A Reformed PSO-Based High Linear Optimized Up-Conversion Mixer for Radar Application

A reformed particle swarm optimization (RPSO)-based up-conversion mixer circuit is proposed for radar application in this paper. In practice, a non-optimized up-conversion mixer suffers from high power consumption, poor linearity, and conversion gain. Therefore, the RPSO algorithm is proposed to optimize the up-conversion mixer. The novelty of the proposed RPSO algorithm is it helps to solve the problem of local optima and premature convergence in traditional particle swarm optimization (TPSO). Furthermore, in the RPSO, a velocity position-based convergence (VPC) and wavelet mutation (WM) strategy are used to enhance RPSO’s swarm diversity. Moreover, this work also features novel circuit configurations based on the two-fold transconductance path (TTP), a technique used to improve linearity. A differential common source (DCS) amplifier is included in the primary transconductance path (PTP) of the TTP. As for the subsidiary transconductance path (STP), the enhanced cross-quad transconductor (ECQT) is implemented within the TTP. A benchmark function verification is conducted to demonstrate the effectiveness of the RPSO algorithm. The proposed RPSO has also been compared with other optimization algorithms such as the genetic algorithm (GA) and the non-dominated sorting genetic algorithm II (NSGA-II). By using RPSO, the proposed optimized mixer achieves a conversion gain (CG) of 2.5 dB (measured). In this study, the proposed mixer achieves a 1 dB compression point (OP1dB) of 4.2 dBm with a high linearity. In the proposed mixer, the noise figure (NF) is approximately 3.1 dB. While the power dissipation of the optimized mixer is 3.24 mW. Additionally, the average time for RPSO to design an up-conversion mixer is 4.535 s. Simulation and measured results demonstrate the excellent performance of the RPSO optimized up-conversion mixer.


Introduction
In recent years, radar technology has evolved significantly in many areas such as automotive safety, aerospace, and industrial automation [1].A typical automotive radar operates at a millimeter-wave frequency near 24 or 77 GHz [2].As an overview, Figure 1 shows the radar system in a nutshell.As seen in the block diagram below, a transceiver module, an antenna, a signal processing unit, and a control interface are the four main components of a typical radar system operating at 24 GHz.In automotive applications, a 24 GHz radar can be employed for adaptive cruise control, collision avoidance, and blind spot detection [3].One of the critical components of a radar system is the mixer, which plays a significant role in signal processing and up-conversion from the RF (Radio Frequency) to the IF (Intermediate Frequency) stage.A radar system requires frequency translation before subsequent processing and analysis.The high-performance mixer in radar systems can detect objects at a wide range of distances and speeds [4].
However, poor linearity results in inadvertently producing signals outside of the spectrum allocated to radar applications, which can result in interference with other communication systems [5].This is why it is imperative that communication systems and radars adhere to strict linearity standards so that harmonious coexistence within the dedicated frequency bands can be maintained.For this reason, radar applications require high linearity.High linearity of the mixer ensures that radar signals' modulation characteristics are maintained accurately.Moreover, the linearity and power efficiency trade-off is often one of the major drawbacks of traditional mixer design [6].On the other hand, mixers also suffer from compromised linearity if they attempt to minimize power consumption, limiting their ability to handle interfering signals and weak target echo signals.As a consequence, it has become important to optimize up-conversion mixers geared toward 24 GHz applications.
Specifically, this paper addresses the challenges of linearity in up-conversion mixer design at 24 GHz.A reformed particle swarm optimization (R PSO ) is proposed to design a two-fold transconductance path (T TP )-based up-conversion mixer to achieve high linearity.The advantage of R PSO is it excels at balancing global exploration and local exploitation.Also, in the designed up conversion mixer, the R PSO 's enhanced convergence speed, which allows quick identification of optimal configurations.In mixer design, where multiple parameters must be optimized simultaneously, the algorithm's ability to handle a large solution spaces is helpful.

