \operatorname{Re}(C_F C_1) \quad (12)$$

Substituting the result of Equation (12) into the expression in Equation (7), we arrive at:

$$g_a(\phi) = \frac{a_1 + b_1 \cdot \cos(\phi) + c_1 \cdot \sin(\phi)}{a_2 + b_2 \cdot \cos(\phi) + c_2 \cdot \sin(\phi)} \quad (13)$$

where
* $a_1 = 1 - |C_F|^2 - R_F^2$

* $b_1 = -2R_F \cdot \text{Re}(C_F)$

* $c_1 = -2R_F \cdot \text{Im}(C_F)$

* $a_2 = D_1(|C_F|^2 + R_F^2) - 2\text{Re}(C_F \cdot C_1) + 1 - |S_{22}|^2$

* $b_2 = 2R_F \cdot (D_1 \cdot \text{Re}(C_F) - \text{Re}(C_1))$

* $c_2 = 2R_F \cdot (D_1 \cdot \text{Im}(C_F) + \text{Im}(C_1))$

Now, the problem is reduced to the determination of $\phi$ that leads to the maximum available gain. To this end, the first derivative of $g_a(\phi)$ with respect to $\phi$ is obtained as:

$$g'_{a}(\phi) = \frac{(a_1 b_2 - b_1 a_2) \sin \phi + (c_1 a_2 - a_1 c_2) \cos \phi + (c_1 b_2 - b_1 c_2)}{(a_2 + b_2 \cos \phi + c_2 \sin \phi)^2} \quad (14)$$

To determine the angle $\phi$ at which the maximum gain occurs, we need to solve when the derivative of $g_a(\phi)$ with respect to $\phi$ equals zero, i.e. $g'_a(\phi) = 0$. Setting the numerator of Equation (14) to zero, we find the corresponding values of $\phi$ that maximize the gain. Let's define a denominator called $D$ by the following:

$$D = \sqrt{(a_1 b_2 - b_1 a_2)^2 + (c_1 a_2 - a_1 c_2)^2} \quad (15)$$

$$\cos \alpha \sin \phi + \cos \phi \sin \alpha = \frac{b_1 c_2 - c_1 b_2}{D} \quad (16)$$

Where

$$\cos(\alpha) = \frac{a_1 b_2 - b_1 a_2}{D}$$

$$\sin(\alpha) = \frac{c_1 a_2 - a_1 c_2}{D}$$

and hence

$$\alpha = \arctan \left( \frac{c_1 a_2 - a_1 c_2}{a_1 b_2 - b_1 a_2} \right) \quad (17)$$

The solutions to Equation (16) corresponding to the two extrema are as follows:

$$\phi = -\alpha + \arcsin \left( \frac{b_1 c_2 - c_1 b_2}{D} \right)$$

$$\phi = \pi - \alpha - \arcsin \left( \frac{b_1 c_2 - c_1 b_2}{D} \right)$$

One of the obtained solutions corresponds to the maximum available gain, while the other corresponds to the minimum.

## 4 Software validation

To further validate the concept, we propose to apply this optimization on a similar work in this field. Authors in [12] added an external LNA before the RF front end of
<table><caption>**Table 1** Typical Scattering Parameters, $V_{DS} = 4V$, $I_D = 40mA$.</caption><thead><tr><th>f(GHz)</th><th>S<sub>11</sub></th><th>S<sub>12</sub></th><th>S<sub>21</sub></th><th>S<sub>22</sub></th></tr></thead><tbody><tr><td>1.5</td><td>0.78∠251°</td><td>0.064∠36°</td><td>8.405∠104°</td><td>0.24∠251°</td></tr><tr><td>1.8</td><td>0.73∠229°</td><td>0.074∠27°</td><td>7.024∠87°</td><td>0.22∠229°</td></tr><tr><td>2.0</td><td>0.70∠230°</td><td>0.081∠19°</td><td>6.002∠73°</td><td>0.21∠230°</td></tr><tr><td>2.5</td><td>0.67∠193°</td><td>0.087∠12°</td><td>5.223∠61°</td><td>0.20∠193°</td></tr></tbody></table>

