Home and Office Wireless Networking

Authored by Ron Vigneri Rev: 8-26-13

Note: This material is applicable to any wireless technology including:  radio, television, cellular telephone, radar, etc. Someone adding this knowledge to his skill set is a good employment candidate for wireless computer networking and cellular telephony companies.

The Physics of Wireless Networking

The standard for wireless LANs (WLANs) was completed in 1997 with the release of the IEEE 802.11 specification which became the first major step in the development of wireless network technologies. The spread of the technology is similar to that of cellular telephone. Wireless technology is one the hottest items in networking for the home, office, and even wide area (WAN) applications like high speed Internet access. This is the case with the recent broadband
wireless deployments by AT&T, Verizon, Sprint, and others. The latest IEEE 802.11ac specification has not been finalized, but equipment is now in the marketplace (2013). This article has been updated to include an 802.11ac discussion. All the radio physics presented in this article apply to 802.11b/g/a/n/ac technology.

Let’s see what the physics behind the wireless technology involves in this article.

Radio Wave Physics

A radio wave is an electromagnetic wave that can propagate (travel) through air, water, walls, some objects, and the vacuum of outer space. The wave is comprised of an electric field and an associated magnetic field at right angles to each other. Both these fields can vary periodically in amplitude and frequency. The fields vary perpendicularly to the direction of propagation of the radio wave. The fields, and hence, the radio wave can be generated by applying an alternating current (or voltage) to a dipole antenna. The frequency of the alternating current for our study will be considered to be 2.4 gigahertz (2.4 GHZ).

So, electromagnetic waves consist of the propagation of oscillating electric field and magnetic field components shown in the following diagram. Note that as the radio wave propagates (radiates) out from the dipole antenna source we considered, it will decrease in amplitude (the “height” of the fields in the diagram) as it travels farther from the source.



In the above illustration, the frequency of the electromagnetic wave can be determined from the time period (T). The time period between the start and end of one cycle of the waveform is the wave period, T. The frequency of an electromagnetic wave is related to the period by the formula,

                                                                                    f = 1/T

            where  f = frequency in Hertz

                        T = time period in seconds

From that relationship, the period for a wave with a frequency of 2.4 GHz is 0.4166 nanoseconds (billionths of a second) and that is “pretty fast”.

From famous physicists, Maxwell and Hertz, the frequency and wavelength of an electromagnetic wave are related to the velocity of light by the equation

                                                Frequency (f) x Wavelength (l) = Velocity of Light (c)

Which can be expressed as

                                                            f  x  l = c = 3 x 108 meters per second

where  f = frequency in Hertz

            l =  wavelength in meters

            c = 3 x 108 meters per second (E = exponent, here 10 raised to the 8th power)

Frequency is measured in cycles per second, which has been named a Hertz and is abbreviated as Hz. A gigahertz would be one billion Hertz, represented by 1 GHz, with G meaning giga or 109. The frequency of 2.4 GHz, utilized in the IEEE 802.11b standard, has a wavelength of  0.125 meters, or 12.5 centimeters or about 4.92 inches. The wavelength of an IEEE 802.11a standard frequency of 5.8 GHz would be about 2.46 inches.

The Federal Communications Commission (FCC) regulates the frequency assignments for use in the United States. The 2.4 GHz frequency band from 2.4000   to 2.4835 GHz is a band that can utilized without an FCC license. Also, segments of the 5 GHz frequency band from 5.170 to 5.835 GHz can be utilized without an FCC license. It is a public, unlicensed area of the electromagnetic spectrum that is utilized for WLAN operation. For simplicity, and hpoefully clarity, we will be using the unlicensed 2.4 GHz band for our wireless network examples.

IEEE Spec.

Frequency, GHz

Data Rate, Mbps

















2.4, 5




2.4, 5



Table 1 IEEE Wireless Specifications

The following table shows the US frequency bands for the 802.11 2.4GHz assignments. Note that only three channels do not overlap in frequency. That is why the preferred channels for use in the US are: Channels 1, 6 and 11. A very confusing aspect is the fact that a single channel Wi-Fi signal actually electromagnetically spreads over five channels
in the 2.4 GHz band resulting in only three non-overlapped channels in the U.S. The 2.4000-2.4835 GHz band is divided into 13 channels each of width 22 MHz but spaced only 5 MHz apart, with channel 1 centered at 2412 MHz. The WiFi channel width is +/-11 MHz from the center frequency.

