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Antenna Passive Repeaters For Indoor Recovery of Microwave Cellular Signals

September 17, 2008
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The use of passive repeaters for mobile communications is often discarded because of the inherent losses that these systems introduce. However, the radio signal coverage of indoor areas poses a particularly complex problem in buildings with heavily reinforced concrete walls and shielded or underground infrastructure, which introduce great attenuation. In these particular conditions, active or passive repeater systems can be implemented for recovering the indoor signal to the level of normal reception. In this article, the important potential upgrading of indoor signal coverage is theoretically demonstrated and experimentally proved by use of low-cost passive repeaters for the 900 MHz cellular band.

Assuring adequate signal coverage of indoor areas is an important problem for cellular systems in regions where buildings have high attenuation walls. Active repeaters are often used to solve the problem,1,2 but, in addition to their added cost, they need a power supply and maintenance. Also, the amplified signal has the potential of creating significant interference in those areas that are already covered by a direct signal of the same frequency channel.

In this article, the potential for field coverage improvement by means of antenna passive repeaters is explored, similar to those employed in the microwave radio relay links years ago for redirection of wave propagation over hilly terrain.3,4 In addition, a signal phase shifter is introduced to the traditional antenna passive repeater scheme, aimed at optimizing indoor signal distribution.5

A simplified theoretical study by the authors5 has shown that for wall attenuation less than 10 to 12 dB (a brick wall, single-mesh reinforced concrete wall, wooden wall, etc.), the signal enhancement due to a passive repeater with a medium gain antenna is moderate. Significant benefits can only be expected at limited ranges or by using high gain antennas at the expense of angular coverage. For the case of a high loss wall, however, with an attenuation larger than 20 to 25 dB, a considerable improvement in indoor signal coverage can be easily achieved.

Three exemplary schemes of building passive repeaters have been described initially. The classic one is a single-path, double-antenna repeater, for which the power-transfer equation was worked out. This scheme was implemented for cellular signal recovering in the underground parking sector of a corporate building. It consisted of two different antennas, donor and coverage, connected by a long coaxial cable. By means of this passive repeater the signal coming from a nearby cellular base station was raised by approximately 20 to 25 dB, and normal, low-cost cellular signal coverage was provided in a 70 m2 isolated parking area.

The second scheme is an on-wall twin-antenna passive repeater, which was studied theoretically and experimented in a laboratory indoor environment. It is comprised of two equal antennas, mounted outside and inside on a building exterior wall, and connected through a hole by a short piece of cable and a phase shifter in series. The average signal improvement obtained experimentally with the repeater in a multipath environment (a small furnished room, 4.6 by 2.6 m), ranges from 15 to 17 dB near the repeater to approximately 3 dB at a distance 4 m away.

Fig. 1 Passive repeaters schemes.

The third scheme is a variation of the first scheme, with the coverage antenna replaced by a distributed antenna array. For all of these schemes, the costs of active repeaters would be far higher. Passive repeaters cannot, of course, be expected to substitute in all cases for the need for active radio devices that cover larger areas and will radiate through windows and other low loss sections of the same area. However, passive repeaters can provide significant signal improvement, particularly when limited areas (hot spots) must be covered.


The passive repeater has two antennas, an outdoor antenna aimed at a donor base station and an indoor or coverage antenna, linked back to back by a cable through an exterior building wall or roof. It is a two-way transmitting device, but for the purpose of analysis it is assumed that the outdoor antenna is receiving and the indoor antenna is transmitting.

As shown in Figure 1, there are three possible passive repeater schemes. Scheme 1 has an elevated outdoor high- or medium-gain omni-directional antenna A1 (roof-top mounted, for instance), an indoor wall-mounted coverage antenna B1 and a cable C1. S is a transmitting base station antenna and M is the point where the fixed or mobile wireless unit is located. The power received by the outdoor antenna A1 is transferred to the coverage antenna B1, which in turn radiates into the building’s inner space. This repeater scheme would be appropriate for mobile cellular links.

Fig. 2 Passive repeaters scheme 26.

