# Is the Pathloss Larger at mmWave Frequencies?

The range of mmWave communication signals is often said to be lower than for signals in the conventional sub-6 GHz bands. This is usually also the case but the reason for it might not be the one that you think. I will explain what I mean in this blog post.

If one takes a look at the classical free-space pathloss formula, the received power is

(1)

where the transmit power is denoted by , the wavelength is , and the propagation distance is . This formula shows that the received power is proportional to the wavelength and, thus, will be smaller when we increase the carrier frequency; that is, the received power is lower at 60 GHz ( mm) than at 3 GHz ( cm). But there is an important catch: the dependence on is due to the underlying assumption of having a receive antenna with the effective area

(2)

Hence, if we consider a receive antenna with arbitrary effective area , we can instead write the received signal in (1) as

(3)

which is frequency-independent as long as we keep the antenna area fixed as we change the carrier frequency. Since the area of a fixed-gain antenna actually is proportional to , as exemplified in (2), in practice we will need to use arrays of multiple antennas in mmWave bands to achieve the same total antenna area as in lower bands. This is what is normally done in mmWave communications for cellular networks, while a single high-gain antenna with large area can be used for fixed links (e.g., backhaul between base stations or between a satellite and ground station). As explained in Section 7.5 of Massive MIMO Networks, one can actually play with the antenna areas at both the transmitter and receiver to keep the same pathloss in the mmWave bands, while actually reducing the total antenna area!

So why is the signal range shorter in mmWave bands?

The main reasons for the shorter range are:

• Larger propagation losses in non-line-of-sight scenarios, for example, due to less scattering (fewer propagation paths) and larger penetration losses.
• The use more bandwidth, which leads to lower SNR.

Edit: The atmospheric, molecular, and rain attenuation losses are larger in some mmWave bands, but it is primarily a concern for macro cells with ranges measured in kilometers (see Figures 2-3 in this paper).

## 10 thoughts on “Is the Pathloss Larger at mmWave Frequencies?”

1. Yu says:

I notice that almost all papers are based on i.i.d Rayleigh channel model. If there is any available mmWave channel model for researching?

1. Emil Björnson says:

My book “Massive MIMO networks” (http://massivemimobook.com) shows how to study Massive MIMO with correlated Rayleigh fading, which can be applied to a variety of scenarios.

Moreover, there are actually hundreds of papers on mmWave channel modeling and analysis. You can find many references in the paper “Millimeter Wave Communications for Future Mobile Networks” (https://arxiv.org/pdf/1705.06072.pdf)

2. Reza says:

What about the dielectric loss which is proportional to the frequency?

1. Emil Björnson says:

The interaction with different materials will certainly be frequency dependent. This is what goes into the bullet item “less scattering (fewer propagation paths) and larger penetration losses”

3. Giuseppe Roveda says:

Also the technology limits of real TX and RX devices at growing frequency should be taken into consideration: for example usually you get much lower Ptx at D band (150 GHz) then at E band and so the link budget allows shorter distances.

4. Nir says:

WiFi in 2 GHz has a range of 100-200 m while LTE has few kilometers of range. What is the reason for that?

1. Emil Björnson says:

Larger transmit powers in LTE, elevated deployments, and protocols that are designed to manage lower SNRs and mobility.

5. bob says:

Thanks for the blog. In general, very well written and obviously with a lot of love. However, I must admit that I am not a big fan this “clickbait” style of dissemination of scientific information (which is becoming more dominant in this blog). We do have higher pathloss at higher frequency due to oxygen absorption over the air. Of course, one can compensate it using higher tx power or leveraging antenna gain but that does not make millimeter-waves less

1. Emil Björnson says:

The purpose of this blog post is to emphasize that the free-space pathloss formula (also known as Friis propagation formula) is not suggesting that the pathloss is frequency dependent. The reason is that I had seen and heard the opposite argument being made far too many times.

The reason for the worse propagation conditions in mmWave bands are the ones mentioned in the bullet list at the end of the post, and the one that you mentioned. I didn’t explicit mention the oxygen absorption effect since I don’t believe it is a dominant effect. If one would deploy a macro cell using 60 GHz, then the 20 dB/km loss at those frequencies will be important. However, in the 28 GHz band that is currently in use, the absorption is less than 1 dB/km; see Figure 2 in https://arxiv.org/pdf/1705.06072.pdf