How do I extend a non-Apple router WiFi network using Airport Extreme and Express?

You basically have two options:

1. (Best overall network performance) Connect both the Extreme and the Express to the Arris gateway device by Ethernet and configure all of them for a roaming type network. This would require an Ethernet connection between all of the routers which can be accomplished by either using Ethernet cable or the use of power-line adapters.
2. (Adequate overall network performance) Connect just the Extreme to the Arris by Ethernet, and then, extend the Extreme using the Express.

Which of these would you prefer?

Ok, great.

One of the first things to decide is, whether or not, you want the Extreme (which will be connected to the Arris gateway by Ethernet) is going to be in the same room, or not, as the Arris. The reason behind this is the possibility of Wi-Fi interference between them and how they will need to be configured.

The two options here are:

Option #1 - Same room

My guess is that this will be the desired choice. Regardless, if this is the way you wish to go, then you will need to disable the wireless radios of the Arris gateway. Your extended network will only be provided by the AirPort base stations in this case.

Option #2 - Different rooms

In this option you would still have the Extreme connected to the Arris by Ethernet and have to deal with where to run the cable. In this case the Arris Wi-Fi radios do NOT have to be disabled as they shouldn't interfere with the Extreme's.

Regardless of which choice, we will be configuring both the Arris and the Extreme for a roaming type network ... but with some slight set up differences. I will need your choice of which option you want to go with to process with the detailed instructions for setting up your network.

Ok, then the first step is to disable the wireless radio(s) in your Arris gateway. You will have to refer to the user guide for this device in order to do this.

Once that has been done, we will try to set up a roaming network with both of these devices, and then, configure the Express to extend it.

The good news, outside of disabling the Arris' wireless, is that no other setting should be required for that device.

Assuming that you have the radios disabled, the following are the basic instructions to set up the roaming network using the AirPort Utility:

• Perform a "factory default" reset on the AirPort Extreme. Go ahead and do the same for the Express, except leave the Express powered-off when done.
• After the reset, the Extreme will be in its "out-of-the-box" configuration which is a wireless router that will broadcast an unsecured Wi-Fi network with a network name of something like: Apple Network NNNNNN
• From a Mac, click on the Wi-Fi icon on the OS X menu bar.
• In the drop-down menu you should now find the base station under the title: "New AirPort Base Station."
• Click on it and it should start up the AirPort Utility.
• Just follow the automated steps. It should offer you the option to extend the Arris using Ethernet. That is what you want.
• Once you have completed all of the automated steps, the Extreme should restart and you should now have both devices configured for a roaming network.

Verify that you can access the Internet with a device connected to the Extreme by both wire or wireless. Please post back your results. If successful, we can go on to the next phase using the Express to extend this network.

Since you elected to have the Extreme in the same room as the Arris gateway, the wireless radios on that gateway will need to be disabled so that they don't interfere with the Extreme.

1. Am I correct that the process you've outlined will create a single WiFi channel?

With my comment above, you would end up with a wireless network on each band with one or both of those bands extended by the Express. Which one or ones will depend on the model of your Express. The 1st gen model can extend only one or the other; whereas, then latest version can potentially extend both.

2. Will it be 5GHz or 2.4 GHz?

Most likely, the 2.4 GHz band will be extended as the 5 GHz band has a much more difficult time penetrating through walls.

3a. If yes to #1, what are the downsides to only having a single channel?

Ok, channels and bands are two different, but related, things. Each Wi-Fi radio band (2.4 or 5 GHz) can have a number of channels. For example, in the US, there are 11 channels on the 2.4 GHz band. However, only channels 1, 6, or 11 do not overlap. The AirPort routers try to use a channel which has the least amount of Wi-Fi interference nearby ... so you do not necessarily need to choose a channel. This is also true on the 5 GHz band.

What you are really asking is there any downsides to only having a single band? The answer is: maybe, but it will depend on your networking goals. The 5 GHz band has greater bandwidth (speed) potential, but is limited in range.

3b. Is there another path forward that would both leverage existing equipment AND enable dual channel setup?

Yes ... but it would require using an extending device that is compatible with the Arris gateway. The AirPort base stations were designed to extend other AirPort base stations. This is true with just about any router manufacturer.

With your current networking equipment you will have to make compromises to make it work ... and still may not get the results you are looking for.