In Scheme 2, both antennas, the outdoor antenna A2 and the coverage antenna B2, are set on a building wall and are connected by a short piece of coaxial cable C2.5 For instance, the antennas can be printed patches over ground plates, which, in combination with the lossy wall, will ensure very high electromagnetic isolation between them. This scheme is intended for repeating signals from only one or several base stations located in the small-angle of visibility of the outer antenna A2. The advantage of this scheme is its compactness and high transfer efficiency, owing to minimal cable losses. An illustration of Scheme 26 is shown in Figure 2. It was prepared in accordance with a two-ray tracing model.7

Scheme 3 (A3 – C3 – B3(1) B3(2)…, B3(n)) differs from the first one in the coverage antenna design only. It is not a single antenna, but an array of n on-wall antennas, connected in parallel (or in series) to an indoor coaxial feed cable circuit C3. The distributed coverage antenna array can produce better signal delivery in large indoor areas.


In this section, the analysis is limited to the simplest, single-path repeater scheme (Scheme 1). Here, the indoor rays, transmitted through or reflected by building walls, are neglected. The power PM received by the mobile unit antenna at point M as a function of the coordinate angles φ and θ is given by the modified Friis line-on-sight equation applied to the paths s and r via the passive repeater.5


    P = power radiated by the base station antenna S
    λ = free-space wavelength
    GsAA) = base station antenna gain in the direction of the outdoor antenna A1
    GA = gain of the antenna A1, with the main lobe looking at the base station antenna
    GB (Φ,θ) = gain radiation patterns of the coverage antenna
    GM(Φ,θ) = gain radiation patterns of the mobile unit antenna
    ηc = total cable efficiency


Fig. 3 Two-ray geometry of an on-wall passive repeater in the horizontal plane.

Figure 3 shows the double-ray geometry of a cellular link between the base station S and indoor mobile telephone M (Scheme 2). A plane wave radiated by the base station antenna illuminates the building wall under the azimuth angle Φi. The elevation incidence angle Φi is set to zero. The direct ray crosses the wall through the path S-W-M and the repeater ray goes along the path S-A-B-M. The wall is considered a lossy homogenous plate with a thickness d, relative permittivity εr and conductivity σ. For simplicity, the indoor site is assumed to produce negligible multipath effects. The electric and magnetic field vectors, and the power propagation vector of the incident wave are labeled by respectively. If is parallel to the wall and perpendicular to the plane of propagation (the horizontal plane in the figure), the wave polarization is specified as vertical (v), or . In the case of horizontal (h) polarization, is parallel to the wall and is parallel to horizontal plane.

The electric field E1(v,h) at point M, resulting from the wave passing directly through the building wall, can be expressed as a product of the free-space wave EM and transmission (refraction) coefficient Tw(v,h)i), or

where Tw(v,h)i) = |Tw(v,h)i)|exp (jΨw(v,h)i)) is a complex function with a magnitude |Tw(v,h)i)| and phase angle Ψw(v,h)i). The upper indexes (v, h) refer to the vertical or horizontal polarizations, respectively. The through-wall attenuation is also defined as Aw(v,h)i) = 1/|Tw(v,h)i)|.2

For a given frequency, wall thickness d, permittivity εr and conductivity σ, the complex transmission coefficient Tw(v,h)i) and the attenuation (loss) Aw(v,h)i) are easily calculated by use of the equations for a lossy dielectric plate.4

The field at each indoor point M is found as a vector sum of the field 1(v,h) and the field 2 radiated by the inside antenna B, that is, in this simplified analysis it is assumed that the space behind the wall is not bounded, or that in the case of a bounded space the secondary waves reflected and transmitted by the other building walls and indoor objects are negligible.

Depending on the wave polarization the total field is written as

for vertical polarization, and

for horizontal polarization.

