Synthesizing Omnidirectional Antenna Patterns, Received Power and Path Loss from Directional Antennas for 5G Millimeter-Wave Communications

I. INTRODUCTION

• MmWave’s increased free-space path loss is overcome in links by high-gain directional antennas, which can support links over about 500 m.Such measurements help characterize channels and create statistical models for wireless-system design.Source: §I · p. 1
• Omnidirectional antennas are an alternative for propagation studies, but require much greater transmit power to achieve the same measurement range as directional antennas.Mechanically rotatable horn antennas are being used while electrically steerable antennas remain unavailable to many researchers at mmWave frequencies.Source: §I · p. 1
• Recovering omnidirectional path loss requires combining directional measurements across unique transmit and receive pointing-angle pairs.The antennas are rotated through azimuth and elevation planes to emulate omnidirectional antennas.Source: §I · p. 1
• The paper synthesizes omnidirectional antenna patterns and received power from directional measurements while retaining directional gain.The resulting data can support omnidirectional path-loss models for applications that implement arbitrary directional antenna patterns.Source: §I · pp. 1–2
• Path-loss models estimate signal attenuation over distance and support wireless-system design and network simulations.The paper identifies the close-in and floating-intercept models as two common empirical models.Source: §I · p. 2

1) Close-in Free Space Reference Distance Model:

• The 1 m CI model assumes free-space propagation with n = 2 up to the anchor distance, then fits measured path losses by MMSE to estimate the path-loss exponent n.The exponent quantifies attenuation over log-distance.Source: 1) Close-in Free Space Reference… · p. 2
• Xσ represents zero-mean Gaussian shadowing variation around the mean path loss, with standard deviation σ in dB.The variation is specified at distance d from the MMSE fit.Source: 1) Close-in Free Space Reference… · p. 2
• The 1 m reference is used for mmWave because base stations are shorter or indoors and closer to obstructions, and propagation can be treated as free space within that distance.The model is also described as more stable for extrapolation beyond measured distances and provides an international reference.Source: 1) Close-in Free Space Reference… · p. 2

2) Floating-Intercept Model:

• The FI model uses least-squares regression to fit measured data, extracting an intercept α and slope β [4],.It is used by researchers involved in developing WINNER II and 3GPP channel models,.Source: 2) Floating-Intercept Model · p. 2
• FI is valid only over measured distances and lacks a physical anchor to transmitted power or true path loss in the first meter.For sparse or distance-clustered measurements, β may approach zero or become negative, while α may exceed theoretical short-distance free-space path loss,,.Source: 2) Floating-Intercept Model · p. 2
• In NLOS environments, the FI–CI difference is little relative to typical Xσ values of 7–12 dB, suggesting the CI model is sufficient and easier to use without a second parameter.The 1 m CI model uses one path-loss parameter and allows comparisons across distances, environments, and research groups.Source: 2) Floating-Intercept Model · p. 2

II. MEASUREMENT PROCEDURE

• The 28 GHz and 73 GHz outdoor campaigns used similar 400 Mcps sliding-correlator sounders, 800 MHz RF null-to-null bandwidth, and 2.5 ns multipath time resolution.They investigated mmWave channels in a dense urban micro-cell environment,.Source: §II · p. 2
• At 28 GHz, narrowbeam TX antennas and narrowbeam or widebeam RX antennas were used; RX azimuth sweeps covered 360° at 0° and ±20° elevation, with TX azimuth swept in the final measurement sweep.The narrowbeam HPBWs were 10.9°/8.6° in azimuth/elevation; the widebeam HPBWs were 28.8°/30°.Source: §II · pp. 2–3
• At 73 GHz, 7° HPBW horns were swept in azimuth steps of 8° or 10° at multiple elevations across 36 mobile and 38 backhaul TX–RX combinations.Each averaged PDP recorded 20 instantaneous PDPs and took 818.8 ms.Source: §II · p. 3