Related Literature
In the early 1980s, Eberhart and Kennedy presented an algorithm for optimizing continuous nonlinear functions using the concept of traditional particle swarm optimization (T PSO ), which relies on the collective behavior of social swarms [7].In recent years, T PSO has become one of the most powerful optimization tools due to the fact that each particle represents a feasible solution in the solution space.
However, in practise, it is hard to control circuit configurations accurately with commercial CAD tools.The design process requires a highly skilled individual, and it can be quite time-consuming and complicated [8].In such cases, optimization algorithms are required.It is common to see a lot of discussion in the literature regarding genetic algorithms (GAs), simulated annealing (SA), firefly algorithms (FAs), and particle swarm algorithms (PSOs), all of which are effective when implemented on analog circuits, such as power amplifier (PA), operational amplifier (Op-amp), voltage controlled oscillators (VCO), and, low noise amplifier (LNA) [2].In spite of this, a mixer block optimization has not been studied very widely.A mixer design can be optimized through the exploration of multidimensional parameter spaces and the computation of optimal solutions.As part of our work, we demonstrate how R PSO can be implemented on a mixer circuit.In an integrated RF circuit design process, R PSO has a significant impact because it is an effective and quick method of optimizing complex circuit parameters, reducing the length of the design cycle, enhancing performance, and addressing various differences which affect the performance of RF circuits.
In this paper, Mugadhanam et al. [9] describe a three-stage low noise amplifier (LNA) based on the cascode technique.The proposed work addresses several shortcomings of prior LNAs, including a minimal noise figure (NF), high linearity, and low power dissipation.However, this work may need to conduct further testing to determine whether the design is scalable, robust, and compatible with other technologies, frequencies, or systems.Inverter cascode (InvCas) is a transimpedance amplifier (TIA) for optical receivers that is presented by Elbadry et al. [10].The main objective of this paper is to identify the necessary circuit parameters needed to obtain the target specifications by using particle swarm optimization (PSO) combined with the gm/ID methodology.Even though the paper focuses on the design of the InvCas TIA for the optical receiver's front end, the proposed work is not discussed in any further detail.According to Zhao et al. [11], PSO algorithms are combined with AI-integrated neural networks to create a model for semiconductor optical amplifiers (SOAs).Based on the curve of the tested SOA performance, this model enhances the effectiveness of SOA design.This paper [12], uses the firefly algorithm (FA), particle swarm optimization (PSO), and genetic algorithm (GA) to optimize variable gain LNA (VG-LNA).In VG-LNA, a complementary common gate (CCG) is coupled with a VGA.In comparison to GA and PSO, FA generates better results than all three optimization techniques.A Doherty amplifier is presented in this paper, and a low and a high power region are analyzed [13].The paper also expands the application of the automatic PA design.However, neither a multi-objective optimization strategy for the proposed automatic PA design system nor its specific limitations are discussed in this paper.A genetic algorithm (GA) is used in this study to optimize two Bulk CMOS technology nodes of low noise amplifiers (LNAs) [14].Optimization of the LNA was significantly faster using the interactive optimization tool than using the non-interactive method.
A novel adaptive genetic algorithm (AGA) [15] was applied in this paper that enhances the circuit power-added efficiency (PAE) and solves trapping in local optimum.The proposed optimized PA design is not addressed in terms of its applicability to different frequency bands or to 5G.An optimized balun is achieved with a genetic algorithm by designing and implementing a wideband double-balanced mixer based on a GaAs pHEMT process [16].This paper examines the use of artificial intelligence to optimize and improve the performance of analog and mixed-signal circuits [17].A major challenge in AMS circuit automation is the reliance on circuit knowledge expertise, which can limit the effectiveness of AI-based approaches.Although mathematical optimizations have their advantages, they also carry some drawbacks, such as not being able to capture all the information contained in a complex physical model.In addition to circuit knowledge, AI techniques could be used to improve results.In terms of its computational efficiency, FA is superior to other methods such as particle swarm optimization (PSO), the cuckoo search algorithm (CSA), human behavior optimization (HB-PSO), in terms of simulations, comparative studies, and statistical analyses.In [18], using the current mirror technique, a double-balanced downconversion mixer is designed.Also, to optimize the circuit genetic algorithm (GA), the inclined plane system optimization (IPO) algorithm, and particle swarm optimization (PSO) have been used.As well as IPO, PSO and GA optimization algorithms have been used to optimize circuits.However, this work does not analyze computational efficiency in its entirety, and the proposed method might not be feasible for certain real-time applications.
This paper presents a novel R PSO -based optimization approach that has shown promising results.To maximize linearity and minimize power consumption, we optimized a 24 GHz T TP -based up-conversion mixer using R PSO .By integrating R PSO into the mixer design, a more efficient and reliable radar system is designed.
In this paper, four sections are presented.T PSO and R PSO are discussed in Section 2. Also, Section 2 includes a proposed design for an optimized up-conversion mixer based on R PSO .The results and analysis are presented in Section 3. In Section 4, we draw the final section.

