Towards Neural Network-based Design of Radiofrequency Low-Noise Amplifiers

Mounir Boukadoum, CoFaMic Research Center

Université du Québec à Montréal Montreal, Canada

boukadoum.mounir@uqam.ca

Frederic Nabki CoFaMic Research Center

Université du Québec à Montréal Montreal, Canada

nabki.frederic@uqam.ca

Wessam Ajib CoFaMic Research Center

Université du Québec à Montréal Montreal, Canada

ajib.wessam@uqam.ca

Abstract—The preliminary work on a new methodology to design low noise amplifiers (LNAs) for use in radiofrequency (RF) wireless systems is presented. The methodology aims to find the relevant design parameters faster than current analytical models and optimization procedures. To reach this goal, an artificial neural network (ANN) is used to learn the design task by being exposed to successful design examples. Our preliminary results, using a training set of two hundred design examples, show that a radial basis functions ANN can learn the provided designs perfectly, but a larger training set is required for definite conclusions regarding the prediction of component values for new designs.

I. INTRODUCTION Low noise amplifiers (LNAs) are prevalent in

radiofrequency (RF) wireless systems, and their performance defines many global transceiver parameters such as linearity and noise figure. The design of a RF LNA poses many challenges to the circuit designer [1]. These usually impose many trade-offs between metrics such as input and output matching, noise figure, gain, linearity and power consumption. Additionally, the now more common multi-band operation of RF transceivers requires the design of reconfigurable LNAs or of multiple LNAs operating at different bands, making LNA design require a larger portion of the overall transceiver design time.

Many different techniques have been proposed for LNA design [2]. All of them are relatively time consuming and may take hours to complete depending on user experience and performance specifications, require experienced designers and consist of multiple design iterations. Different optimization methods have been proposed to help with the design process (e.g., [3, 4]), but they can be overwhelmed by the number of parameters to consider, use models that often do not account for all the design variables, and introduce round off errors due to the required numerical computations. In this respect, an artificial neural network-based approach may offer many advantages in comparison. For instance, ANNs learn by

analogy with functional prototypes, have generalization capabilities, and can handle fragmentary input data (specifications in our case). Some ANN models have also been proven to be universal approximators; they can thus learn to reproduce any function or shape without the need for a mathematical expression or formal model to do so. On the negative side, ANNs require the proper tuning of their parameters to learn correctly and there exists no reliable procedure for this; user experience and trial and error are often the only recourse. Fortunately, once an ANN has been trained, no further tuning is needed. Then, its response time to an input is less than a second, at par with analytical formal models when they exist and in contradistinction to algorithmic, optimization and numerical approaches.

The advantages inherent to neural networks have prompted their use in several complex and difficult circuit applications. For instance, global modeling of microwave amplifiers and pre-distortion in power amplifiers were demonstrated using neural networks [5-8]. In addition, synthesis and device sizing of digital and analog circuits such as simple gates and two-stage operational amplifiers have been proposed with promising results [9-11]. Still, one cannot find reports on neural network-based methodologies for RF LNAs circuit design, which differs from normal digital or analog design in many respects (e.g., impedance matching, noise figure, GHz-range gain). This paper presents initial findings in the implementation of one such LNA design methodology. The paper first discusses the LNA circuit that is considered. Then, the neural network input/output configuration and structure are described, followed by our experimental protocol. Training results and a discussion are subsequently presented, and are followed by a conclusion.

II. LNA CIRCUIT The topology evaluated is a cascoded common source with

degeneration and inductive load, as shown in Fig. 1. This is a popular LNA configuration for current CMOS designs as it

provides high gain and low noise (at the expense of higher supply voltage in comparison to using a single transistor). The degeneration inductance LS allows the circuit to have a more linear response and contributes to input matching via a gyrator effect; this relieves the LNA from the thermal noise introduced by adding a real matching resistor. Load inductor LD forms a resonator with the drain capacitance of Q2 and allows for additional gain at specific lower frequencies. Transistor Q2 acts primarily as a current buffer to reduce the miller effect of the gate-drain capacitance of Q1, with the result of increased frequency response of the transistor pair.

VB

Output matching network

VDD

Input (50Ω)

Output (50Ω)

Q1

Q2

LS

LD

Input matching network

Fig. 1: Studied Cacode LNA schematic.

The cascode configuration was selected first as it exhibits close to unilateral behavior and, as such, is usually simpler to design (easier matching, stability, etc.). In addition, all inductances, including those in the matching networks, were assumed to be non-ideal with Q-factors of 10, in order to be representative of what can be achieved with current CMOS fabrication processes.

The purpose of the ANN is to determine the geometries of Q1 and Q2 and the values of LD and LS while providing input/output matching network topologies and component values for given frequency, gain, linearity (1-dB compression point and IIP3), and noise figure specifications. Different two-element matching network topologies, shown in Fig. 2, are considered to match the input and the output to the 50 Ω source and load resistances. The type (i.e., network 1, 2 or 3), and component values are output by the ANN.