III. POWER SYNTHESIZING THEORY

• The omnidirectional received signal is modeled as a sum of MPCs, with each component characterized by amplitude, phase, and propagation delay.Because resolvable MPC delays differ, the double sum in the received-power expression is zero for k ≠ i.Source: §III · p. 3
• Directional measurements retain antenna gains in the received voltage signal, providing gain and distance extension unavailable from a typical 0 dBi omnidirectional antenna.For each directional measurement, the square roots of the transmit and receive power gains are included in the received voltage signal.Source: §III · p. 3
• Summing received powers over non-overlapping AOD/AOA combinations yields omnidirectional received power after antenna gains are removed.The directional gains provide greater path-loss measurement range than standard omnidirectional antennas.Source: §III · p. 3
• Linearly combining adjacent directional antenna power patterns produces an approximately flat synthesized pattern, including near beam edges.The summed pattern is reasonably flat, so MPCs received near a directional pattern edge experience the same gain as those received at boresight.Source: §III · p. 4

A. 28 GHz Measurement Data

• The measurements compared a 30°-HPBW widebeam antenna with nine 10°-angle samples, substituting available ±20° elevation scans for unavailable ±10° scans.Three NLOS RX locations were selected; the narrowbeam scans used elevations of 0°, -20°, and 20°.Source: A. 28 GHz Measurement Data · pp. 4–5
• Fig. 2 depicts the normalized equivalent pattern formed by overlapping horn patterns at azimuth offsets of 0°, ±10° and elevation offsets of 0°, ±8°.The horn’s azimuth and elevation HPBWs were 10° and 8°, respectively.Source: Figure 2 · p. 5
• Most received power came from the strongest elevation angle, so the missing immediately adjacent elevation patterns did not create substantial error.The available ±20° elevation samples replaced the intended ±10° samples.Source: A. 28 GHz Measurement Data · pp. 4–5
• In both azimuth and elevation planes, linearly combining power amplitudes from 3×3 narrowbeam antennas spaced across consecutive HPBW intervals yields a power difference of only 0.08 dB versus a single widebeam antenna.Source: A. 28 GHz Measurement Data · p. 5
• The synthesized 3×3 narrowbeam received powers matched widebeam measurements across three RX locations, with a maximum difference of 2.9 dB.At RX 19, one example differed by 1.7 dB: -67.0 dBm synthesized versus -68.7 dBm measured.Source: A. 28 GHz Measurement Data · p. 5
• The path-loss exponents were identical for widebeam and narrowbeam antennas in both discrete-angle and entire-azimuth-plane comparisons.The comparison used the 1 m CI path-loss model.Source: A. 28 GHz Measurement Data · p. 5

B. 73 GHz Measurement Data

• Unlike the 28 GHz measurements, the 73 GHz measurements acquired power-delay profiles at elevation intervals of 5° or 8°, close to the 7° antenna HPBW.This provided adjacent-HPBW elevation measurements for examining received-power distribution.Source: B. 73 GHz Measurement Data · p. 5
• The strongest azimuth plane accounted for over 70% of the power in that plane plus its two adjacent planes, reaching 95% with only a 0.2 dB difference.Table II reports this ratio from 73 GHz measurements in New York City.Source: B. 73 GHz Measurement Data · pp. 5–6, Table II · p. 6
• When time or resources are limited outdoors, omnidirectional path loss may be obtained by scanning across azimuth at the strongest elevation or a few adjacent elevations.The measurements used adjacent azimuth planes separated by 5° or 8°, close to one HPBW.Source: B. 73 GHz Measurement Data · pp. 5–6
• Indoor ceiling and ground reflections may require more diverse elevation pointing angles for omnidirectional path-loss data.Source: B. 73 GHz Measurement Data · p. 6

• Summing received powers from non-overlapping directional HPBW pointing combinations synthesized the omnidirectional pattern, received power, and path loss, and theoretical analyses and measurements validated the method.Source: §V · p. 6
• Different beamwidths yielded almost identical synthesized received power and path loss over systematic azimuth scans, while 3×3 narrowbeam received power agreed relatively well with a single widebeam.Source: §V · p. 6
• Fig. 3 compares 28 GHz NLOS effective directional path loss for widebeam and narrowbeam antennas at three RX locations, contrasting discrete pointing combinations with entire azimuth-plane scans.Source: Figure 3 · p. 7
• 72% to 95% of received power arrived in the strongest azimuth plane across it and two adjacent planes; considering only the strongest plane captured all but about a dB.Source: §V · p. 7
• Directional antennas substantially improved dynamic measurement range and coverage distance over low-gain omnidirectional antennas, which require much greater transmit power for the same range.Source: §V · p. 7