1.
In this paper, we present a novel algorithm, reformed particle swarm optimization (R PSO ), which is designed for the optimization of the up-conversion mixer.2.
In particular, R PSO is designed to avoid the problems of local optima and premature convergence associated with traditional particle swarm optimization (T PSO ).Thus, this paper enhances the ability to explore a wider solution space and find better design configurations.

3.
We introduce two novel R PSO strategies to improve diversity: velocity position-based convergence (VP C ) and wavelet mutation (W M ).In this way, the proposed algorithm explores a broader range of solutions, resulting in a more robust and diverse search process.4.
The core concept behind the design of the optimized up-conversion mixer is the twofold transconductance path (T TP ).The objective of this proposed circuit is to increase the mixer's linearity, which is a crucial feature for radar applications.This work achieves a high linearity and a high conversion gain through the proposed algorithm.

Research Methodolgy
The research methodology focuses on the use of R PSO , which is adapted to meet specific challenges posed by up-conversion mixer challenges, to achieve high linearity.This study is likely to include simulation and experimentation phases to validate the methodology proposed in the study.Figure 2

Traditional PSO (T PSO )
A popular and effective optimization technique based on the social behavior of birds and fish is known as T PSO [19].

1.
A particle population is initialized in T PSO , each representing a potential solution.
The particles are assigned random positions and velocities in the search space.2.
In the T PSO process, we need to define each particle's best-known position (individual best or p best ) as its initial position, and the global best-known position g best as the best position among all particles in the swarm.

3.
Moreover, the next phase involves evaluating the particle's current fitness in accordance with the objective function of the optimization problem, and comparing the particle's current fitness to its best-known fitness p best .4.
The position should be updated if it is better than the current one.5.
Then compare each particle's p best to its g best .Whenever a particle's p best is better than a particle's current g best , update g best accordingly.The algorithm of T PSO can be seen in Figure 3.

Proposed Reformed PSO (R PSO )
In this work, the R PSO refers to a modification of the T PSO algorithm [20].The R PSO aims to enhance the efficiency, convergence speed, robustness, and performance of the proposed mixer circuit.In the proposed R PSO , the choice of modification depends on the strategy of velocity position-based convergence (VP C ) and wavelet mutation (W M ).In the below, we describe the strategy of VP C and W M .Figure 4 shows the proposed R PSO algorithm.

Velocity Position Based Convergence (VP C ) Strategy
The VP C is a modification introduced in R PSO to enhance its convergence speed and solution quality.The VP C adapts particle velocity and position updates to their historical information and swarm-wide best solutions.There is a set of best-known solutions maintained by the algorithm for each particle, referred to as the g best and p best .A combination of historical and current data is used to determine velocity and position updates.The g best position represents the best solution found by any particle in the entire swarm.Particles are attracted towards this position to exploit promising regions in the search space.Until now, each particle has maintained its p best position.This encourages particles to explore regions that have been successful for them individually.
The VP C strategy combines the exploration ability of the g best position and the exploitation ability of each particle's p best position, promoting a balanced exploration-exploitation trade-off.The flexibility of adjusting the velocity based on both global and personal information contributes to the algorithm's ability to converge efficiently towards optimal solutions in the search space.
The VP C can be expressed as from Equations ( 1)-( 3): Here, ξ = index of the g best particle; zξd(t) = Optimizes the position of the particle globally P gd (t); ωxξd(t) = a present search; ρ(t)(1 − 2j 2d (t))= samples array 2ρ(t); P = a scaling factor designated below determines the g best position.
S c , f c = denotes a current threshold.There are consecutive successes and failures determined by the terms ∼ successes and ∼ failures.The failure here is defined as f (p g (t)) = f (p) g (t − 1)), while the success is the exact opposite.
The VP C strategy combines the exploration ability of the g best position and the exploitation ability of each particle's g best position, promoting a balanced exploration-exploitation trade-off.The flexibility of adjusting the velocity based on both global and personal information contributes to the algorithm's ability to efficiently converge toward optimal solutions in the search space.

