Closed-Form Capacity Bounds for the Exponential Version of the Dirty Paper Channel

This letter presents closed-form capacity bounds for an exponential version of the dirty paper channel (EDPC). The EDPC can be used to model the non-coherent Gaussian dirty paper channel (GDPC). First, a superposition modulation-like technique is used to obtain a capacity upper bound for the EDPC. Then, a closed-form capacity lower bound for the EDPC is obtained by using a Costa-like strategy. Using this lower bound and exploiting the asymptotic properties of high signal to noise ratios (SNRs), we obtain the high-SNR capacity of the EDPC which is intriguingly analogous to the complex-valued GDPC. Finally, a closed-form capacity lower bound for the EDPC is given which is useful in the weak interference regime.