Channel No.

Frequency, MHz




No spectrum overlap















No spectrum overlap















No spectrum overlap

Table 2 2.4 GHz Channel Center Frequencies

The 802.11ac Gigabit Wi-Fi specification supports larger channels at 80 MHz and 160 MHz widths instead of 20 MHz. This yields increased peak performance and bandwidth for wireless APs and clients. Planning of channel assignment and widths on APs and the channel plan for a WLAN deployments must be made prior to deployment. The full 802.11ac topic is beyond the scope of this article, but the basic radio parameters are presented because the future of wireless systems lies within this complicated technology. The Addendum presents a discussion of the IEEE 802.11ac specification.

Radio Frequency (RF) Power

A typical radio system will consist of a transmitter with a transmitting antenna sending radio waves through some media to a receiving antenna connected to a receiver. The radio system transmits information (data packets within a radio frequency modulation scheme) to the transmitter. The RF signal containing the data packets is transmitted through an antenna which converts the signal into an electromagnetic wave. The transmission medium through which the electromagnetic wave propagates is free space. The electromagnetic wave is intercepted by the receiving antenna which converts it back to an RF signal that is the same as the transmitted RF signal. The received RF signal is then demodulated by the receiver to yield the original information.

Because of the wide range of power levels in RF signals, the measurement of power is expressed in decibels (dB) rather than the Watt as the electrical unit of power. For analyzing a radio system, the dBm convention is more convenient than the Watts convention. The RF power level can be expressed in dBm (the subscript “m” meaning the
power is expressed in milliwatts) using the relation between dBm and Watts as follows:                                         

PdBm = 10 x Log Pmw

where PdBm = power in decibels

            Pmw  = power in milliwatts

Some examples are: 1 Watt = 1000 mW;    PdBm = 10 x Log 1000 = 30 dBm
                                                500 mW;    PdBm = 10 x Log 500   = 27 dBm

                                                100 mW;    PdBm = 10 x Log 100  = 20 dBm

                                                  50 mW;    PdBm = 10 x Log 50   = 17 dBm

                                                  30 mW;    PdBm = 10 x Log 30   = 14.8 dBm

                                                  15 mW;    PdBm = 10 x Log 15   = 11.8 dBm

Please note that whenever the power is halved that the dBm value decreases by 3 dBm. This type of number is a logarithm, which is the exponent expressing the power to which a fixed base number must be raised to produce a given number. We are using a base of 10 for our logarithms.

Note: Refer to a Logarithm Table.

Signal Attenuation

An RF signal will fade (decrease in or lose power) as it propagates through any medium or media. The media could consist of two layers of sheetrock plus fiberglass insulation and wood framing through which an RF signal propagates, for example, going from one antenna to another. This attenuation (fading) is expressed in decibels which are not specifically referenced to milliwatts. The units of power only need be expressed in the same units in the relation

                                                            PdB = -10 x Log (Pout/Pin)

where Pin = the incident power level at the input of the attenuating media

            Pout = the output power level at the output of the attenuating media

            PdB = the attenuation loss expressed in decibels (dB)

A diagram for attenuation is shown below.


For example: If half the power is lost due to attenuation (Pout/Pin = ½), the attenuation in dB is -10 x Log (½) = -3 dB

Path Loss

The Path Loss is the power loss of an RF signal traveling (propagating) through space or obstructions. It is expressed in dB and depends upon:

The distance between the transmitting and receiving antennas (or access points)

        • The Line of Sight clearance distance between the receiving and transmitting antennas (or access points)
        • The height of the antenna or access point
        • The loss in passing through walls or objects between antennas or access points.

Using the loss value for a sheetrock wall (listed in a the table presented later in this lesson) the path loss would be:

Path Loss = Pl = 5 dB

We will use the path losses in the analysis of received RF signal strength in following sections of this lesson.

