Ths is what the 1973 prototype cell phone looked like
Motorola early analog phone.
The late 60's early 70's bag phone version was like this, and you had to be near NY, Boston, Chicago, Miami or SF to use one. They were usually made by
Motorola or
GE.
For the most part, they were puchased by larger companies for support staff, as they cost over $1k and they ran about 30 min on their lead-acid batteries, which is where most of the weight came from.
Toward the end of the recently ended analog era, they were revived for those who lived and worked in fringe areas with notoriously poor reception. Those 3 watt phones with newer ciruitry would far outreach the 100 milliwatt wonders we use. But the goverment ended all that this past year.
Could the picture be a "small" transistoried AM radio? Transistors were invented in 1947, but the first usable portable battery powered radios were sold in the 60's, although they had been around mostly as curiosities since the Germans came out with one in '53.