Does amplify-and-forward cooperative relay improve OFDM/OFDMA ergodic capacity?

The ergodic information rate for Orthogonal Frequency-Division Multiplexing / Orthogonal Frequency-Division Multiple Access with amplify-and-forward (AF) relaying systems in the presence of frequency offsets is evaluated. Unlike previous work, per-subcarrier adaptive power allocation is performed on each relay to optimize the system ergodic information rate. For a given frequency offset and total number of relays M, the AF ergodic information rate is proven to be a monotonically increasing function of a (the ratio of the power allocated to the source node and the total transmit power), implying that the maximum ergodic information rate can be obtained at α=1 (i.e., there is no cooperative relay). Furthermore, the proof of "cooperative relays cannot improve the AF ergodic information rate in a quasi-static wireless channel" is also provided in this letter.