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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 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.

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

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,

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 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. It is a public, unlicensed area of the electromagnetic spectrum that is utilized for 802.11b WLAN operation. In other words, we will be using the unlicensed 2.4 GHz band for our wireless network exampless.

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.

The advent of using multiple antennas and multiple radios in wireless routers and access points ushered in the MIMO (Multi-In Multi-Out) architectures that is widely utilized currently. The use of MIMO plus two radio frequencies is basicly the scheme of the IEEE 802.11n specification. All the radio theory in this article still applies.

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:

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

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

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

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:

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 recived 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:

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

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)

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.

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.

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.

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.

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.

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.

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.

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.

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:

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

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 P_out = 10 dBm, which is a power of 10 milliwatts.

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:

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:

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.

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 +

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.

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 WiFi systems are not formally designed with Si or SOM analyses, but rather WiFi 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.