Check out the spec for "Incoming Bandwidth" to see if it will really support the full load. 1080p @ 30fps takes about 2-4mbps incoming, 4MP would take 4-8mbps incoming on the main stream. So for 16 cameras recording at 4MP you would need an Incoming Bandwidth of 128mbps.

This 16 Channel NVR advertises that it can do 4MP (2K) on all 16 channels, and has 160mbps Incoming Bandwidth so you wouldn't have to worry. It says it can even do "up to ten 4K cameras" which is impressive for an NVR that affordable.

I've gone through a lot of Lorex, Q-See, and other junk from Costco, Best Buy, and Amazon and my recommendation is to stay far away from anything you can find in the box stores, or at least call their Support line before you purchase to make sure they 1) answer the phone, 2) speak English, and 3) know what they are talking about.

This looks a lot like the Hikvision NVR, and they build a lot of OEM equipment that is branded under other names, and it's usually even a little bit better quality than the stuff you find with their name on it. They usually use a better firmware that can easily be updated too. I've been looking at this one because of it's 4K capabilities but if you just want 4MP then this one would do that easily, plus you can upgrade to 4k later!