The analysis that follows is for vertical polarization only; the case of horizontal polarization can be treated in a similar manner. By use of Equation 3, the total field E ≡ E(v) can then be easily expressed as

where , with GSi) being the gain pattern of the base station antenna in the direction of the passive repeater; Ψ1 = β0r' - Ψwi) and Ψ2 = β0s + √εrcd + r) - ΨΦ are the phase-shift angles, corresponding to the direct field E1 and repeater field E2; ΨΦ is the phase angle, introduced by the repeater phase shifter; , (εrc is the relative permittivity of the cable dielectric) and r' = r0/cosφi; and Arep is the total attenuation (loss) factor, which includes the antenna, cable and mismatch loss.

The repeater recovering efficiency or gain as a power ratio g is defined at the receiver point M, which gives the local power density increase (or decrease) due to the passive repeater

If the transmitter and receiver points S and M are at positions normal to the repeater, that is if Φi = Φ = 0, then bearing in mind that s >> r0 and r = r0, Equation 6 becomes the following simple equation:



can be considered as a repeater quality factor.

For the case of real antenna impedances and low mismatch, the phase-delay angle is equal to . As Q is always a positive quantity, it is evident from Equation 8 that the maximum value of the recovering efficiency g is obtained from Ψ = 0, or for

and is given by the following simple expression:

For a specific building wall, the passive repeater can be tuned for maximum power at the receiver. The repeater delay angle Ψrep is easily calculated. For a known wall structure and electrical parameters, the transmission phase angle Ψw is also computable. Thus, according to Equation 10, the phase-shifter angle can be set to the optimum value of ΨΦ. If, however, the wall is not specified, the optimum value of ΨΦ can be found only by indoor field trials. Also, in typical practical cases, the multipath propagation will result in a much more complex interference environment making optimum angle prediction very difficult, as will be illustrated by an empirical study.


To provide numerical examples for the improvement in signal coverage that can be expected in real situations, the recovering efficiency for three specific walls of thickness d = 0.28 m and an infinite extent were calculated and compared. It was assumed that each wall can be modeled with an acceptable accuracy as a homogeneous structure with an effective relative permittivity εr and conductivity σ. The following types of walls were assumed: a brick wall, a doubly-reinforced concrete wall with two steel meshes,8 and an extremely-lossy or shielded wall. The incident wave is assumed to be vertically polarized.

Tables 1 and 2 show the measured wall parameters εr and σ,8,9 and the computed values of Aw and Ψw for a normal wave incidence (Φi) are given for the three types of walls. The shielded wall electrical parameters and transmission loss values are assumed equal for both frequencies.

Figure 4 illustrates the calculated recovering efficiency g in the area behind a large brick wall versus the normal distance r0 for φI = φ = 0 (normal wave incidence) and different values of the extra phase shift ΨΦ. Figure 5 illustrates the same relations for a concrete wall. In both figures, the recovering efficiency graphs g(r0) are calculated for two cellular frequencies: 0.9 and 1.8 GHz. The efficiency graphs correspond to the phase shifters tuned for maximum (gmax) and minimum (gmin) recovering efficiency.

It is concluded that, for the brick wall, the passive repeater is effectively tuned by the phase shifter, but its potential for signal improvement is moderate and reduces with the distance from the wall. The recovering efficiency can be further increased only by use of more directive antennas (A and/or B). In contrast, in the case of a double steel-mesh concrete wall, the potential recovering efficiency is much higher for a significant range of distances.

Fig. 4 Recovering efficiency vs. normal distance from coverage antenna for a brick wall.

The worst-case curves suggest that a proper choice of ΨΦ is again very important. It must be stressed, however, that these figures refer only to the situation at a specific angular position and that usually the goal is improvement of area coverage. As will be discussed later, the empirical results show that in a practical case, with significant multipath propagation, the average improvement over an area is little affected by the choice of phase shift. This is due to the fact that the phase shift basically changes the position of the regions of constructive and destructive interference, not their size.

Fig. 5 Recovering efficiency vs. normal distance from inside antenna B for a reinforced concrete wall.

The recovering efficiency as a function of the offset distance y of point M is illustrated in Figure 6 for the double steel-mesh reinforced concrete and for the shielded wall. The distance r0, measured from the receiver point M to the passive repeater antenna B, is kept constant (r0 = 2 m). The recovering efficiency is approximately 10 dB for the reinforced wall, while the shielded wall has much higher values: 45 dB for y = 0 m and larger than 25 dB in the range of y = ±10 m. For the latter case, the direct (through-wall) signal is practically zero, and naturally the phase shifter becomes superfluous.

