Looking at the 3 phones that exist which have this feature, they don't have anything in common in their chipsets:
HTC u11: Qualcomm Snapdragon 835 processor, Android 7.1.
Moto x4: Qualcomm Snapdragon 630 processor, Android 7.1.
Huawei Mate9: 1.8Ghz octa-core.
Is there a special low-energy chip that is not listed? The Qualcomm Snapdragon 845 mentions in its specs that it offers improved voice recognition and low-power voice processing, and it implies that low-power voice activation controls to wake are a function of the OS, not of the hardware.
Basically, if I wanted to build a phone that supports always-on alexa like the 3 listed above, from a hardware standpoint, do I need anything beyond the listed CPUs, or are they enough to do the job (without totally killing the battery)? In the current world, I imagine the chip I would use is the Snapdragon 845.