Estimating transmission range for Zigbee and proprietary short-range wireless devices in 900MHz and 2.4GHz ISM band

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:



Where Pt is the transmitted power, Pr(d) is the received power. It is a function of the transmit-receive separation d, Gt is the transmitter antenna-gain, Gr is the receiver antenna-gain, d is the T-R separation in meters, and is the wavelength in meters.

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

An important terminology to estimate the wireless transmission range is the path-loss (PL) which represents signal attenuation in dB. It is defined as the difference (in dB) between the transmit-and-received power at the antenna. From Equation 1, the path-loss is Pt /Pr(d). The PL in dB is defined as:



To simplify Equation 2, both the transmitting and receiving antennas are assumed to have unity gain. This results in:



This equation also can be expressed in this useable form:



where d is the distance in meters.

The Friis free-space formula can estimate the received power level only for values of d, which are in the transmitting antenna’s far-field. The far-field, also known as Fraunhofer Region of a transmitting antenna, is defined as region beyond the far-field distance df.

The far-field distance df for an antenna is given by:



where, D is the antenna’s largest physical linear dimension. Also df must be greater than D and to be in the far-field region. As mentioned earlier, this path-loss formula only applies for ideal systems with clear line-of-sight, and should only be used for initial estimates only.

Propagation models use the close-in distance, d0, as the received power-reference point. The received power Pr(d) at any distance d > d0 has to be calculated with reference to Pr(d0). The value Pr(d0) can be predicted from Equations 1 and 4. Or, it can be measured in the radio environment by taking average received power at many points from a close-in distance d0 from the transmitter. The close-in reference distance d0 has to be selected so that the far-field region, i.e., d0>df.

Using this information, the received power at any distance d is calculated using the formula:



In the 1-2GHz range, the reference distance d0 for practical systems 1m was chosen for indoor environments, and 100m for outdoor environments.

Most RF power-level units are either in dBm or dBw rather than absolute power-levels.
Equation 5 can be rearranged as:



The above concepts are explained with the following example:

Assuming a transmit frequency of 900MHz, the transmit power of 6.3mW (8dBm) and the unity gain transmit and receive antennas, determine the received power at 1200m distance in an outdoor line-of-sight environment.

For an outdoor environment, the reference distance d0 is 100m. Hence the received power at 100m (Pr (d0)) must be determined. The wavelength at 900MHz is 1/3m.
Using these values in Equation 1, we obtain:



To calculate the power in dBm, the power needs to be expressed in mW as:



Therefore, Pr(100) in dBm = 10log (0.44 x 10-6 mW) = –63.6dBm.
Using Equation 6 to obtain the received power at 1200m, results in:



Using Equation 4, the same value of received power obtained can be verified.

An ideal unobstructed outdoor line-of-sight (LOS) environment shows that the received power at a 1200m distance when the transmit power is 8dBm is approximately –85dBm. In reality, the actual received power will be much lower than that level since the environments will likely have obstructions in the LOS path or worse, no LOS path at all.
More practical path-loss formulas will be shown in the next section.

For the previous example, the path-loss is calculated as: Pt(dBm) – Pr(dBm). Therefore, path-loss = 8dBm – (–85dBm) = 93dB.

Link Budget

For any practical wireless sensor system, it’s important to know the maximum reliable data transmission range. This wireless system range directly depends on a parameter called the link budget and is defined as link budget
(dB) = Pt (dBm/dBw) +Gt (dB) + Gr (dB) - Receive Sensitivity (dBm/dBw) (Equation 6a)

Where Gt and Gr are the transmit-and-receive antenna gains, respectively, the receive sensitivity is defined as the minimum RF signal that the system can detect with an acceptable signal-to-noise ratio (SNR). The receive sensitivity is shown by this formula:
S (dBm) = –174dBm/Hz + NF (dB) + 10log B + SNRmin (dB)
• -174dBm/Hz is the thermal Noise Floor
• NF is the overall receiver noise figure in dB
• B is the overall receiver Bandwidth

If the total path-loss between the transmitter and the intended receiver is greater than the link budget, there is “loss” of data and communications cannot be achieved. 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.

Practical Path-Loss Model for Outdoor Channels

Log-Distance Path-Loss Model:

Any propagation model (either theoretical or measurement-based) indicates that the average received signal power decreases logarithmically with distance, in both outdoor and indoor channels. The average large-scale path loss for any T-R separation is expressed as a function of distance d by using a path-loss exponent n as:



The path-losses in the above equations are expressed in dB.