III. NEURAL NETWORK ARCHITECTURE Different neural network architectures can be

implemented. They differ only in the following architectural aspects: the topology, the activation function for the different neuron elements and the training algorithm. Of the different architectures that have been used in the literature for circuit design and modeling, the multilayer perceptron with error backpropagation learning (MLP-BP) [12] is the most popular, arguably because theoretical proofs exists for it being a universal function approximator. However, other architectures exist with the same claim, of which the radial basis functions neural network (RBFNN) [13][14]. The latter can constitute a bridge between neural networks and support vector machines (SVMs), the statistically-inspired alternative class of

classifiers that is also efficient, but can be computationally expensive when used for non binary classification problems.

Network 1 Network 2 Network 3

CM LM

CM CM

LM

LM

Fig. 2: Matching network topologies used.

Both the MLP-BP and RBFNN models consist of three layers of neurons, an input layer, an output layer and a hidden/association layer in between1. The input layer neurons simply hold the elements of the input vector to the network, x∈RN. The hidden layer neurons perform weighted summations. The output of hidden neuron k in the MLP-BP network is given by

= ∑

=

N

iiik xfy

1ωθ (1)

where xi is the output of an input layer neuron (i.e. one of the N elements of the input vector to the network), ωi is a weight, and f() is an output function with parameter vector θ that is common to all the hidden layer neurons. f() is often s-shaped, typically a sigmoid.

The output of middle layer neuron k in a RBFNN is given by:

∑=

=M

iiik xy

1);( θψω (1)

where x and ωi are the same as before and ψi is a basis function with parameter vector θ; a Gaussian shape is commonly used in the literature (the Gaussian is also a kernel function, hence the connection with SVMs) The Gaussian basis function is defined by

∏=

−−=

N

j j

jji

cxx

12

2

exp);(σ

θψ (2)

where cj and σj2 are respectively the center and the width of

the Gaussian basis function for the ith hidden unit and N is the dimension of the input vector.

The neurons of the output layer also perform a weighted summation as in (1), but f() is identity in the RBFNN case while it can take other forms in the MLP-BP network.

Both MLP-BP and RBF-NN can be trained with the error backpropagation algorithm [15] or one of its derivatives. The purpose of training is to determine the values of their parameters based on two sets of input-output vector pairs, a training set and a test set. N-tier cross-validation can be used to insure consistent training results.

Both neural network architectures were investigated in this work. Each neuron in the input layer was associated with

1 The MLP architecture can have more than one hidden layer

one design specification and each output neuron was meant to specify one desired design parameter. The input variables were gain, bandwidth, noise figure, power, 1db compression, IIPP3, and central frequency; the sought outputs were the widths of transistors Q1 and Q2 (Wn1, Wn2), the values of inductors LD and LS, the type of matching network at the input and its L and C components values (top1, comp1, comp2), the type of matching network at the output and its L and C components values (top2, comp1, comp2) and the bias voltage (Vbias). A gate inductor (LT) for Q1 is also specified as a potential substitute for the input matching network. The number of units in the hidden layer was set via trial and error, starting with an equal number of units as in the input layer (twelve), and increasing their number by twenty five iteratively until either a very small mean squared prediction error was obtained or a maximum of one hundred seventy five hidden units was reached.

To build the training and test sets, two hundred LNA designs were randomly specified in CMOS 0.18µm technology from TSMC and simulated with the spectreRF circuit simulator, each design requiring several simulations and iterations to complete. The design methodology was performed by first selecting the values for LD to achieve a certain frequency of operation. Then, the different size and biasing for Q1 were chosen to generate different specification designs. The size of Q2 was also varied for each design generated in order to create designs with information on the impact of Q2 on specifications. In addition, LS was varied to reach different linearity specifications. For each design, the input and output were matched by using matching networks.

Table I summarizes the range of specifications that were considered for the LNA designs. Ten-fold cross-validation was used for training. For each fold, the designs were split into eighty percent training and twenty percent testing records. The data were normalized to the range [-1, 1] before training. All experiments were done with the Matlab Neural Network Toolbox.

Table I: Overview of the LNA design space.

Characteristic Min Max

Center frequency (GHz) 2,089 4,898

Bandwidth (MHz) 332,1 1964,04

Noise Figure (dB) 1,82 4,6093

S21 gain (dB) 4,878 15,52

1-dB comp. point (dB) -18,84 8,7584

IIP3 (dB) -5.577 5,585

S11, S22 (dB) -31,19 -14,0548

IV. RESULTS AND DISCUSSION Both neural networks were incapable of satisfactory generalization, with the RBF-NN offering the worst classification accuracy (25-45% correct output values for new designs). The latter also performed poorly on the training set, contrarily to the RBF-NN which had one hundred percent accuracy when used to recall stored designs. Fig. 3 and 4

show the average correct predictions and corresponding standard deviations for the sought design parameters as obtained by the RBF-NN. These results were obtained with twelve neurons in the hidden layer since increasing their number did not improve lead to prediction improvement.

As Fig, 3 shows, the RBF-NN model offered good prediction accuracy for some parameters (e.g. the width of transistor Q1 and the type of input matching network) and a poor one for others (e.g. component values for the input matching network). As an attempt to improve performance, we tried turning the prediction problem into one of classification by predicting ranges instead of specific parameter values. However, this did not change the results significantly, nor did changing the number of folds in the cross-validation from five to twenty in increments of one.

