I am not an antenna expert, but one of the things to understand about antenna design is that the shape of the antenna changes its transmission properties. In this case, you end up with a directional antenna.

In the case of a WiFi mesh network, you'd really want a set of omnidirectional antennae. An omnidirectional antenna with a 1/4 mile radius would need a lot more power to operate. Further, in a place like new york, you have to start worrying about 3 dimensions (skyscrapers are tall!) and obstructions (buildings can be difficult for radio signals to pass through).

Edit: removed redundant phrasing.

> In the case of a WiFi mesh network, you'd really want a set of omnidirectional antennae. An omnidirectional antenna with a 1/4 mile radius would need a lot more power to operate. Further, in a place like new york, you have to start worrying about 3 dimensions (skyscrapers are tall!) and obstructions (buildings can be difficult for radio signals to pass through).

The last part (buildings) is incredibly important to remember. WiFi signals—which are typically in the 2.4GHz or 5GHz bands—are extremely susceptible to attenuation in this manner, due to the higher frequency.

Note that, in part, this is why carriers are so hungry for the sub-GHz bands (i.e. 700MHz in the US, 850-900MHz in Australia, etc) for their 3G/LTE+ deployments. The lower frequencies exhibit significantly better building penetration, offset by the need to deploy more cells in order to get similar bandwidth capacity (considered a worthwhile trade-off).

An omni that could broadcast 1/4 mile (400m) in Manhattan at 2.4GHz would need to have a VERY high transmit power. It would likely be illegal, and it would also be dangerous.

2.4GHz in Manhattan? You're making me laugh. There are so many WiFi (and other Part 15.247) devices in Manhattan that the noise floor is sitting around -90dB.

You're not going to build a mesh network in 2.4GHz in NYC.

Or you have an omni antennea for local users and one of these as the backbone link to one of few core routers linked to a decent ISP connection

Don't conflate a strong signal with increased bandwidth. A good "tin can" antenna still isn't going to allow you to exceed 802.11g/n/ac speeds. Chances are you'll still saturate the link.

due to the loss of orthogonality in the channel matrix, you're not going to get anything from 802.11n, other than perhaps the double-wide channels.

No, I'm saying that if you needed a wifi network for say a campsite or outdoors event, or even a private muni-sized network.

You would use a regular omni-antennae for local client connectivity in each zone then a bunch of these to provide the backbone link to connect those zones to some centrally better connected point. Rather than trying to do a pure peer-per mesh

One thing about cantennas is that they are linearly polarised, so you could go from half to full duplex on the same frequency by having four of them, two at either end, rotated 90 degrees apart.

I believe Steve Song's wonderful Village Telco project is about doing just that -- creating a low-cost wifi mesh to share connections. It certainly deserves a mention here!

http://villagetelco.org/