In Equation 7, the bars indicate the ensemble average of all the different path-loss values at a same distance d. The path-loss exponent n indicates the rate at which the path-loss increases with distance, d0 is the close-in reference distance, and d is the T-R separation distance. As explained earlier, d0 is chosen to be 1m in indoor channels and 100m in outdoor channels. The value of the path-loss exponent n depends on the specific propagation environment. In “free” space, n is equal to two. When obstructions are present, n will have a larger value. Table 1 lists the typical path-loss exponent values that are documented in the literature.

Table 1: Path-Loss Exponents in Different Environments



Calculating the value of path-loss PL (d0) at distance d0 of 100m using Equation 3 and applying it to Equation 7 results in:



Using the value of n=2 (free-space), the path-loss formula for outdoor channels is:



Log-Normal Shadowing

Equation 7 only predicts the average path-loss value and does not consider the deviation created by surrounding environment “clutter” that can be vastly different for two locations with the same T-R separation. This may lead to the actual path-loss values varying significantly from the average values predicted.

Through extensive measurements by several researchers it has been shown that the path- loss PL(d) at any distance d is log-normally distributed (normal in dB) about the mean value given by Equation 7. This is given by:



For an outdoor channel with unity gain, transmit-and-receive antennas and free-space propagation (n=2), Equation 8 can be simplified as:



where is a zero-mean Gaussian Random variable (in dB) with standard deviation .

The log-normal distribution describes the random shadowing effects which occur for individual measurement locations with the same T-R separation, but with different propagation path obstructions. This effect is called log-normal shadowing.

Log-normal shadowing indicates that the path-loss at a certain distance d, has a Gaussian (normal) distribution with the mean-value given by Equation 7. However, if the wireless devices are stationary, the effects of can be ignored and Equations 8 and 9 can be substituted by Equation 7.

Equations 8 and 9 can be used to statistically model the value of the path-loss and, hence, the received powers for an arbitrary distance d for outdoor channels. The range of a wireless transmission then can be calculated to be the maximum distance d that results in path-loss not exceeding the actual link budget. Due to a wireless propagation environment’s statistical nature, it is necessary to consider a safety margin of a few dB in the link budget calculation.

There are several other outdoor propagation models outlined in the literature. The Longley-Rice Model, Durkin’s Model, Okumara Model and Hata Model are more suited for cellular propagation environments (distances greater several km) and are not suitable for short-range wireless devices.

Indoor Propagation Models

Most wireless sensor devices operate in indoor environments. This final section presents a model used to estimate the path-loss in indoor channels.

The indoor radio channel differs from the outdoor channel in terms of having smaller distances to cover and higher variability in the path-loss. Thus, there are larger variances in the received signal power. As discussed, however, if the wireless devices are stationary, the variability in the received signal power will be negligible.

The propagation indoor (inside buildings) is strongly influenced by specific features such as the building’s layout, type, construction materials, etc.

In general, researchers have shown that indoor channels may be classified as either line-of-sight (LOS) or obstructed (OBS), with varying degrees of clutter.

Partition Losses (On the Same Floor)

A building’s internal and external structures have a wide-variety of partitions and obstacles. Partitions used depend on whether it’s a home or office environment. Partitions in a building’s structure are hard partitions. Partitions that can move and do not span to the ceiling are soft partitions. Houses typically use wood frame partitions while 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 have been conducted to tabulate signal losses for common material types shown in Table 2.

Table 2: Average signal loss for radio paths obstructed by different material types



Partition Loss between Floors

The partition loss between floors is represented by Floor Attenuation Factors (FAF).
This data recorded for a specific building is tabulated in Table 3.

Table 3: Floor Attenuation Factor (FAF) for signal penetration across multiple floors



Practical Path-Loss Model for Indoor Channels

Log-Distance Path-Loss Model

The indoor path-loss has been shown to follow the distance power law equation as shown:



If the devices are stationary, the effects of can be ignored.

Calculating the value of path-loss (d0) at distance d0 of 1m using Equation 3 and plugging it into Equation 10 results in:



The value of n does not vary much with frequency and depends on the surroundings and the building type as is tabulated in Table 4.

Table 4: Path-loss exponent and standard deviation measured in different buildings



Attenuation-Factor Model

An in-building propagation model that includes the effect of building type as well as the variations caused by obstacles is described in literature. This model provides flexibility and was shown to reduce the standard deviation between measured and predicted path-loss to around 4dB, as compared to 13dB when only a log-distance model as shown in Equation 11 is used. The Attenuation-Factor Model is represented by:



Where nSF represents the path-loss exponent value for the same floor measurement and can be selected from Table 4. The FAF value can be determined from the values in Table 3.

Summary of Formulas
Table 5: Summary of Path-Loss Formulas




About the Author

Shreharsha Rao is a Systems Engineer at Texas Instruments where he researches application development for low power wireless and RFID systems. He has a Masters in Electrical Engineering and likes hiking, sports, and is in a poker league.