Gain Isn’t Everything: SNR in Receive Phased Arrays

My core argument is this: the best receive direction is not always the direction with the largest signal. Sometimes the decisive improvement comes from rejecting an interferer, reducing a noisy sector or changing the balance between wanted signal and spatially structured noise. But “quiet” counts only when the wanted signal survives better than the noise.

A Directional Antenna Can Reject Noise Too

A Yagi is not blind to noise rejection. Its receive pattern applies to every incident field: wanted signals, atmospheric noise, ground noise and man-made interference. An off-axis source can be attenuated by a side or rear lobe, while an on-axis source can be received strongly. Height does not inherently make a Yagi collect more atmospheric noise; height, ground, nearby structures, polarization and the three-dimensional installed pattern change which fields reach the feedpoint.

A phased receive array offers a different control surface. Its element signals can be weighted to form another beam or null without mechanically turning the structure. That can be valuable when the wanted path and a dominant interferer have sufficiently different spatial signatures. It is not automatic superiority. A fixed Yagi can already have the useful pattern, while a small array may have limited aperture, unstable nulls, coupling or receiver-channel errors.

Array Factor Is Only the Ideal Geometry Layer

For a far-field plane wave at one frequency, an ideal array factor adds one complex contribution per element. With element position r_n, wave vector k and complex weight w_n, a common convention is:

This equation assumes identical element responses and a declared phase convention. It is useful for first-pass spacing and steering work. The installed response is instead a weighted sum of the embedded element patterns: each element's pattern while it sits in the array, with the other ports terminated in their stated impedances.

Mutual coupling, individual element pattern, ground, supports, cables and nearby conductors change those embedded responses. At HF, element spacing measured in wavelengths also changes substantially across a multiband span. A geometry that is electrically compact on one band can develop different lobes, ambiguities and coupling on another.

The same boundary applies to elevation. A horizontal array does not acquire a guaranteed low-angle lobe merely because its azimuth weights are steerable. Element height, vertical aperture, ground properties, polarization, coupling and three-dimensional weights determine the elevation pattern. Claims such as a fixed 5–15° response at a fixed low height require an installed model or measured pattern for the stated band and site.

Signal and Noise Combine by Different Correlation Rules

Let the complex samples from the element channels form vector x, and let weight vector w produce output y = w^Hx. If a wanted signal has steering vector a_s, input power P_s and the channel noise has covariance matrix R_n, then a narrowband output-SNR model is:

The numerator describes coherent addition of the wanted signal after channel and geometric phase are included. The denominator retains every channel-to-channel noise correlation. That matrix is why “three elements give three times the SNR” is not a universal rule.

In the ideal special case of N identical channels receiving the same wanted signal with correct phase, equal gain and mutually uncorrelated equal-power receiver noise, coherent voltage addition gives N² signal power while independent noise powers add to N. The SNR improvement is then N, or 10 log₁₀(N) dB, relative to one channel.

Change the correlation and the result changes. A coherent interferer arriving from the wanted direction can combine like the wanted signal. A dominant interferer from another direction may be nulled if its spatial signature is stable and sufficiently independent. Diffuse atmospheric, galactic, ground and urban noise can be partly correlated or uncorrelated depending on spacing, element patterns, frequency and surroundings. Receiver noise can be independent, but shared supplies, local oscillators, clocks, crosstalk and mutual coupling can add correlation.

Current ITU-R radio-astronomy interference guidance uses the spatial covariance matrix for exactly this reason: interference subspaces can support nulling, but weak or changing interference, limited samples and model error constrain the result. A nulling algorithm is a tool, not a guarantee that all noise is subtractable.

A Lower Noise Reading Is Not Automatically Better SNR

Attenuating every array branch makes both signal and external noise quieter. A badly phased combiner can do the same. So can a pattern null that happens to include the wanted station. Test at least these quantities under the same receiver settings:

• wanted-signal level or decoded quality in the declared bandwidth;
• noise-plus-interference level immediately beside or during an appropriate signal-off interval;
• the resulting SNR or task metric;
• receiver gain, attenuation, AGC state, filtering and detector;
• array weights, channel calibration and switch state; and
• time separation between compared states.

ITU-R P.372 describes external radio noise statistically by frequency and environment. A local switching supply may behave as one or several directional sources; atmospheric noise can arrive over a broad angular region; skywave propagation can make both wanted signal and interference time varying. The array's useful advantage is therefore site-, path-, frequency- and time-dependent.