Free Space Loss

The Free Space Loss is an attenuation of the electromagnetic wave while propagating through space. We will consider the loss to be the same in air as in the vacuum of space. It is calculated using the following formula:

                                    Free Space Loss = 32.4 + 20 x Log(FMHz) + 20 x Log(RKm)

where FMHz = the RF frequency expressed in MHz = 2,400 MHz for 802.11b systems

            RKm = the distance in Kilometers between the transmitting and receiving antennas

The formula at 2.4 Ghz is:  Free Space Loss = 100 + 20 x Log(RKm)

In the following figure, The distance (D) can be expressed in kilometers or miles, as we will discuss later in this section and consider the conversion factors between kilometers and miles.


The Free Space Loss is not usually a factor in the home and office wireless network, but can be a factor in linking separate buildings, and definitely should be included in a discussion of wireless link parameters. To calculate the loss in units of miles and megahertz, the equation becomes:

Free Space Loss = 36.6 + 20Log10(Frequency in MHz) + 20Log10 (Distance in Miles)

Antenna Characteristics

Isotropic Antenna

An Isotropic Antenna is an idealized, theoretical antenna having equal radiation intensity in all directions. The Isotropic Antenna is used as a zero dB gain reference in antenna gain (directivity) calculation.

Antenna Gain

The Antenna Gain is actually a measure of directivity and is defined as the ratio of the radiation intensity (power) in a given direction to the radiation intensity that would be obtained in the same direction from an Isotropic Antenna. Antenna Gain is expressed in dBi (in other words, it is referenced to an isotropic radiator). Some of the considerations
in placing (mounting) antennas include down-tilt angle (if any), beamwidth and aiming, and polarization. Most home and office antenna mountings align the antenna with no down-tilt, especially if it is an omni-directional antenna. Directional antennas may be mounted with down or up-tilts depending upon the area of coverage desired in a high or multi-floor level building. A diagram illustrating antenna tilt geometery follows.


The antenna in the above diagram has an axis that aligns with the electric field vector of the RF signal, which is usually set in a vertical plane (aligns with gravity vector at any point on the planet). In some point-to-point wireless network designs, pairs of antennas may be rotated 90 degrees so that the electric field variation is in the horizontal plane. The
plane in which the electric field variation (vector) aligns is known as the plane of polarization. So the antenna polarization can be vertical or horizontal. If multiple wireless networks are operating near one another, even on separate channels, interference can sometimes be eliminated by changing the polarity of one set of network antennas. Signal interference from many sources (including 2.4 GHz microwave ovens) can sometimes be eliminated by a change in antenna polarization, as well as physical location.

Another consideration in down-tilt antenna mounting is reflecting off surfaces that the main lobe contacts. In a home or office with walls, ceilings, and floors to bounce (reflect) the RF signal, aiming is important. Try to minimize the reflections by keeping the angle of incidence as perpendicular (normal) to surfaces as possible. Low angles of incidence cause more trouble than normal incidence for RF signals.

These considerations are very important when designing outdoor RF signal links where distances of  miles between
antennas exist. Even in modest home and office link distances, these geometries should be considered. The following diagram presents a tilted antenna configuration.


Radiation Pattern

A Radiation Pattern is the spatial energy distribution of an antenna. The spatial distribution can be shown in rectangular or polar coordinates. The spatial distribution of a practical antenna exhibits main lobes or lobe, and side lobes. The antenna manufacturer will specify the radiation pattern for an antenna. The following illustration shows the main lobe containing most of the RF signal power (energy), and side lobes containing less RF signal power. The RF

signal power radiates outward from the antenna in all the lobes. This spreads the energy in the RF signal ever wider which means that a receiving antenna farther away from the transmitting antenna will receive a lower RF signal power level than a closer located receiving antenna.

Side Lobes

Radiation lobes in directions other than that of a main lobe(s) are known as Side Lobes. The antenna manufacturer will specify the radiation pattern for an antenna. See the previous illustration. Side lobes can transmit enough RF signal power to allow connection between other antennas.