Wavelet Mutation (W M ) Strategy
The W M strategy is an innovative technique employed in R PSO to enhance the exploration capability of the algorithm.The goal is to provide an efficient method for exploring a variety of different regions within the search space through the integration of wavelet transformation principles into the mutation process of R PSO .
Based on the historical information in R PSO that particles evolve by adjusting their p best and g best positions and velocities.There is no doubt that R PSO is highly effective for optimization.However, by incorporating a mutation strategy into the search process, the whole process will be diversified and will be able to avoid becoming stuck in local optima.The W M strategy introduces wavelet transformations to generate diverse perturbations in the search space.Wavelet transformations are mathematical operations that decompose a function into different frequency components, allowing for both global and local information extraction.
In the W M , mutation probability determines whether an individual particle will mutate; P m ϵ [0, 1].An individual particle position generates a random number (in between 0 to 1).Therefore, to be specific, x i (t) = [x i1 (t), x i2 (t), x ij (t), x iD (t)] consider a present selected particle, where x ij (t) = is the position of the j th dimension in the iteration i th .

Proposed R PSO -Based Optimized Up-Conversion Mixer
In the context of RF electronics, a Gilbert mixer is a fundamental building block used in various applications, particularly in frequency conversion processes [21].Gilbert mixers often suffer from nonlinearity, which means that the output signal contains unwanted harmonics and intermodulation products.This nonlinearity can lead to signal distortion and degradation in receiver performance.Also, some traditional mixers may suffer from LO leakage, where a portion of the LO signal leaks into the RF or IF path, causing unwanted interference and degradation of the desired signal.To address these issues, prior research has developed various techniques and improved mixer architectures to enhance linearity.

Circuit Design Explanation
This work proposes an up-conversion mixer design based on R PSO .Figure 5 shows its schematic.The design mixer includes the enhanced cross-quad transconductor (E CQT ) and differential common source (D CS ) amplifier to amplify the input IF signal in the twofold transconductance path (T TP ).D CS amplifiers are implemented by transistors M 1 , M 2 .In addition to R 7 and R 8 , transistors M 7 and M 8 relate to a feedback resistor R 1 .The IF is applied at M 3 and M 4 's gate nodes in E CQT .With cross-coupling transistors M 5 -M 7 and M 6 -M 8 , transistors M 3 and M 4 form a current mirror.To increase the mixer's gain, the inductors L 1 , L 2 , and C 3 are connected to the common nodes of the transconductance and switching stages.The transistors M 9 -M 12 are connected to the gate nodes of transistors in the switching stage to receive a differential LO signal of 21.6 GHz.The switching stage translated the input of T TP into a 24 GHz differential RF signal.A 50 Ohm output match is achieved by complementary MOS transistors M n and M p and resistor Rf, which act as the load for the RF stage.n/pMOS transistors M n and M p serve as the push-pull output buffer.The primary transconductance path (P TP ) and subsidiary transconductance path (S TP ) are the two transconductance paths in the T TP stage of a designed mixer.In the P TP , a pair of CS amplifiers operates in the saturation region, whereas the S TP is composed of an E CQT amplifier.The E CQT is implemented in S TP to improve linearity and transconductance.We have incorporated an E CQT -based S TP into the designed mixer due to the linearity being the main concern at a frequency of 24 GHz, whereas only a P TP -based transconductance is not sufficient for radar applications.The E CQT was chosen to enhance the g m in the designed mixer.Positive feedback is avoided in E CQT by using current mirror transistors M 5 , M 7 , and M 6 -M 8 at the drain terminals, while linear output signals are taken at the source terminals.In our work, to optimize the up-conversion mixer using R PSO , the cost function we use is:

