Ultra-high Efficiency Phased Arrays for Astronomyand Satellite Communications

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Karl F. WarnickDepartment of Electrical and Computer EngineeringBrigham Young University, Provo, UT, USA

Collaborators:

Brian D. Jeffs, Junming Diao, Zhenchao Yang, Kyle Browning, and Matt Morin, Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT, USAJ. Richard Fisher, Roger Norrod, Anish Roshi, and Bob Simon National Radio Astronomy Observatory, Green Bank, West Virginia, USAPeter Russer, Technische Universität München, GermanyLeo Belostotski, University of Calgary, Canada

November 2014

Brigham Young University

Location: Provo, Utah, USAStudents: 34,000#10 in U.S. in number of graduates who go on to earn PhDs

Brigham Young University

Radio Astronomy

PulsarsCosmic jetsGravitational lensesGalactic centerBlack holesAstrochemistryAge of the universeCosmology About 96% of the stuff in the universe

isn’t the protons, photons, etc. we know about – it’s dark matter and dark energy!

Images courtesy of NRAO/AUI

Astronomical Instruments

Last 75 years: Single-pixel large dish antennas Last 50 years: Sparse aperture synthesis arrays Last 5 years: Multi-pixel cluster feeds (moderately sparse) Present: Dense aperture phased arrays and phased array feeds

http://www.astro.virginia.edu/whyastro/gbt+140.jpg

Images courtesy of Neil Roddis, SKA PDO

Types of Dense Phased Arrays

Aperture arrays - direct view to skyLOFAR – Low frequency array, Northern EuropeSKA Core

Phased array feeds (PAFs)Large reflectors – GBT, Arecibo, WesterborkSmall reflectors – SKA

Phased Array Feed Applications

Large single-dish radio telescopes GBT, Arecibo, China FAST,

etc. High cost, low quantity (one) High sensitivity Ultra-low noise, cryogenic Digital beamforming 300 MHz bandwidth or more

Mid-size synthesis array telescopes ASKAP and other SKA pathfinders Moderate to high quantity (tens to

thousands) High sensitivity Uncooled (ambient temp.) or

cryogenic Digital beamforming 300 MHz bandwidth or more

Small dish applications Satellite

communications, direct broadcast satellite (DBS) or very small aperture terminals (VSAT)

High quantity to very high quantity (100 –100,000+)

Low noise, uncooled Analog beamforming 1 GHz bandwidth, 50

MHZ instantaneous

Current Research on Active Receiving Arrays

Multipixel L band phased array feed on Arecibo Radio Telescope

Cryogenic array feed on National Radio Astronomy Observatory 20-Meter Dish

Digitally beamformedphased array receivers-FPGA implementations-Array calibration-Multiple simultaneous beams

World-record sensitivityfor a phased array antenna

Current Research on Active Receiving Arrays

Magnetic resonance imaging (MRI) coil arrays

Near Field MIMO arrays

Satellite Communications Terminals

What do all these applications have in common?

The key figure of merit in all cases is….

Higher SNR = more customers, more science, better quality of service, more revenue, better image quality, longer range, lower power usage, less bandwidth. SNR is the “money parameter” for billion dollar satellite communications networks, cellular systems, astronomical instruments, and deep space networks.

Noise Considerations are Critical

For terrestrial communications applications, the thermal noise environment is ~290 K or the channel is interference limited improving antenna radiation efficiency and reducing receiver noise leads to only a modest SNR improvement

The microwave sky is much cooler than ambient temperature (~4 K at L band, 20-40 K at K band) radiation efficiency and receiver noise are dominant

Radio astronomy and satellite communications: When the signal comes from the sky, high radiation efficiency and low noise electronics are critical

Key question: can phased arrays achieve noise performance and efficiency comparable to horn feeds?

What’s going on right now in antenna theory?

Basic antenna design is a mature field Multiband antennas, ultrawideband antennas, small

antennas are well understood and widely used in industry Current hot topics include active phased arrays, ultra-high

sensitivity array receivers, array feeds reconfigurable antennas, cognitive radio, multiple input multiple output (MIMO)

These are mostly practical applications Are there any open theory questions? Lets go back to basics to figure that out…

What is this quantity?

Antenna efficiency, not aperture efficiency!