Omni-directional Antenna

An Omnidirectional Antenna radiates and receives equally in all directions within a “pancake” shaped volume (spatial
distribution). The antenna manufacturer will specify the radiation pattern for an antenna. See the following illustration.



Directional Antenna

The radiation pattern of a Directional Antenna is predominantly in one direction. The antenna still has side lobes, but the main lobe contains most of the radiated and received power.  The antenna manufacturer will specify the radiation pattern for an antenna. Refer to the previous Antenna Radiation Power diagram as an example of a directional antenna radiation pattern.

Antenna Beamwidth

The Antenna Beamwidth is defined as the RF Power included angle of a directional antenna. The definition is the angle between two half-power (-3 dB) points on either side of the main radiation lobe. The antenna manufacturer will specify the radiation pattern for an antenna.  Refer to the previous illustrations.

System Characteristics

Receiver Sensitivity (Ps)

The receiver sensitivity is the minimum RF signal power level required at the input of the receiver for satisfactory system performance. This parameter is usually specified by the radio equipment manufacturer. Ps in dBm is the receiver sensitivity.

Effective Isotropic Radiated Power (EIRP)

The EIRP is the antenna transmitted power, which equals the RF signal output power minus antenna cable loss plus the transmitting antenna gain. The equation is:

                                    EIRP = Pout – Ct + Gt

where Pout  = transmitted output RF power to antenna in dBm

            Ct = transmitter cable attenuation in dB

            Gt = transmitting antenna gain in dBi


Effective Received RF Signal Power  (Si)

The effective received signal power can be calculated using the following equation:

                                    Si = EIRP – Pl + Gr –Cr = Pout – Ct + Gt – Pl + Gr – Cr

where Pl = Path loss in dB

            Gr = receiving antenna gain in dBi

            Cr = receiver cable attenuation in dB

Example:  Wireless System Link Analysis

            Frequency = 2.4 GHz

            Pout = 4 dBm (2.5 mW)

Tx and Rx cable loss for 10 meter cable type RG214 (0.6 dB/meter)

            Ct = Cr = 6 dB

Tx and Rx antenna gain

            Gt = Gr = 18 dBi

Distance between antennas RKm = 3 Km

            Pl = 100 + 20 x Log(RKm) = 110 dB

Receiver sensitivity  Ps = -84 dBm


                        EIRP = Pout – Ct + Gt = 16 dBm

                        Si = EIRP + Gr – Cr = 16 – (110) =  -82 dBm

Analysis of the above result: The received signal power (Si) is above the sensitivity threshold of the receiver (Ps), so the link should work. However, Si should be at least 10 dB higher than Ps. In this case, the signal is only 2 dB higher and we really should consider another loss factor, Signal Fading. A better system solution would be to increase the
transmit RF signal power to Pout = 10 dBm, which is a power of 10 milliwatts.

Signal Fading

RF signal fading is caused by several factors including: Multipath Reception, Line of Sight Interference, Fresnel Zone Interference, RF Interference, Weather Conditions.

Multipath Reception – The transmitted signal arrives at the receiver from different directions, with different path lengths, attenuation, and delays. An RF reflective surface, like a cement surface or roof surfaces, can yield multiple paths between antennas. The higher the antenna mount position is from such surfaces, the lower the multiple path losses. The radio equipment in the 802.11 specifications utilizes modulation schemes and reception methods such that multiple path problems are minimized.

Line of Sight Interference – A clear, straight line of sight between the system antennas is absolutely required for a
proper RF link for long distances outdoors. A clear line of sight exists if an unobstructed view of one antenna from the other antenna. A radio wave clear line of sight exists if a defined area around the optical line of sight is also clear of obstacles. Remember that the electric and magnetic fields are perpendicular to the direction of propagation of the RF wave. In setting up wireless networks in buildings, propogation of the RF signal through walls and other items is a fact of life. If you recall the signal attenuation discussion earlier, we can evaluate the related losses. A following table presents loss values for typical items through which we want our networks to transmit and receive.