Validation of R PSO Using Benchmark Functions
This paper evaluates the effectiveness of R PSO algorithms by conducting a benchmark function verification experiment.In this study, R PSO and T PSO are compared and analyzed.The simulations are all implemented in MATLAB R2023a.Equations ( 8)-( 13) represent the benchmark functions for R PSO validation.9) An interactive comparison of T PSO algorithms versus R PSO algorithms is illustrated in Figures 6-11.Based on Figures 6-11, the R PSO algorithm converges significantly faster than the T PSO algorithm.Furthermore, R PSO has the lowest log(J) value, indicating that it performs optimization more accurately than T PSO .A boxplot of performance comparisons is shown in Figure 12, for benchmark functions F 1 to F 6 .A comparison of benchmark functions T PSO and R PSO is presented in Tables 1 and 2.

Results and Discussion
In this study, a proposed optimized up-conversion mixer is designed using 65 nm CMOS technology.It has been shown by experimental results that the high-linear upconversion mixer that uses the R PSO -based algorithm can significantly improve key performance metrics when applied in radar applications.The mixer's linearity, a critical factor in radar signal processing, has been notably enhanced through the application of the proposed R PSO algorithm.The R PSO algorithm effectively optimized the mixer's parameters, leading to a substantial improvement in linearity.
A simulation of the return loss of T PSO at RF, IF, and LO ports is shown in Figure 13.In Figure 13     For a 24 GHz-optimized up-conversion mixer, Figure 17 shows the simulated and measured result of conversion gain (CG) versus frequency.According to measured results, the proposed mixer achieves 2.5 dB CG, whereas the simulated mixer achieves 4.67 dB.As shown in Figure 18, the simulated result of conversion gain (CG) versus frequency as compared with the results of another optimization algorithm such as NSGA-II, GA is shown in Figure 18.According to the simulation results, the CG of the mixer using R PSO achieved 4.67 dB, while NSGA-II and GA achieved 4.2 dB and 2.81 dB, respectively.

Time Complexity
In optimization algorithms, time complexity is one of the most significant parameters.It measures how quickly an algorithm solves a problem as a function of the input size.Figure 22 shows the time complexity analysis using T PSO , R PSO , NSGA-II, and GA.Our work shows that R PSO has a lower time complexity than traditional GA, since particles traverse the solution space.As opposed to GAs, which work by crossovers and mutations, GAs tend to be more time-complex, especially when large populations are involved.Also, NSGA-II, designed specifically for multi-objective optimization and its time complexity, is influenced by the number of objectives and the size of the population.It takes an average of 4.535 s for R PSO to design a up-conversion mixer.According to T PSO , it is 6.527 s, for NSGA-II it is 6.315 s, and for GA it is 8.785 s.

Conclusions and Future Research
In conclusion, this study focused on developing an R PSO -based high linear optimized up-conversion mixer for radar applications.The proposed mixer design demonstrated significant improvements in terms of linearity and overall performance.The optimized mixer's OP 1 dB and CG are 4.2 dBm and 2.5 dB, respectively.Furthermore, the measured isolation between the LO-RF port, the RF-IF port, and the LO-IF port for the R PSO is −20.3, −26.1, and −24.5 dB, respectively.The return losses at the three ports-the RF port, the IF port, and the LO port-were measured as −23.8 dB, −25.2 dB, and −26.1dB, respectively.The proposed R PSO algorithm has been evaluated in terms of performance by comparing with other optimization algorithms such as T PSO and GA, as well as NSGA-II.Simulated results indicate that R PSO mixers achieve a CG of 4.67 dB while NSGA-II mixers attain 4.2 dB and GA mixers reach 2.81 dB.Also, Simulated NFs of optimized up-conversion mixers based on R PSO , NSGA-II, and GA are 2.4, 3.7, and 4.6, respectively.In addition, we explained and presented the result of the time complexity.In accordance with the R PSO and T PSO , the computational time is 4.535 s and 6.527 s, for the NSGA-II it is 6.315 s, and for GA it is 8.785 s.
This study has a limitation in that the effectiveness of the R PSO algorithm heavily depends on the specific characteristics of the up-conversion mixer as well as the operating conditions of the mixer, so it has the potential to be less versatile for different types of mixers.Future work may focus on further refining the optimization process, exploring additional parameters, and addressing practical implementation challenges for seamless integration into radar systems.Also, develop and explore strategies for reducing noise in the mixer, aiming to further enhance the signal-to-noise ratio.In addition, we could also explore the possibility of multi-objective optimization, where the optimization considers multiple conflicting objectives simultaneously.
depicts the overall flow chart of the research methodology.