Nulls Are More Sensitive Than Main Lobes

A null is made by cancellation. For two nominally equal contributions, a small fractional amplitude error ε and small phase error Δφ in radians leave an approximate normalized residual:

A 1° phase error is about 0.0175 rad, corresponding to roughly −35 dB residual amplitude when it is the only error. A 0.5 dB amplitude mismatch is about a 5.9% voltage-ratio error, leaving roughly −25 dB when it is the only error. Real arrays combine both errors with element mismatch, coupling, multipath, common mode, quantized weights, finite receiver dynamic range and a moving interferer.

Report a null with frequency, angle, polarization, bandwidth, source stability, calibration state and measurement floor. A receiver display that bottoms out establishes only a lower bound. Deep spot-frequency cancellation does not establish null bandwidth or repeatability after temperature change, reconnection or rain.

Calibration Includes the Whole Element Channel

Equal cable length does not prove equal complex transfer. Each branch includes the sensing element, mutual-coupling environment, matching or active interface, protection, filter, gain, cable, connector, switch, phase or delay network and receiver input. Characterize amplitude, phase and group delay across the intended bandwidth at declared reference planes.

NIST's over-the-air phased-array calibration work demonstrates an important general lesson: a calibration derived for one steering state need not transfer to another. Its 28 GHz hardware is not an HF antenna prescription, but the metrology principle is directly useful—calibrate the state and quantity that will actually be used, then verify it independently.

Analog combining and digital beamforming impose different requirements:

• Analog combiner: branch loss, phase slope, impedance, isolation, temperature drift and the single downstream receiver set the result.
• Multiple coherent receivers: channel gain, noise, filtering, sample timing, local-oscillator and clock coherence, ADC headroom, latency and weight precision must all be controlled.
• Switched states: switch repeatability, settling, state-dependent loss and calibration age belong in the record.

More array gain cannot repair compression or intermodulation already created in an element head or early amplifier. Test the complete channel against the strongest expected composite input, and place filtering or attenuation before the stage that needs protection.

Common Mode Adds an Unplanned Array Element

High circuit CMRR does not prove low installed common-mode pickup. CMRR describes a device or path under stated source impedances, frequency, amplitude and termination. Exterior current on coax shields, power leads, control lines and masts is a different measurement.

If one cable exterior receives the field, it contributes another complex signal whose amplitude and phase depend on routing, choke impedance, bonds and surroundings. That unintended element can distort a beam, fill a null or make a calibration change when a cable moves.

Map exterior current on every branch at repeatable positions. Swap receiver channels while leaving physical elements in place; then swap physical feeds while retaining channel assignments. Reroute or add a characterized common-mode impedance to one path at a time and repeat the pattern. A choke is useful only when it changes the diagnosed current path without creating unacceptable loss, resonance or coupling elsewhere.

A Fair Array-versus-Yagi Field Test

A comparison must give both systems a fair reference plane and avoid propagation drift masquerading as antenna performance:

• Define the objective. Name band, wanted heading, interferer or noise sector, polarization, elevation region, bandwidth and success metric.
• Document both installations. Record height, element geometry, surroundings, feed routes, matching, loss and receiver boundary.
• Calibrate the array. Save per-channel amplitude, phase, delay, noise and clock state across the test band.
• Protect linearity. Verify that every active element, combiner and receiver channel remains below compression, intermodulation and ADC-overload limits.
• Switch quickly. Use A/B/A or A/B/B/A comparison with identical receiver bandwidth, detector, gain and attenuation; restore the first state to reveal drift.
• Measure the pattern claim. Use controlled sources or enough stable azimuth/elevation observations to distinguish a lobe, null and measurement floor.
• Repeat. Test frequency, time, weather and representative noise conditions instead of publishing one best trace.

A receive array can beat a Yagi for one job when its steerable pattern rejects the limiting noise or interference while preserving the wanted signal. A Yagi can win when its fixed aperture, pattern, loss, simplicity or height better serves that path. Neither label decides. The installed SNR evidence does.

Gain isn’t everything. Quiet is useful only when the wanted signal becomes clearer.

Primary and authoritative references

• IEEE 145-2025 — Standard for Definitions of Terms for Antennas
• IEEE 149-2021 — Recommended Practice for Antenna Measurements
• NASA — Array Phase Shifters: Theory and Technology
• NBS/NIST Technical Note 1082 — Array synthesis, coupling and measured field verification
• NIST — Over-the-Air Calibration of a Dual-Beam Phased-Array Channel Sounder
• NIST — Phased-array calibration and clock-drift compensation in channel sounding
• ITU-R P.372-17 — Radio noise
• Report ITU-R RA.2126-2 — Spatial covariance and interference nulling

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