In this paper, we derive the capacity of the Gaussian degraded â cheapâ relay channel, consisting of nodes using â cheapâ
radios operating in TDD mode when transmitting and sending in the same frequency band. The TDD model captures a practical limitation of most of the RF radios used in commercial wireless systems. The proof of achievability relies on a combination of superposition encoding and list decoding, while the converse is derived using the min-cut max-flow theorem for networks with â cheapâ nodes (previously derived by the authors). Even with â cheapâ radios, our capacity analysis shows that cooperative coding is beneficial and has a capacity advantage over direct transmission.