An industrial roll includes: a substantially cylindrical shell having an outer surface and an internal lumen; a polymeric cover circumferentially overlying the shell outer surface; and a sensing system. The sensing system includes: a plurality of sensors embedded in the cover, the sensors configured to sense an operating parameter of the roll; and a signal-carrying member serially connected with and extending between the plurality of sensors. The signal-carrying member follows a helical path over the outer surface of the shell, wherein the signal-carrying member extends between adjacent sensors and extends over more than one complete revolution of the shell outer surface (and, preferably, an intermediate segment of the signal-carrying member extends over more than a full revolution of the roll between adjacent sensors).