Should I always keep my smartphone with me?

No, once installed your iHealth Wave runs completely independently.

You only need your smartphone when you want to synchronize the data.

*credit to Sylvain of iHealth Labs EU

https://helpcenter.ihealthlabs.eu/hc/en-gb/articles/115000670165-iHealth-Wave-AM4-Should-I-always-keep-my-smartphone-with-me-