<table><caption>**Table 2** Typical Noise Parameters, $V_{DS} = 4V$, $I_D = 40mA$.</caption><thead><tr><th>f(GHz)</th><th>F<sub>min</sub> (dB)</th><th>Γ<sub>opt</sub></th><th>R<sub>n</sub>/50</th></tr></thead><tbody><tr><td>1.5</td><td>0.17</td><td>0.73∠49°</td><td>0.11</td></tr><tr><td>1.8</td><td>0.2</td><td>0.7∠60°</td><td>0.10</td></tr><tr><td>2.0</td><td>0.22</td><td>0.66∠67°</td><td>0.09</td></tr><tr><td>2.5</td><td>0.28</td><td>0.6∠85°</td><td>0.07</td></tr></tbody></table>

the USRP B210 to extend its dynamic range, reduce the noise figure, and increase the gain.

The Hewlett-Packard Agilent ATF-34143 pHEMT transistor is a low-noise device optimized for low noise applications.

The S-parameters and noise figure data of the selected transistor are provided in Tables 1 and 2, corresponding to typical operating conditions in a 50Ω system [15].

Table 3 compares the global noise figure and available gain for three cases:

* Only SDR B210,

* LNA optimized for minimal noise figure preceding the B210,

* LNA optimized for maximum available gain preceding the B210.

Calculations use Friis' formula of (2) for cascaded noise figure.

The overall noise figure of the testbed in Fig. 2 for the cascaded system is 0.76 dB in the optimal gain configuration and 1.16 dB in the minimal noise figure configuration. This corresponds to a significant improvement of 7.24 dB and 6.84 dB, respectively,

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Diagram of noise figures and gains in the component cascade of the USRP B210 receiver.</figcaption></figure>
<table><caption>**Table 3** Comparison of Global Noise Figure and Gain for Different Configurations</caption><thead><tr><th>Case</th><th>F<sub>global</sub> (dB)</th><th>G<sub>global</sub> (dB)</th></tr></thead><tbody><tr><td>SDR B210 Only</td><td>8.00</td><td>40.00</td></tr><tr><td>LNA (Min. Noise) + SDR</td><td>1.16</td><td>53.45</td></tr><tr><td>LNA (Max. Gain) + SDR</td><td>0.76</td><td>57.14</td></tr></tbody></table>

compared to the standalone B210's noise figure of 8.0 dB [12]. As a result, the system achieves an enhanced sensitivity, enabling the detection of much weaker signals.

In particular, a slight increase in the noise figure from 0.22 dB to 0.35 dB results in a gain improvement of 3.69 dB, demonstrating the trade-off between noise performance and amplification. In addition, the configuration increases the sensitivity of the B210 by a factor of 5 on the linear scale while significantly improving the overall gain and dynamic range.

## 5 Conclusion

This study demonstrates the significant performance gains achieved by integrating an optimized LNA prior to USRP B210. By carefully balancing the noise figure and available gain, we were able to reduce the overall noise figure from 8.0 dB to as low as 0.76 dB, representing a substantial improvement in the sensitivity of the system. This enhancement enables the detection of much weaker signals, effectively extending the dynamic range of the SDR.

Furthermore, we observed that a slight compromise in noise figure (from 0.22 dB to 0.35 dB) allows a notable gain increase of 3.69 dB, highlighting an important trade-off in LNA design. In general, this configuration improves the sensitivity of the SDR by a factor of 5 on a linear scale, significantly improving its performance in practical applications.

These findings underscore the importance of front-end optimization in SDR-based systems, paving the way for improved CS in low-SNR environments. Future work could explore adaptive LNA tuning strategies to further optimize performance under varying signal conditions.

## 6 Data Availability

The validation of the proposed mathematical approach was performed using standard S2P (Touchstone) file data, which is publicly available and widely used in the field of RF and microwave engineering. These files can be obtained from various open-access datasets and component manufacturers' websites. No proprietary or restricted data was used in this study.

## 7 Conflict of interest

The authors declare that they have no conflict of interest.
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