Fig. 6 Power gain vs. offset distance.

Complex conditions, such as the effect of multiple arriving wave fronts and reflecting objects, which are difficult to analyze theoretically and which will vary with position inside a room, are best treated through an empirical study to collect statistically relevant data. The procedures described as follows concentrate on this aspect, providing the results of a real implementation and its comparison with the simplified theoretical model.

A passive repeater illuminating a small room is sketched in Figure 7. Shown are the horizontal room layout and the repeater ray-interference scheme at the receiver point M (direct or transmission ray r', repeater ray r and three reflected rays: r1, r2 and r3). The room is 2.6 m wide, 4.6 m long and 3.5 m high and comprises an exterior brick and mortar wall with a metal door D1 and partition walls with doors D2, D3 and D4. The ceiling and the floor are made of reinforced concrete. S1, S2 and S3 are metal stands, 1.8 m (height) × 1.20 m × 0.50 m each. The passive repeater device under examination consisted of two equal or “twin” plane-reflector antennas A and B with vertical polarization, each 21 × 21 × 5 cm, a nominal gain of 8 dB at 0.9 GHz, VSWR = 1.5 and a horizontal-plane beam width of 80°. The repeater twin antennas were mounted on the metal door, at a height of 1.6 m above the floor. In order to increase the through-wall attenuation, simulating a very high loss wall, the outer side of the wall was loosely covered (shielded) by an anti-mosquito metal mesh.

Fig. 7 Passive repeater illuminating a small room; horizontal plane layout.

The power gain associated with the use of the passive repeater was determined for the case of a continuous wave signal. The procedure involved first measuring the received power in the chosen indoor area, under normal conditions, that is when the passive repeater was switched-off. This was done over a wide range of positions in the room according to a square measurement grid of a size equal to one wavelength. Both the transmitter antenna and receiver antenna were held at the repeater’s height. The transmitter antenna was placed outdoors at a distance much larger than the far-field extent from the shielded wall.

Fig. 8 Measured received power with repeater switched off and angle of incidence φi=0.

An element of uncertainty in any real situation is the angle of arrival of the outside signal with respect to the bore sight of the receiving antenna. Any practical repeater for cellular telephony would be expected to cover a wide azimuth range, as the base station position serving a call is not usually known. That is why the measurements included positioning the transmitter antenna to “see” the passive repeater from several different angles Φi ranging between 0° and 60°, in increments of 10°. Because the antennas have relatively low directivity, there exists a potential for significant multipath signal propagation, a condition representative of an urban environment. The measured values without the repeater were contrasted with the theoretical free space received power. This provides information on the combined effect of the wall obstructing the direct path, and the multipath interference due to the surrounding building elements and furniture. For each position inside the room, the corresponding value of received power with the repeater switched-on was subsequently measured. An extra phase shift, ΨΦ = 0°, 90°, 180° or 270°, was introduced by means of the phase shifter in order to test the influence of this parameter. For a quasi-plane wave incident on a large wall, in an environment devoid of multipath effects, the optimum phase shift can be evaluated numerically.

Fig. 9 Measured received power with repeater switched on with φi=0 and Ψφ=270°.

Figure 8 shows the distribution of the power received from the outdoor test transmitter as measured inside the room, when the passive repeater is switched-off. The indoor coverage antenna is placed at x = 0 and its bore sight direction is +x. On the average, the measured power level values vary from -90 to -110 dBm. Figure 9 shows the measured power in the same room, when the passive repeater is switched-on, with a phase-shifter tuned at ΨΦ = 270° and for a normal incidence of the outside wave. On average, 10 to 15 dB higher power levels are observed, with multipath fluctuations that are similar to those when the repeater is switched-off. Measurements performed for other values of the phase shift show similar results. As expected, it was observed that in the region where the repeater power dominates, the phase shift is of little consequence. In contrast, in the region where the repeater output is comparable to the signals entering through the walls, the diagram changes significantly.