Aperture Efficiency

How is aperture efficiency actually defined in the IEEE Standard Definition of Terms for Antennas?

antenna [aperture] illumination efficiency: The ratio, usually expressed in percent, of the maximum directivity of an antenna [aperture] to its standard directivity. Syn: normalized directivity; See: standard [reference] directivity. standard [reference] directivity: The maximum directivity from a planar aperture of area A, or from a line source of length L, when excited with a uniform-amplitude, equiphasedistribution.NOTE 1— For planar apertures in which A >> λ2, the value of the standard directivity is 4πA/λ2, with λ the wavelength and with radiation confined to a half space.

[IEEE Standard Definition of Terms for Antennas, IEEE Std 145-2013]

For most aperture antennas, antenna efficiency is the product of radiation efficiency and aperture efficiency.

Other Non-standard Antenna Terms

Does gain include the effect of losses due to impedance mismatch between a driving amplifier and an antenna?

No, but realized gain does “Total gain” (not defined in the IEEE standard) “Total efficiency,” “overall efficiency” (also not defined in the

standard) “Multiple element antenna efficiency” for MIMO “Absorption efficiency” for receiving antennas “Decoupling efficiency” for array antennas Many others…

IEEE Standard for Antenna Terms

The IEEE Standard had a rigorous, complete, elegant system of figures of merit that was worked out many years ago

Approximately 50% of common antenna textbooks get concepts like efficiency stuff wrong, and none agree completely on basic antenna terms! (Credit to Wim Van Capellen, ASTRON, The Netherlands.)

So, not only are the open areas in antenna research practical rather than theoretical, we’ve actually forgotten some of what the giants of antenna theory knew in the 1900s!

Does this mean there are no meaningful problems left to solve in basic antenna theory?

Let’s think deeper!

A few basic concepts from microwave network noise theory…

In microwave networks, noise at the system output is often referred to an equivalent power at the system input

Since the signal and equivalent noise experience the same gain scale factors in the system, minimizing equivalent noise referred to the input actually maximizes SNR

This is why noise theory is really important Noise power at the output can be converted to an equivalent

noise temperature in Kelvin at the input using

where B is the system bandwidth and kB is Boltzmann’s constant.

What is the gain of this “antenna”?

ReceiversLNAs Digital BeamformingArray

Beam output power:

Directivity

Directivity is easy! Measure the power at the receiver output for a plane wave

coming in from a bunch of angles, integrate the total power, divide...

…but we still don’t know the gain, since that requires knowing something about losses in the antenna.

What is the “radiation loss” for an antenna that includes amplifiers? Downconverters? Digital signal processing?

One issue is that we normally extend gain and directivity to receivers using reciprocity, but complex active array receivers aren’t reciprocal (how do you input a signal into a digital beamformer with analog to digital converters, amplifiers, etc. and get it to come out of the array? …you can’t!)

Gain

Somehow, the antenna performance should be worse if the array elements are lossy than if they are lossless.

How/why does it get worse? Hmmm..that’s a tantalizing clue! Before we go there, are there other figures of merit already

available for this active antenna in the IEEE standard or in the literature?

Existing Active Array Figures of Merit

Receiving pattern directivity Solid-beam efficiency: ratio of the power received over a specified solid angle

when illuminated isotropically by uncorrelated and unpolarized waves to the total received power (in the IEEE Standard, but rarely used)

Embedded element efficiency: measures the efficiency of a radiating element in a large array, taking into account mutual coupling (used in the classical array antenna literature)

Array gain or SNR gain: ratio of array output SNR to SNR of a single sensor (commonly used by the array signal processing community, and a very important concept)

“Array efficiency”: array gain divided by standard directivity [Jacobs, A figure of merit for signal processing reflector antennas, TAP, 1985] Important but obscure paper, cited only four times in Google scholar (and three of the citations are in my papers.)This helps a bit but still raises lots of questions…is array gain equal to antenna gain? What if we want the “efficiency” of the whole antenna and not an embedded element efficiency? Why aren’t solid-beam efficiency or array efficiency used very often? What if we just want the plain old gain of the array antenna?

Simple Example

Passive antenna followed by an amplifier:

What is the gain of this antenna?

We could break the connection, but what if we don’t want to or can’t?

Is the antenna gain arbitrary? Does it increase if we increase the amplifier gain?

Radiation Efficiency

Gain is directivity multiplied by radiation efficiency.