Fresnel Zone Interference – The Fresnel (FRA-nel) Zone is a circular area perpendicular to and centered on the line of sight. In radio wave theory, if 80% of the first Fresnel Zone is clear of obstacles, the wave propagation loss is equivalent to that of free space.

The equation for calculating the first Fresnel Zone utilizes distances to a point in the line of sight with a possible obstruction in the path is:

                        FZ =  72.1 x sq. root (D1 x D2 / x Rm)

where   f = frequency in GHz

                        Rm = distance between antennas in miles

                        D1  =  first distance to obstruction in miles

                        D2  =  second distance to obstruction in miles = Rm – D1

                        FZ  =  radius of Fresnel Zone in feet from direct line of sight

We will calculate a Freznel Zone radius later in this discussion.  In the home and office network in a building, the Fresnel Zone calculation is usually unnecessary because of all the wall/ceiling/floor pass- through considerations for
any RF signal path. But in outside RF signal paths (links), the Fresnel Zone calculations can be very important from quarter mile distances and longer.

My experience with tall loblolly pines on a project is a good case in point. A wireless link was designed and setup for two medical facilities (two-story structures) in Wilmington, NC that were located 0.5 and 0.75 miles from an eleven story hospital. There was no direct line of sight between the two medical facilities, but there was from both buildings to the hospital roof. After securing proper approvals, an RF signal link was setup from each building antenna to hospital roof-mounted antennas. Even though there was a good visual path from one building to the hospital roof, some very tall, very scrawny loblolly pines were infringing into the Fresnel Zone radius that was calculated for the link. It was just a few branches with the wide-spaced loblolly needles, but we had to top the trees to obtain a satisfactory signal-to-noise ratio for dependable communication. It is amazing how much microwave (2.4 GHz) energy those long needles absorbed,
reflected, deflected, and/or scattered.

In the earlier wireless link analysis example using the 3 Km distance between antennas and assuming a mid-path constriction (D1 = D2), the Fresnel Zone is calculated as follows using common conversion factors for US standard measurements.                        

Convert 3 Km to miles by dividing by a conversion factor of 1.6 kilometers per mile, which yields using f = 2.4 GHz:

Rm = 3Km / 1.6Km/mile = 1.88 miles

D1 = D2 = 0.94 mile

FZ = 31.9 feet

The 80% Freznel Zone radius for Free Space Loss equivalence would be obtained by multiplying FZ by 0.8, which yields a radius of 25.5 feet. So the clear path concentric cylinder around your systems line of sight for the distances and
frequency analyzed would be 51 feet in diameter at the middle of the RF link.

System Operating Margin (SOM)

SOM (System Operating Margin), also known as fade margin, is the difference of the receiver signal level in dBm minus the receiver sensitivity in dBm. It is a measure of the safety margin in a radio link. A higher SOM means a more reliable over the air connection. We recommend a minimum of 10 dB, but 20 dB or more is the best.

SOM is the difference between the signal a radio is actually receiving vs. what it needs for good data recovery (i.e. receiver sensitivity). By using the transmit and receive RF signal power, the cable losses, the antenna gains, and the free space losses as considered in this lesson, we can calculate the SOM. Thus we have a method for designing and
analyzing RF signal links used in wireless networking.

Rx Signal Level = Tx Power - Tx Cable Loss + Tx Antenna Gain – Free Space Loss + Rx Antenna Gain - Rx Cable Loss

System Operating Margin =
SOM = Rx Signal Level - Rx Sensitivity

We can modify the SOM expression to consider attenuation losses due to transmission through walls, etc., in an actual building wherein a home or office network would be installed. It is simply adding more loss terms to the SOM equation. But first we will have to consider the level of losses through various materials. The signal attenuation loss for 2.4 GHz transmission through the following structures can be included in the Rx Signal Level equation for each pass-through in the straight line signal path (line of sight). The dB loss values will be subtracted from the transmitted signal power to
reflect the loss of passing through the material structures.