Aside from the relatively small size of the training and test sets, or possibly because of it, one possible explanation for the lack of generalization capability by the networks is the disparate correlation between the input and output variables. For instance, the width of transistor Q2 is expected to have minimal impact of design specifications, and may thus be more difficult to predict with a small training set. Table 2 shows the obtained correlation matrix between inputs and outputs. It reveals weak to very weak correlation between most of the predictive and predicted variables. The only exceptions were bandwidth which was strongly correlated to the type of input matching network (top1) and its component values and the type of output matching network (top2), and frequency which was strongly correlated to drain and source inductors of the cascode circuit.

There appears to be no other work on RF LNA design using a neural network-based approach. The closest one we could find addresses the issue of matching network design

Average Recognition Rate

0.8929

0.2845

0.61010.4767

0.74300.8262

0.1032 0.0708

0.6992

0.0487 0.0437

0.5468

0.00000.10000.20000.30000.40000.50000.60000.70000.80000.90001.0000

Wn1Wn2

Ltran

sistor

sLd

rain

Lsou

rce top1

compo

sante

1

compo

sante

2top

2

compo

sante

1

compo

sante

2Vbia

s

Fig. 3 : Average accuray of the RBF-NN for ithe different design parameter.

Standard Deviation of Recognition Rate

0.1210

0.2999

0.1405

0.04780.0137

0.1065

0.0227 0.020.0654

0.0059 0.0235

0.0900

0.0000

0.05000.1000

0.15000.2000

0.25000.3000

0.3500

Wn1Wn2

Ltran

sistor

sLd

rain

Lsou

rce top1

compo

sante

1

compo

sante

2top

2

compo

sante

1

compo

sante

2Vbia

s

Fig. 4 : Standard deviation of the prediction results of RBF-NN.

Table 2. Correlation matrix between predicted and predictive variables

BW DB1 f IP3 NF PDISS S21 LD 0.46 -0.49 -0.83 -0.09 0.26 0.16 0.15 LS 0.16 -0.10 -0.65 -0.18 0.24 -0.05 -0.20 LT 0.09 0.40 0.13 0.07 0.30 -0.06 -0.37

Top1 -0.86 0.48 0.39 0.07 -0.37 -0.17 -0.11 Comp1 0.76 -0.42 -0.46 -0.03 0.28 0.18 0.10 Comp2 -0.80 0.35 0.26 0.07 -0.45 -0.13 0.04 TopP2 -0.86 0.48 0.39 0.07 -0.37 -0.17 -0.11 VBIAS -0.05 -0.11 0.30 0.10 -0.42 0.49 0.48

Comp1 -0.87 0.41 0.07 0.10 -0.36 -0.16 -0.05 Comp2 -0.61 0.20 0.04 0.07 -0.16 0.12 -0.05

WN1 0.43 -0.25 -0.54 0.03 0.16 0.19 0.05 WN2 0.32 -0.18 -0.50 0.04 0.24 0.24 -0.02

corr<0.40 Very weak 0.40<corr<0.6 Weak corr>0.60 Average to strong [0.75-0.86]

with a neural network model of the Smith chart [16]. As a result, it is not possible to compare our result to those of other researchers. On the other hand, there exist several reports in the literature on using neural networks to determine the design parameters of other types of circuits (see Introduction). The reported accuracies vary considerably among these works and it is hard to draw definite conclusions from the reported performances as overtraining and no cross-validation are often found in the works that claim very high accuracies (ninety percent and more; e.g. [8]). In this respect, one can only conclude that the efficient use of neural networks for circuit design, RF or other, is still under construction and more studies are needed before the field reaches maturity. On the other hand, our result show that a RBFNN can easily learn a set of LNA designs if the user only needs to store them in a content-addressable memory for later recall. It can thus serve as a repository of completed designs.

The prediction accuracy results obtained in this work also compare favourably with those of classical machine learning techniques. For instance, we investigated the use of a k-nearest neighbour classification algorithm to design the LNA and varied the value of k form one to five, but could not match the performance of the RBFNN network. The best prediction accuracy provided by the k-NN algorithm was of the order of forty-five percent.

V. SUMMARY AND CONCLUSION This paper presented a neural network approach to RF LNA design. Two neural network models, the MLP-BP and the RBFNN, were investigated for the purpose using a database of 200 designs generated by a standard methodology using the spectreRF circuit simulator. The obtained results show that neither network had enough generalization capability to predict the component values of arbitrary designs, but the RBFNN could easily memorize complete designs and recall them via their specifications with one hundred percent

accuracy. However, this work is based on only two hundred sample designs used for training the neural networks. This number is relatively low if one considers the twelve input variables and eight output variables. Based on the available knowledge about neural network, one can reasonably expect better prediction accuracy for the LNA components if a larger database of examples is built.

ACKNOWLEDEMENT The authors would like to thank Joel Yonli, Moussa Ganséré Touré and Salim Lahmiri for help in collecting the data used in this study.

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