Since we can get the directivity of this antenna, what we really need is the radiation efficiency.

But, we can’t put a signal into the amplifier output to see how much power is radiated.

There’s no way to get Prad/Pin!

What do antenna losses really do to a receiver?

Super lossy antenna

What happens at the output?

The signal is attenuated…But we could amplify the signal.

The output SNR is low, because the lossy antenna adds noise. No way to fix that.

Noise is the key!

Basic Antenna Noise Theory

For a passive antenna in a thermal environment with brightness temperature T0 in Kelvin, the available power at the antenna port is

where B is the system bandwidth and kB is Boltzmann’s constant.

Radiation Efficiency for an Active Antenna

Let’s try this:(External thermal noise

divided by total thermal noise)

…measures noise added by antenna losses

What is the thermal noise due to antenna loss?

Radiation Efficiency for an Active Antenna

Back to our attempt at radiation efficiency:

This is the radiation efficiency of the antenna if it were disconnected from the amplifier and used as a transmitter!

If the antenna system is so complex we can’t break it apart and isolate the antenna losses, maybe we should call this “receiving efficiency” instead of radiation efficiency

Noise Theory

This gives us a really nice clue as to how to define radiation efficiency, gain, etc. for active antennas:

Use received noise instead of radiated power

The beauty of this idea is that it’s equivalent to the usual definitions for passive, reciprocal antennas, but can also be applied to nonreciprocal antenna systems that can’t be disconnected and used as a transmitter

More importantly for modern antenna applications, we can handle antenna systems that include digital processing!

This includes MIMO systems, phased arrays, active array feeds, etc.

Can we use this idea to answer other questions?

Where do we put mismatch between the antenna and amplifier?

What does mismatch do to a receiver?Does it reduce the directivity?No – the directivity is only a function of the receiving pattern.Does it reduce the gain?No – gain is directivity reduced by the radiation (or receiving) efficiencySo, what does it do?For a transmitter, it reduces the realized gain, but it’s not clear how that applies to active receivers.Answer: For receivers, mismatch increases the amplifier noise figureThere’s noise again. Can we use noise theory to create a new receiver figure of merit that captures mismatch effects?

Classical Amplifier Noise Matching

Matching Network LNA

Optimal source admittance

When the source admittance is equal to the amplifier’s optimal source admittance parameter, there is an optimal compromise between signal power transfer and amplifier noise minimization, and SNR at the output is maximized

Goal: Maximize SNR at LNA output

Noise Matching Efficiency

Let’s define a new receiver figure of merit, “noise matching efficiency”

Noise matching efficiency is the receiver noise at the antenna system output with all amplifiers ideally noise matched to the antenna, divided by the actual receiver noise

– Measures noise increase due to impedance mismatches Analogous to receiving efficiency (thermal noise without

antenna losses divided by thermal noise)– Measures noise increase due to losses

Works for active antennas, active arrays, systems with any number of noisy amplifiers or active components

Process for New Standards

Antenna Definitions Working Group

Antenna Standards Committee

IEEE Antennas and Propagation Society

IEEE Standards

Association

This all seems pretty cool. Now, how do we get these ideas into the IEEE Standard?

Process for New Standards

The real process….

Latest Version of the IEEE Standard for Antennas

New IEEE Standard Antenna Terms for Active Arrays

isotropic noise response. For a receiving active array antenna, the noise power at the output of a formed beam with a noiseless receiver when in an environment with brightness temperature distribution that is independent of direction and in thermal equilibrium with the antenna.

active antenna available gain. For a receiving active array antenna, the ratio of the isotropic noise response to the available power at the terminals of any passive antenna over the same bandwidth and in the same isotropic noise environment.

active antenna available power. For a receiving active array antenna, the power at the output of a formed beam divided by the active antenna available gain.

2.251 noise temperature of an antenna. The temperature of a resistor having an available thermal noise power per unit bandwidth equal to that at the antenna output at a specified frequency.NOTES1—Noise temperature of an antenna depends on its coupling to all noise sources in its environment, as well as noise generated within the antenna.2—For an active antenna, the temperature of an isotropic thermal noise environment such that the isotropic noise response is equal to the noise power at the antenna output per unit bandwidth at a specified frequency.