Figure 2 .
Figure 2. Overall flow chart of research methodology.

Figure 5 .
Figure 5. Schematic of a proposed optimized up-conversion mixer.

Figure 6 .
Figure 6.Function F 1 comparisons for convergence process T PSO and R PSO .

Figure 7 .
Figure 7. Function F 2 comparisons for convergence process T PSO and R PSO .

Figure 8 .
Figure 8. Function F 3 comparisons for convergence process T PSO and R PSO .

Figure 9 .
Figure 9. Function F 4 comparisons for convergence process T PSO and R PSO .

Figure 10 .
Figure 10.Function F 5 comparisons for convergence process T PSO and R PSO .

Figure 11 .
Figure 11.Function F 6 comparisons for convergence process T PSO and R PSO .

Figure 12 .
Figure 12.A boxplot comparison between T PSO vs. R PSO , we show the simulated return loss for T PSO for RF, IF, and LO at −21.5, −22.1, and −24.2 dB, respectively.In addition, it shows the simulated return loss w/o PSO as −22.5, −23.8, and −25.1 at the RF, IF, and LO ports, respectively.

Figure 13 .
Figure 13.T PSO and w/o PSO-based return loss of the proposed mixer.

Figure 14 .
Figure 14.R PSO -based return loss of the proposed mixer.In contrast, at 24 GHz, the isolation for T PSO is equal to −18.1, −24.2, and −22.1 dB for the LO-RF port, RF-IF port, and the LO-IF port, respectively, is shown in Figure 15.As a result, the isolation between the LO-RF port, RF-IF port, and the LO-IF port without PSO is −19.2, −25.3, and −23.5 dB, respectively.Observing the results, it is evident that the mixer is performing well within the operating frequencies.

Figure 15 .
Figure 15.Mixer's port isolation for T PSO and w/o PSO.In the case of the R PSO , the simulated isolation between the LO-RF port, the RF-IF port, and the LO-IF port are equal to −17.1, −23.5, and −21.1 dB, respectively, at 24 GHz as shown in Figure 16.Additionally, the isolation for the R PSO , measured between the LO-RF port, the RF-IF port, and the LO-IF port, is equal to −20.3, −26.1, and −24.5 dB, respectively.

Figure 19
Figure 19 shows the R PSO -based mixer NF vs. RF frequency.The measured NF of the optimized up-conversion mixer is 3.1 dB.

Figure 20
Figure20shows the mixer NF vs. RF frequency using R PSO , NSGA-II, and GA.The simulated NF of the optimized up-conversion mixer using R PSO , NSGA-II, and GA is 2.4 dB, 3.7 dB, and 4.6 dB, respectively.Linearity is a crucial parameter in radar applications as it directly impacts the accuracy and reliability of the received signals, especially in the presence of strong interference.The study utilized a R PSO -based optimization technique to enhance the linearity of the up-conversion mixer.Figure21depicts the R PSO -based mixer RF output power vs. the IF input power.The OP 1 dB of the optimized mixer is 4.2 dBm.The results indicate a significant improvement in linearity.Table3shows the performance comparison of the R PSO -based optimized up-conversion mixer with the prior research.

Figure 21 .
Figure 21.R PSO -based mixer RF output power vs. IF input power.

Table 1 .
T PSO results of benchmark functions.

Table 2 .
R PSO results of benchmark functions.

Table 3 .
Performance comparison of R PSO -based optimized up-conversion mixer.