# Speed vs. Distance

### All things being equal, a high data rate system will not transmit as far as a low data rate system, leading to trade-offs.

Years ago, computer folks took an old adage-"You can't be too rich or too thin"-and made their own maxim: "You can't have too much speed or too much memory."

Maybe you've heard an ill-advised corollary about wireless applications: "You can't have too much speed or too much range."

While speed and memory in a computer are independent variables, such is not the case with wireless. Speed (or data rate) and distance (or range) are inversely proportional. That is, other things being equal, a higher data rate system will not transmit as far as a lower data rate system.

Radio frequency (RF) signals of a given carrier frequency, such as 2.4 gigahertz (GHz), lose power as they propagate. Called path loss, this is similar to the way a sound is softer the farther it is from the source. Path loss in decibels (dB) increases with the square of the distance and is relatively easy to estimate when the path is unobstructed. The free space loss equation at 2.4 GHz is simply this:

path loss in dB = 40 dB + 20 log
(distance in meters)

The following table illustrates the impact of distance on path loss. Notice each time distance in kilometers (km) doubles, path loss increases 6 dB (this applies only in the 2.4-GHz band).

To determine whether two radios can hear each other over a given range, you should consider two other variables: transmit power and receive sensitivity. Transmit power is simply how "loud" the signal is. Transmit power is expressed in dB and is usually a positive number. Often, transmit power is expressed in dB relative to a milliwatt (dBm). For example, 20 dBm is 100 milliwatts (see sidebar on dB vs. dBm).

Receive sensitivity is the ability of the receiving radio to "hear" the signal. The receive sensitivity of a radio indicates what level of signal strength must be present to correctly receive data at a specified bit error rate.

Here's another way of looking at receive sensitivity: It tells you how much a signal can reduce before you can't hear it anymore. Expressed in dBm, it is usually a negative number indicating the amount of path loss a signal transmitted at a 0 dBm (1 milliwatt) level can experience and still be received at the specified bit error rate. Receive sensitivity takes into account noise levels, signal-to-noise ratio, and, most importantly, the over-the-air data rate. You don't need to calculate a device's receive sensitivity; it is a specification the equipment manufacturer provides.

If the transmit power minus the path loss is greater than the receive sensitivity, the radios can communicate. If antennas with gain are used, the gain of the antennas at both ends is added to the transmit power. Take a typical situation: a 20 dBm transmitter, 2 dB antennas at each end, and a receiver with a -93 dBm receive sensitivity. This system could communicate over a range with a path loss of 20 + 2 + 2 + 93 = 117 dB. Good RF design provides for 10 dB of cushion, so in practice a path loss of 107 dB could be tolerated while maintaining good link reliability.

### DATA RATE ALSO A FACTOR

So how does speed or data rate figure into the equation? The over-the-air data rate, the rate at which the radios communicate, is a component in determining the receive sensitivity of a radio.

This is true regardless of the type of spreading method or modulation technique. For every doubling of the data rate, the receive sensitivity is reduced by 3 dB. You can see this in the various receive sensitivities of an 802.11b radio. The receive sensitivity for the 11 megabits per second (Mbps) rate is much lower than the receive sensitivity for the 2 Mbps rate.

How does one correlate a reduced receive sensitivity to range? In free space (outer space, not line-of-sight space), every 6-dB reduction in receive sensitivity results in a halving of the range. In the terrestrial world, you can observe a more severe penalty, where a 6-dB reduction in receive sensitivity results in less that half of the original range. This is why an 802.11b radio reduces the over-the-air data as the distance between radios increases. When it comes to coverage area, which varies with the square of the range, a reduction in range by half requires four times the number of access points.

In indoor applications, a phenomenon called "multipath" occurs. The transmitted signal bounces off objects in its path, creating multiple copies of the same signal. These signals arrive at the receiver at different points in time and with different phases. When multiple copies of the transmitted signal arrive at the same time but with different phases, they can partially cancel each other out, thereby reducing the signal. This reduction is independent of the over-the-air data rate.

With another multipath effect, called intersymbol interference, other copies of the signal may arrive slightly later in time, interfering with a subsequent data bit rather than the original data bit. Intersymbol interference reduces range by requiring a higher-power original signal to be able to be distinguished from some "old" signals.

The amount a signal delays by bouncing around in indoor applications is pretty short: less than 500 nanoseconds (nsec). As long as the over-the-air data rate has a bit time of more than 500 nsec, you can ignore the delay effect. A data bit time of more than 500 nsec corresponds to an over-the-air data rate of less than 2 Mbps. While the impact of this phenomenon is hard to measure, it is nonetheless significant.

What can a wireless system designer do to get the most from the wireless network? First match the speed of the over-the-air data rate with the speed required by the application. With wireless, speed isn't free. If you are sending tens of kilobytes wirelessly between two radios, you don't need 11-Mbps speed.

By matching the speed of the radio to the data needs of the application, you will achieve the best range. You will have the best receive sensitivity and avoid some of the multipath effects. Good RF system design techniques always help with range and reliability, but other things being equal, a higher-speed radio system will go a shorter distance than a lower-speed system. IT

## Behind the byline

Tim Cutler, vice president of sales and marketing for Cirronet Inc., has spent more than 15 years in senior marketing positions at high-tech companies such as Quadram Corp., Nynex Business Centers, and AER Energy Resources. Cutler holds two patents for microprocessor-based design.