# Why is receiver RSSI so much lower than the output power of a transmitter?

When we measure the output power of a small transmitter we might see something around 30 dBm (1W) but a receiver/WLAN card/UE right next to the transmitter will report a RSSI in the range of -40dBm, for example.

Why is this such a large power loss (30dBm - -40dBm = 70 dB ~= output power is 10000000 x greater)?

• Are you comparing apples with apples here? Is the small transmitter a WLAN transmitter? What device are you using to measure the 30dBm and might you be expecting too much of a WLAN card to work at this sort of input level? – Andy aka Jul 1 '13 at 20:06
• AFAIK that transmitter output is the MAXIMUM, and the transmitter will crank itself down when it finds out that the receiver can live with a lower signal strength. – Wouter van Ooijen Jul 1 '13 at 20:07
• That is a good question - they are both dealing in terms of power (dBm) but they might represent different things? Is it also just the power allocated to that receiver? – Stuart Jul 1 '13 at 20:07
• Based on what Wouter says maybe trying measuring power independently when the WLAN is present? – Andy aka Jul 1 '13 at 20:09
• In this setup, the transmitter increases power as receivers are added (to a limit, largest increase is the first added receiver.) The idle output power with nothing attached is still around 24-26 dBm. And to answer Andy's question, the output power is measured with an RF Power meter. This range is typical of receiver/transmitters though, see this page: en.wikipedia.org/wiki/DBm – Stuart Jul 1 '13 at 20:13

Strictly speaking, the RSSI reported by an 802.11 interface is in arbitrary units. There is no requirement that it be in $dBm$ or anything else; the only requirement is that stronger signals are bigger.

But let's just say that your RSSI is indicating received power in $dBm$. It will necessarily be much less than the AP's transmitter power for two reasons:

1. An intelligent AP will not transmit at full power unless necessary, to reduce interference with adjacent APs.

2. Most of the electrical energy radiated by the transmitter goes uselessly into space, where the receiver isn't.

Point #2 is essentially the inverse square law. If the transmitter emits 1W, than that means for any sphere centered on that antenna, then there is 1J of energy passing through that entire sphere each second. Neglecting things that might absorb or reflect that energy, this is true no matter how big the sphere is. But since the sphere has an increasing area as it gets bigger, the energy available in a given area is smaller. Dividing the transmitter power by the sphere area gives you the power available per unit of area at some distance $r$:

$$\frac{P}{4 \pi r^2}$$

So say 1W transmitter, 10m away, the field strength (assuming an isotropic antenna) would be:

$$\frac{1W}{4 \pi (10m)^2} \approx 796\mu W / m^2$$

Given that your typical antenna in these systems is a lot smaller1 than $1m^2$, you'd expect to receive a lot less than even $796\mu W$, or $-1dBm$, even though $1W$, or $30dBm$ was transmitted.

Of course, this is just an approximation. Earth will reflect some of the power. Walls will absorb some of it. The efficiency of the power coupling between antennas depends on their relative orientation and polarization. No antenna is isotropic. But the basic truth still holds: most of the energy went off uselessly into space, simply because there wasn't an antenna around to receive it.

1: really what we care about here is the antenna aperture, which is related to the physical size of the antenna but is also influenced by other aspects of its design. For an example of an antenna with an aperture much larger than it's physical size, see the loopstick antenna. Still, that's a rather special case, and your typical wi-fi antenna is still going to have an aperture smaller than $1m^2$.

• +1 answered before me, and included some great formulas. :) – JYelton Jul 1 '13 at 20:26

Power emitted from an antenna, as electromagnetic radiation, follows the inverse square law, which states that:

a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.

Most of the transmitted energy is not going directly to the receiver. Even though you might be in close proximity, the receiver will only "see" a small portion of the total output.

If you use a coaxial cable and coupled the RF output of the transmitter directly to the receiver input, you would theoretically see a value much closer to the output power. However, I doubt the receiver would be capable of dealing with that much power.

That aside, Wikipedia states:

There is no standardized relationship of any particular physical parameter to the RSSI reading. The 802.11 standard does not define any relationship between RSSI value and power level in mW or dBm."

I therefore wouldn't compare RSSI (Received Signal Strength Indicator) to a measured or known output power from a transmitter; they are not the same thing.

• Great answer also. Indeed, the transmitter output power was measured by feeding a RF cable directly into the power meter. The RSSI on the receivers in the particular set up I referred to (cell phones) does report received power in dBm but it may not be completely accurate either. – Stuart Jul 1 '13 at 20:39

It sounds like you are comparing two different things: The power the transmitter is putting out and the power received by one actual receiver. The two are so vastly different because most of the transmitted power is not going to be intercepted by the antenna of the receiver, even if it is close.

Think of the transmitter like a lightbulb emitting radio waves in lots of directions. Now consider the size of a small antenna on a receiver. Even "right next to" the transmitter, that little antenna will only interept a small fraction of the power radiated by the transmitter.