Clear Glass Window 
Brick Wall  
Brick Wall next to a Metal Door 
Cinder Block Wall  
Sheetrock/Wood Frame Wall 
Sheetrock/Metal Framed Wall    
Metal Frame Clear Glass Wall  
Metal Screend Clear Glass Window
Metal Door in Office Wall
Wired-Glass Window
Metal Door in Brick Wall 

Table 5 Absorption Loss Approximations

The loss for each structure passed through should be included in the calculations of Rx Signal Level and SOM. The minimum SOM suggested is 10 dB, but a 20 dB margin should be used in all designs as the real world losses are almost always higher than the theoretical.


Using the contents of this lesson any wireless network can be designed or analyzed. All of the content of this article was presented to lead up to the ability to understand and apply all the factors that comprise a wireless network's Effective Recieved RF Signal Power (Si) and the System Operating Margin (SOM). These two parameters are central to the design, analysis, installation, and operation of any wireless network.

That said, most wireless systems are not formally designed with Si or SOM analyses, but rather wireless components are selected from available products in a price range of interest. The system is then configured, installed and tested. Sometimes it works satisfactorily and sometimes not. If not, the above radio physics topics can be utilized to analyze the problem.


ADDDENDUM: IEEE 802.11ac Wi-Fi Discussion

The 802.11ac Gigabit Wi-Fi specification supports larger channels at 80 MHz and 160 MHz widths instead of 20 MHz. This yields increased peak performance and bandwidth for wireless APs and clients. Planning of channel assignment and widths on APs and the channel plan for a WLAN deployments must be made prior to deployment. The full 802.11ac topic is beyond the scope of this article, but the basic radio parameters are presented because the future of wireless systems lies within this complicated technology. This Addendum presents a discussion of the IEEE 802.11ac specification.

The standard method to denote 5 GHz channels has been to always use the 20 MHz center channel frequencies for both 20 MHz and 40 MHz wide channels. Starting with 802.11n, 40 MHz channels were referenced as the primary 20 MHz channel plus an extension channel either above or below the primary channel. An example would be a 40 MHz channel consisting of channel 36 (primary) + 40 (extension above).

802.11ac allows larger channel widths. Instead of continuing to reference the 20 MHz extension channel(s), the reference is the center channel frequency for the entire 20, 40, 80 or 160 MHz wide channel.

The valid channel numbers for various channel widths are:

Channel Width
Valid Channel Numbers
20 MHz 36, 40, 44, 48, 52, 56, 60, 64, 100, 104, 108, 112, 116,
120, 124, 128, 132, 136, 140, 144, 149, 153, 161, 165, 169
40 MHz 38, 46, 54, 62, 102, 110, 118, 126, 134, 142, 151, 159
80 MHz 42, 58, 106, 122, 138, 155
160 MHz 50, 114

Table 3 5 GHz Channel Frequencies

Channel numbers increment by one for every 5 MHz increase in frequency. This will probably be easier to reference through the following graphic. In the graphic below, identify the center of each 80 MHz and 160 MHz channel block, follow it up to the 20 MHz IEEE channel numbers, then split the difference between the two 20 MHz channel numbers that it falls between. For example, the 80 MHz channel block is centered between channels 40 and 44; splitting the difference gives us channel 42. The center frequency is calulated in MHz as 5 MHz bandwidth multipled by the channel number added to 5000 MHz.

Figure 1 Unlicensed 5 GHz Band Channels

We will restrict our consideration to channels that are available 802.11ac devices at this time (indicated in the yellow
highlighted boxes in Figure 1. They are presented in the following table.

Channel No.
Center Frequency, MHz

Table 4 5 GHz Channel Center Frequencies

The advent of using multiple antennas, multiple streams, and multiple radios in wireless routers and access points ushered in by the MIMO (Multi-In Multi-Out) architectures that are in the IEEE 802.11n and 802.11ac specifications have significantly advanced the technology. All the radio theory in this article still applies to all the latest radio specifications. The 802.11ac specification presents a significant increase in performance capability by somewhat complicated means which yield greatly improved throughput rates over earlier specifications. Wireless devices should be configured with frequency selections that minimize possible interference. And mixing the types of devices will yield throughput speeds of the lowest level of device that is connected.


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