By Shreharsha Rao, Texas Instruments -- EDN, 5/24/2007

As home, building, and industrial-automation applications go wireless, short-range wireless devices are receiving a lot of attention. Typically, these applications use either proprietary or standards-based approaches, such as ZigBee in the 900-MHz and 2.4-GHz ISM (industrial/scientific/medical) bands.

With the increased popularity of short-range wireless devices, it’s more important than ever for end-system designers to fully understand the range of wireless communications.

This article discusses wireless propagation and develops models to estimate the path loss and range for short-range wireless devices in indoor environments. These models give system designers an initial estimate on a wireless-communication system’s performance.

Before exploring range-estimation formulas, designers need to understand the wireless channel and propagation environment. The wireless-radio channel is the transmission path between the transmitter and its intended receiver.

Unlike wired channels, which are stationary and predictable, wireless channels are random, time-variant, and difficult to model. So, designers need to use statistical modeling for these random channels.

Radio-wave-propagation models have traditionally focused on predicting the average received-signal strength at a given distance from the transmitter, as well as the signal’s strength variability in close proximity to a location. Propagation models that predict the mean signal strength for an arbitrary transmitter-receiver separation are large-scale propagation models and are useful in estimating the transmitter’s range.

Conversely, propagation models characterizing the rapid fluctuations of the received-signal strength over distances of a few wavelengths are small-scale, or fading, models. This article focuses on the large-scale propagation model, which estimates the range of wireless transmission.

The free-space-propagation model predicts the received signal’s strength when the transmitter and the receiver have a clear, unobstructed line-of-sight path between them.

The free-space model predicts that the received-signal strength “decays” as a function of the transmitter-receiver separation distance raised to the nth power—the “power-law” function. The free-space power that the receiver’s antenna receives is separated from a transmitting antenna by a distance, which the Friis free-space equation defines:

   (1)
 
where PT is the transmitted power; PR(d) is the received power and is a function of the transmit-receive separation, d; GT is the transmitter-antenna gain; GR is the receiver-antenna gain; d is the distance between the transmitter and the receiver in meters; and λ is the wavelength in meters.

The Friis free-space equation shows that the received power “falls off” as the square of the transmitter-to-receiver separation distance. This result suggests that the received power decays with distance at a rate of 20 dB/decade.

An important term in estimating the wireless-transmission range is path loss, which represents signal attenuation in decibels. Path loss is the difference in decibels between the transmitted power and the received power at the antenna. From Equation 1, you can deduce the path loss as the transmitted power divided by the received power. Equation 2 defines the path loss as:

  (2)
 
where PL is path loss. To simplify Equation 2, assume that both the transmitting and the receiving antennas have unity gain, and this assumption results in:

  (3)
 
You can also express this equation in the following usable form:

PL=20log10(fMHz+20log10(d)–28, (4)
 
or

PR=PT–PL,  (5)
 
where d is the distance in meters.

The Friis free-space formula can estimate the received-power level only for values of d that are in the transmitting antenna’s far field. The far field, Fraunhofer region, of a transmitting antenna is the region beyond the far-field distance, dF.

For an antenna, dF is 2D2/λ, where D is the antenna’s largest physical linear dimension. Also, dF must be greater than D and must be in the far-field region. This path-loss formula applies only to ideal systems with clear lines of sight, and you should use it only for initial estimates.

Propagation models use the close-in distance, d0, as the received-power reference point.

You must calculate the received power, PR(d), at any distance greater than the received-power reference point with reference to PR(d0), whose value you can predict from equation 1 and equation 4. Alternatively, you can measure it in the radio environment by taking average received power at many points from a close distance from the transmitter.

You must select the close-in reference distance so that the far-field region is greater than the close-in distance.

Using this information, you can calculate the received power at any distance using the following formula:

 (6)
 
The reference distance for practical systems operating at 1 to 2 GHz is 1m for indoor environments and 100m for outdoor environments.

Most RF power-level units are either in decibels referred to milliwatts or decibels referred to watts rather than absolute power levels. You can rearrange Equation 6 as:

 (7)
 
The following example explains these concepts. Assuming a transmitting frequency of 900 MHz, the transmit power of 6.3 mW (8 dBm), and the unity-gain transmitting and receiving antennas, determine the received power at 1200m distance in an outdoor-line-of-sight environment. For an outdoor environment, the reference distance is 100m, and you must determine the received power at 100m. The wavelength at 900 MHz is 0.33m.

Using the values in Equation 1, you obtain

 (8)
 
To calculate the power in decibels referred to milliwatts, you must express the power in milliwatts as:

PR(100)=0.44×10-6 mW.  (9)
 
Therefore,

PR(100)=10log(0.44×10-6mW)=–63.6 dBm.  (10)
 
Using Equation 7 to obtain the received power at 1200m yields:

 (11)
and

PR(1200)=–63.6 dBm–21.58 dB=–85 dBm.  (12)
 
Using Equation 5, you can verify the same value of received power.

Thus, for an ideal, unobstructed-outdoor-line-of-sight environment, the received power at a 1200m distance when the transmit power is 8 dBm is approximately –85 dBm. The actual received power will be lower because the real-world environment will likely have obstructions in the line-of-sight path or, worse, no line-of-sight path at all.

For the previous example, you calculate the path loss as PT–PR. Therefore, path loss is 8 dBm–(–85 dBm)=93 dB.