2.115 effective area (of an antenna) (in a given direction). In a given direction, the ratio of the available power at the terminals of a receiving antenna to the power flux density of a plane wave incident on the antenna from that direction, the wave being polarization matched to the antenna. See: polarization match.NOTES1—If the direction is not specified, the direction of maximum radiation intensity is implied.2—The effective area of an antenna in a given direction is equal to the square of the operating wavelength times its gain in that direction divided by 4pi.3— For an active antenna, available power is the active antenna available power.

Receiving efficiency. For a receiving active array antenna, the ratio of the isotropic noise response with noiseless antenna to the isotropic noise response, per unit bandwidth and at a specified frequency.NOTE—Equivalent to radiation efficiency for a passive, reciprocal antenna.

Noise matching efficiency. For a receiving active array antenna, the ratio of the noise power contributed by receiver electronics at the output of a formed beam, with receivers impedance matched to the array elements for minimum noise, to the actual receiver electronics noise power at the formed beam output, per unit bandwidth and at a specified frequency.(K. F. Warnick, M. V. Ivashina, R. Maaskant, B. Woestenburg, “Unified Definitions of Efficiencies and System Noise Temperature for Receiving Antenna Arrays,” IEEE Antennas and Wireless Propagation Letters, 2009)

New terms:Isotropic noise responseActive antenna available gainActive antenna available powerReceiving efficiencyNoise matching efficiencyUpdated terms:Noise temperature of an antennaEffective area

New Antenna Terms

Isotropic noise response

Active antenna available gain

Active antenna available power

Receiving efficiency

Effective area (for active arrays)

Noise temperature(for active arrays)

Noise matching efficiency

Receiver Sensitivity

New efficiencies should always enter into the overall system performance in a known way. Few authors bother to do this, but it’s very important, and helps to avoid all sorts of misunderstandings and mistakes!

How does all of this relate to SNR?

Measurement Techniques

All figures of merit require the isotropic noise response How can it be measured?

– Full receiving pattern measurement: gives external part of isotropic noise response

– Network analyzer: array mutual resistance matrix based on Twiss’s theorem– Free space Y factor method: gives external part of isotropic noise response

Hot source:

Cold source:

How can we realize a very cold isotropic noise field?How can we realize a very cold isotropic noise field?

R’s are noise correlation matrices

NRAO Green Bank Cold Sky/Warm Absorber Facility

The sky is quite cool at microwave frequencies…Ground shield blocks thermal radiation from warm ground

The sky is quite cool at microwave frequencies…Ground shield blocks thermal radiation from warm ground

Can we go even deeper into the theory?

Network Theory and Signal Correlation Matrices

We’ve only just scratched the surface! If we break apart the array and look at noise in terms of microwave network theory and signal correlation matrices, we can develop a whole new framework for working with array antennas!

Array Signal Processing

Theory

Microwave Network Theory

Antenna Theory

Analysis Frameworkfor Array Antennas

Array Signal and Noise Model

ReceiversLNAs Digital Beamforming

Array

Array output correlation matrix:Array output signal and noise contributions before beamforming:

External thermal noise

Noise due to antenna losses

Noise due to electronics

Beam output power:

“Fundamental Noise Theorem” of Array Receivers

Embedded element pattern overlap integral matrix

Part of array mutual resistance matrix due to antenna lossesReal part of array mutual impedance matrix

Relates array radiation properties (element patterns) and loss part of mutual impedance matrix to the array noise response

Isotropic noise response

External noise contribution

Loss noise contribution

Twiss’s theorem:

By conservation of energy:

Array noise response:

Correlated Receiver Noise

Assuming that the front end amplifier noise correlation admittance parameter is zero, the receiver noise correlation matrix is

Transformation from antenna open circuit loaded voltages to receiver output voltages

Amplifier optimal source resistance parameter

Array mutual impedance matrix

In signal processing analysis and research, noise is often taken to be a scaled identify matrix

Correlated noise matters in most modern array applications

Amplifier minimum equivalent noise temperature

Optimal Noise Matching

Active reflection coefficients:

To maximize SNR at array output with respect to receiver noise: Design antenna elements so that active impedances are close to 50Ω, or Match front end amplifiers to the active impedances Active impedances depends on beamformer weights – more complicated

than single port antenna impedance

How do we use all of this to build better array antenna technologies?