The large amount of collected data, and the variations that are to be expected for these types of measurements, require the use of statistical processing of the data in order to be able to draw general conclusions. From the measured power data, the average recovering efficiency gave at a given distance from the repeater wall was calculated: gav(dB) = Pav (dBm) – P1,av (dBm).

Fig. 10 Average recovering efficiency vs. normal distance for an on-wall passive repeater.

The average empirical recovering efficiency curves as a function of distance from the repeater to the door D4 are drawn in Figure 10 for two values of the phase shift ΨΦ 90° (blue line, best case) and 180° (red line, worst case). As a reference, the green line in the same figure illustrates the theoretical function gr0 for the ideal case of a transmitter and receiver located on the axis of the repeater antenna beams. It was calculated, using Equation 6, for Aw = 28 dB, Arep = 1.3 dB, ΨΦ = 90° and GAmax = GBmax = 8 dBi. As can be seen, on average, the difference between best and worst case is not large, far less than the extreme conditions depicted previously. It is evident that the average signal recovering efficiency oscillates and decreases quickly with the distance, ranging from approximately 15 dB near the repeater, to approximately 3 dB at the far end of the room.


Encouraged by the laboratory results presented in the previous section, it was decided to use a passive repeater in a real setting. The corporate building of a cellular service provider had an interesting signal coverage problem that needed to be solved. The building had two levels of underground parking and a storage space. Due to space limitations in the building, the storage area of the lowest floor was considered for emergency use as a meeting room. An assessment of the received power levels was performed on the selected underground area (70 m2) using the TEMS CellPlanner Universal® instrument developed by Ericsson.10 The signal levels recorded in the selected area were approximately -105 to -115 dBm, as can be seen in Figure 11. Cellular coverage was desirable, but not available in that space without the use of some kind of repeater.

Fig. 11 Underground storage area where cellular coverage is provided by means of a passive repeater.

To make the repeater installation, an external 12 dBi gain Yagi antenna was positioned on a 7 m high terrace of the building and aimed at a line-of-sight, close-by base station. The level of received power, measured with the TEMS on the terrace near the Yagi antenna, was found to be approximately -61 dBm. The passive repeater 8 dBi gain coverage patch antenna was placed on one of the walls of the underground storage at a height of 1.65 m and was connected to the Yagi antenna by means of a 100 m long, 7.5 dB loss coaxial cable. As a result of the repeater installation, with a total antenna gain of 20 dB, and the inevitable effect of cable and mismatch losses, power levels of approximately -73 dBm were now observed near the interior patch antenna by means of the same measurement setup used on the terrace. At a distance of 10 m, the power level dropped to approximately -88 dBm, but was still adequate for a normal cellular call.

Fig. 12 Cellular coverage prior to installation of a passive repeater.

Comparing Figure 12 with Figure 13, it is seen that the use of passive repeaters in certain practical settings such as underground spaces, where propagation losses through walls are considerable, may be an attractive, cost-effective alternative for achieving a large signal improvement in reduced spaces.

Fig. 13 Cellular coverage after passive repeater installation.


The potential for improvement of indoor signal coverage by use of an on-wall passive repeater for the 900 MHz cellular band has been studied theoretically and demonstrated experimentally. A phase shifter, a novel element in passive repeating, was added and its impact on the indoor signal level and a distribution was studied. The numerical repeater link analysis and measurements confirmed that for the specific case of an 8 dB antenna repeater, illuminating a small building room with a high loss exterior wall and a realistic indoor environment, moderate signal recovering is achieved, ranging from 15 to 17 to approximately 3 dB depending on the distance from the repeater. Multipath propagation tends in practice to make the phase-shift choice uncritical when larger areas need to be covered, as improvements in certain small regions due to the choice of the proper phase shift are made at the expense of deterioration in other areas. It was observed that in the region where the repeater power dominates, the phase shift is of little consequence. In contrast, in the indoor areas where the repeater output was comparable to the signals entering through the walls, the field distribution changes considerably.