Practical path-loss formulas

For any practical wireless-sensor system, it’s important to know the maximum reliable data-transmission range. This wireless-system range directly depends on the link-budget parameter:

LB=PT+GT+GR–RS,  (13)
 
where LB is the link budget in decibels, PT is the transmitted power in decibels referred to milliwatts or watts, GT is the transmitter-antenna gain in decibels, GR is the receiver-antenna gain in decibels, and RS is the receiver sensitivity. Sensitivity is the minimum RF signal that the system can detect with an acceptable SNR (signal-to-noise ratio). Equation 14 shows the receiver sensitivity:

S=–174 dBm/Hz+NF+10logB+SNRMIN,  (14)
 
where –174 dBm/Hz is the thermal noise floor, NF is the overall-receiver-noise figure in decibels, B is the overall receiver bandwidth, and SNRMIN is the minimum SNR.

If the total path loss between the transmitter and the intended receiver is greater than the link budget, loss of data ensues, and communications cannot take place. Therefore, it’s important for designers developing end systems to accurately characterize the path loss and compare it with the link budget to obtain initial estimations of the range.

Path loss in indoor channels

The indoor-radio channel differs from the outdoor channel because the indoor channel has shorter distances to cover, higher path-loss variability, and, thus, greater variance in the received-signal power. However, variability in the received-signal power is negligible for stationary wireless devices. Building layout, type, and construction materials strongly affect indoor propagation.

Research classifies indoor channels as either line-of-sight or obstructed channels with varying degrees of clutter (Reference 1). A building’s internal and external structures have a wide variety of partitions and obstacles. Partitions depend on whether the structure is a home or an office environment.

Partitions in a building’s structure are hard partitions, and partitions that can move and do not span to the ceiling are soft partitions. Houses typically use wood-frame partitions, whereas office buildings use soft partitions with metal-reinforced concrete between floors.

Partitions vary widely in their physical and electrical characteristics, making it difficult to apply generic models for indoor channels. However, extensive investigations tabulate signal losses for common material types (Table 1). Floor-attenuation factors represent the partition loss between floors (Table 2). Equation 15 shows the practical path-loss model for indoor channels using the log-distance path-loss model:

 (15)
 
where X is a zero-mean gaussian random variable in decibels and σ is standard deviation. If the devices are stationary, you can ignore the effects of Xσ. Calculating the value of path loss at a distance of 1m using Equation 4 and plugging it into Equation 15 results in:

PL(d)=20log10(fMHz)+10nlog10(d)–28+Xσ.  (16)
 
The value of n does not vary much with frequency and depends on the surroundings and the building type (Table 3).

An in-building propagation model includes the effect of building type as well as obstructions. This model provides flexibility and can reduce the standard deviation between measured and predicted path loss to approximately 4 dB compared with 13 dB when you use only a log-distance model. Equation 17 represents the attenuation-factor model:

PL(d)=20log10(fMHz)+10nSFlog10(d)–28+FAF,  (17)
 
where nSF represents the path-loss exponent value for the same floor measurement and FAF is the floor-attenuation factor (Table 3). You can determine the FAF value from (Table 2). The following examples demonstrate how to use the foregoing tables and equations: For example, calculate the path loss for an outdoor free-space environment at a distance of 1200m at 915 MHz and 2.4 GHz. Using

20log10(fMHz)+20log10(d)–28,  (18)
 
you can deduce PL at:

915 MHz=20log10(915)+20log10(1200) –28=92.8 dB,  (19)
 
and PL at:

2400 MHz=20log10(2400)+20log10(1200) –28=101.2 dB.  (20)
 
Propagation at a higher frequency results in higher path losses, which results in the reduction of wireless-transmission ranges at higher frequencies: For example, wireless devices operating in the 2.4-GHz range suffer from an approximately 8.4-dB reduction in path loss compared with a device operating at 915 MHz in an outdoor, free-space environment.

In another example, using the information in Table 2, calculate the path loss for an indoor-office environment with hard partitions at a distance of 100m at 915 MHz and 2.4 GHz across the same floor and three floors. For the same floor, from Table 3, the average path loss is 3 dBm. Using this value of n=3 in:

20log10(fMHz)+10log10(d)–28+Xσ,  (21)
 
yielding PL at:

915 MHz=20log10(915)+10(3)log(100) –28+Xσ=91.2 dB,  (22)
 
where σ=7 dB. And PL at:

2400 MHz=20log10(2400)+10(3)log (100)–28+Xσ=99.6 dB,  (23)
 
where σ=14 dB.

From Table 2, you can calculate the FAF for propagation for three floors as approximately 24 dB with a standard deviation of 5.6 dB. Using the information in

20log10(fMHz)+10log10(d)–28+Xσ,  (24)
 
you can deduce PL at:

915 MHz=20log10(915)+10(3)log10(100) –28+24=115.2 dB,  (25)
 
where σ=5.6 dB, and PL at:

2400 MHz=20log10(2400)+ 10(3)log10(100)–28+ 24=123.6 dB,  (26)
 
where σ=5.9 dB.

In a third example, estimate the transmission range at 915 MHz for the above two examples assuming a system with unity-gain transmitting and receiving antennas, a transmitting power of 8 dBm, and a receiver sensitivity of –100 dBm. The system’s link budget is 8–(–100)=108 dB.

It’s a good idea to have a link-budget margin of approximately 10 dB to account for the standard deviations in the path-loss formulas. Thus, the available link budget is 98 dB, which exceeds the path loss of 92.8 dB from the first example; therefore, you can consider 1200m to be outdoor range.

In the indoor environment, path loss is 91.2 dB, and the available link budget is approximately 98 dB, assuming a 10-dB margin, which exceeds the path loss. Therefore, you can consider 100m to be the indoor range of that system.