Active Impedance Matching Strategies

Ignore active impedance variation and match to self-impedances– This may be adequate for communications systems, but is not an option for radio astronomy,

satcom, and other noise-limited applications Add a decoupling network so the impedance matrix is diagonal

– Again, this is practical for communications, but the network would add more noise due to loss than the savings in improved matching

Design LNAs so that the optimal source impedance is equal to the active impedance for one beam (boresight)

– Sensitivity decreases as the beam scans away from the matched beam– Element port active impedances are different - more convenient if all LNAs are identical– Active impedances can be outside the unit circle on the Smith chart

Design LNAs so that the optimal source impedance is a compromise over the array field of view or scan range

– Requires LNAs matched to nonstandard impedance value

Our strategy: Design the array to maximize sensitivity (G/T)– Tune array elements to present active impedances as close as possible to 50Ω to the LNAs

over the array field of view (low noise)– Simultaneously tune array element radiation patterns to maximize aperture efficiency (high

gain)

Design Optimization Process

Computationally challenging!

Single Element

7 x 2 Element

Array

19 x 2 Element

Array

HFSS

Sensitivity Cost Function

(System Model - Reflector,

LNAs, Receiver Chains,

Beamforming Algorithm)

Infinite Array

Unit Cell

Wideband Dual-polarized Dipole Element for Green Bank Telescope PAF

Similar structure to famous Goubauantenna

− Fully utilizes the space in the bounding box around the antenna (low aspect ratio)

− Fields evenly distribute on dipole arms

Broad bandwidth Dual polarization High isolation Ultra low loss Unbalanced feed line (ideal for LNA

design)

Complex multiobjective design goals: Optimized jointly for the current cryo PAF

element spacing and a future larger cryostat that will increase gain and tighten the feed pattern for the larger f/D and narrower opening angle of the GBT dish geometry (compared to 20 m telescope)

The dish matters in the array feed element design!

Sievenpiper, Daniel F., et al. Antennas and Propagation, IEEE Transactions on 60.1 (2012): 8-19.

Goubauantenna

(Single-pol)

GBT antenna (Dual-pol)

ka

BYU/NRAO Cryogenic PAF Development

Reducing electronics noise yields huge gains in sensitivity – cryocooledfront end amplifiers (in the Cornell Arecibo cryo PAF design, the elements are also cooled)

PAF development cryostat containing 38 SiGe low noise amplifiers for 19 dual-polarized antenna elements.

Closed cycle refrigerator cools LNAs to 15K Thermal transition to element feed lines

First Test of Cryogenic PAF on 20-Meter Dish

Mounted on Green Bank 20-Meter Telescope in early 2011

Measured sensitivity figure of merit:

Instrument ModeledTsys/Efficiency

MeasuredTsys/Efficiency

Green Bank Telescope L-band Single Pixel Feed

25 ±3 K

Room Temp PAF 68 K 87 K

Cryo PAF on 20-Meter(May 2011)

30-40 K 49.6 K Highest demonstrated phased array sensitivity to date

Lower is better

First Test of Cryogenic PAF on GBT (Dec. 2013)

GBT: 100m aperture diameter –largest fully steerable antenna in the world

“Kite” dipole element was used in 2013 experiment (two generations old)

38 channel data sampled with narrowband ADCs and streamed to disk (~300 kHz bandwidth)

Correlation, beamforming, and imaging done in postprocessing

Focal L-Band Array for GBT (FLAG) – Full System in Development

Cry

osta

t

XB Engine: Correlator/Beamformer, Spectrometer

Array aperture, Antenna elements,LNAs, Cryosystem,Down converters

Ch. 1

ROACH II

FPGA

12 TB SATARAID 0 Disk Array

Rack Mount PC

48 X

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12

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Eth

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Mel

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System control and data storage (existing)

(× 5)(×40)

Ch. 8

Ch.40

CPU/GPU(Blade server +

2× nvidia GTX680)

LNA

Ant.