The passive repeating principle was then applied in an office building environment, where cellular coverage was practically non-existent in a specific region of interest, an underground storage and parking area. After checking that sufficient signal could be received with a directional antenna from a given base station to compensate for coaxial cable losses, the passive repeater system provided the necessary cellular coverage with low installation and maintenance costs. Although situations like the one described may not be frequent, the use of passive repeaters in underground subway and pedestrian walkways may be an interesting commercial application to exploit passive repeaters for mobile service providers.

While the analysis in this article stressed the improvement in signal coverage in an extended area (mobile situation), for the case of fixed-terminal communication systems the signal level can be further increased using more directive repeater antennas or antenna arrays that cover only certain angular positions.


The authors thank the Chilean National Science Agency CONICYT for the support received through the PBCT ACT-11/04 and UTFSM 23.07.21 projects. The experimental and data processing work completed by Danilo Torres, Carlos Báez and Francisco Mejías is greatly appreciated.


1. B.J. Leff, “Application Engineering Considerations for Cellular Repeaters,” 1989 Vehicular Technology Conference Digest, Vol. 2, pp. 532–534.

2. QUALCOM Engineering Group, “Repeaters for Indoor Coverage in CDMA Networks,” QUALCOM White Paper, 2003.

3. R.C. Johnson, Ed., Antenna Engineering Handbook, Third Edition, McGraw Hill, New York, NY, 1993.

4. H.D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas, Artech House Inc., Norwood, MA, 2000.

5. H.D. Hristov, R. Feick and W. Grote, “Improving Indoor Signal Coverage by Use of Through Wall Passive Repeaters,” 2001 IEEE International Antenna and Propagation Symposium Digest, Vol. 2, pp. 158–161.

6. “Passive Repeater Improves Indoor Coverage,” Wireless Europe, September 19, 2002, p. 16.

7. H.D. Hristov, D. Torres, R. Feick and W. Grote, “Passive Repeater for Mobile Signal Coverage of Lossy-wall Building Rooms,” 2002 International Wireless Design Conference Proceedings, pp. 165–168.

8. D. Peña, R. Feick, H.D. Hristov and W. Grote “Measurement and Modelling of Propagation Losses in Brick and Concrete Walls for the 900 MHz Band,” IEEE Transactions on Antennas and Propagation, Vol. 51, No. 1, January 2003, pp. 31–39.

9. C.F. Yang, C.J. Ko and B.C. Wu, “A Free Space Approach for Extracting the Equivalent Dielectric Constants of the Walls in Buildings,” 1996 IEEE International Antennas and Propagation Symposium Digest.

10. Ericsson, TEMS Cell Planner Universal, network_plan/cellplanner.shtml.

Hristo D. Hristov received his PhD degree in 1973 from Technical University (TU)-Varna and his DSc degree in 1987 from TU-Sofia, Bulgaria. He was with the department of radiotechnics at TU-Varna from 1965 to 2004, when he retired as a full professor. He is currently a research professor in the department of electronics engineering at the Universidad Técnica Federico Santa María, Valparaiso, Chile. His interests include high-frequency electromagnetism, antennas, radio propagation, quasi-optics, microwave and millimeter-wave devices, and wireless communications.

Walter Grote obtained his degree of ingeniero civil electrónico from the Universidad Técnica Federico Santa María, Valparaiso, Chile, in 1975, and his PhD degree in electrical engineering from Polytechnic University in 1992. He has been with the department of electronics engineering at the Universidad Técnica Federico Santa Maríía, Valparaiso, Chile, since 1974. His current interests include wireless access protocols, digital communications, microwave system design and RF measurements.

Rodolfo Feick received his ingeniero civil electrónico degree from the Universidad Técnica Federico Santa María, Valparaiso, Chile, in 1970, and his MSc and PhD degrees in electrical engineering from the University of Pittsburgh, Pittsburgh, PA, in 1972 and 1975, respectively. He has been with the department of electronics engineering, Universidad Técnica Federico Santa María, Valparaiso, Chile, since 1975, serving as head of the wireless communications group. His interests include wireless communications, microwave devices and systems, channel modeling and measurements, and communication antennas.

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