Back End (Jansky Lab)Front End (GBT)

LNA

Ant. Signal

Transport:Optical fiber

(× 5)

CPU/GPU(Blade server +

2× nvidia GTX680) 8

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10 Gbe 40 Gbe

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40 Gbe

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NRAO DDL System

BYU CorrelatorBeamformer

In Mezzanine I/F Slot

ROACH II

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I-Q mix, ADC,Serialize &Optical Xmit

I-Q mix, ADC,Serialize &Optical Xmit

LO

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Front end – Analog Subsystem

PAF, LNAs, Electronics(BYU/NRAO)

Digitizers, Fiber Links, Polyphase Filterbank

(frequency channelization), Packetization

(NRAO)

Correlation, Beamforming, Data Formatting, Streaming

to Disk(BYU/WVU)

Array Feeds for SatCom

Motivation:– Fine, fast target tracking for mechanically steered dishes– Compensate for mount degradation, roof sag, mispointing– Reduced total cost of terminal ownership– Low profile feed geometry

Opposite end of spectrum in terms of cost requirement – ultra-cheap, ultra-small, and mass manufacturable…

…yet noise performance and efficiency must be state-of-the-art Fabricated and demonstrated array feeds:

– Dielectric resonator antenna (DRA) array– Passive arrays with patch type elements– Single band and dual band (transmit/receive)– Linear and circular polarization– Active analog beamsteered array

Traditional Horn Feeds vs. Planar Array Feeds

Conventional horn feeds Bulky size Heavy Complicate design especially

for dual band dual polarization

Planar array feeds Low cost Low profile Easily fabricated Integrated with circuits

58

Antenna Design Process

Single Element

2 x 2 Dual Band Array

Fabrication and Test

Rx Feed Network

Tx Feed Network

The Competition:

- Very high efficiency- Bulky, costly to build

Impact of radiation, spillover, and aperture efficiencies on G/T

/4 /

1 1

1 dB efficiency change

ƞrad ƞap ƞsp

SNR Variation 2.4 dB 1 dB 1.25 dB

40 50 60 70 80 90 100-6

-5

-4

-3

-2

-1

0

1

2

3

Efficiency (%)

SN

R V

aria

tion

(dB

)

Radiation EfficiencyAperture EfficiencySpillover Efficiency

Current Design Basis

Each curve shows the independent impact of the corresponding efficiency on the SNR improvement or degradation, compared with current design.

Radiation efficiency is most critical.

Various recently developed advancedantenna types are not useful for satcomdue to low efficiency.

Efficiency can be optimized by careful choice of substrate dielectric constant and thickness and rigorous

design optimization

Measurement Results

Averaged measurement results from three methods Good agreement between measurement and simulation (only study of its kind

that we know of) Best radiation efficiency 93% reported to date for 2x2 microstrip antenna

array (better even than previously reported single elements!)

Measurements courtesy of Christopher L. Holloway U.S. National Institute of Standards and Technology (NIST), Boulder, CO, USA

Array Feed Designs

62

Stacked shorted annular patch element (SSAP) Individual element

matched to dish illumination

Ultra-high radiation efficiency

Non-planar

Hex feed, two variants Planar fabrication Multilayer PCB with feed

network

4x4 Ku band beamformedarray feed Planar fabrication Electronic beamsteeringEdge-fire Vivaldi Array

Square ring slot dual circular polarization antenna element Unsolved problem in antenna world! High isolation, low loss, good cross

pol

This work on array noise theory and sensitivity optimization applies to wide range of antennas…

– Active arrays– Nonreciprocal antennas– Mutually coupled arrays– Digitally beamformed arrays

…and applications:– Astronomical array receivers – L band through mm-wave– SatCom phased arrays and array feeds– MIMO antennas– MRI coil receivers– Near field communication (NFC) arrays

Conclusions

Conclusions

The IEEE Standard for Antenna Terms offers an elegant, time-tested system of figures of merit

– It should be taught in classes and referred to in textbooks– Software packages, books, and articles should use terms consistent with the standard!

However, traditional antenna concepts are inadequate for modern antenna systems, particularly digitally beamformed receiving arrays

Using noise theory, gain, radiation efficiency, and other antenna parameters can be extended to phased arrays and arbitrarily complicated receivers yet to be built

For simple antennas, the new terms agree exactly with existing definitions Although the new terms apply to any type of antenna that can receive a signal,

some of the new terms are given the qualifier “active antenna” in the IEEE Standard to highlight the motivation and logical link between them

Don’t introduce a new efficiency or antenna parameter without:– Checking to see if one is already defined that does the job– Making sure you know how it enters into the overall system performance measure

(usually SNR) Measurable using a free space Y factor method, augmented by mutual

impedance/S-parameter measurements See IEEE Standard 145-2013!