# A Decentralized Receiver in Gaussian Interference
## 5 Conclusions  
One upper bound and three lower bounds on communication rate were developed. A simple upper bound (Remark 1) was derived, achievable when the LAN constraint is stringent (small \(L\)), and achievable in limit as the LAN constraint is relaxed (\(L\to\infty\)). An achievable rate (Theorem 5) considering quantizers which add Gaussian distortion was seen to provide large gains in interference over a rate that does not fully use the distributed receive array (Remark 2). The rate (Theorem 7) achieved when a distributed compression stage is added to the previous technique provides gains over Theorem 5 when interference is strong and helper-to-base communication is limited, but may be more difficult to implement.  
Leaving SNR fixed, performance is mostly unchanged in high-scattering versus low-scattering environments, although the profile of helper-to-base communication changes: In high-scattering environments, some helper observations are ignored by the base, while, in line-of-sight environments, each helper informs the base equally. The presence of a strong interferer dampens this effect, since in this regime the base needs more spatial diversity to mitigate the interferer.  
An immediate goal for future work is to devise practical implementations of the presented strategies. This may include refining the models of the LAN and helpers to more precisely reflect system capabilities.  
The following are available online at [[http://www.mdpi.com/1099-4300/20/4/269/s1](http://www.mdpi.com/1099-4300/20/4/269/s1)]([http://www.mdpi.com/1099-4300/20/4/269/s1](http://www.mdpi.com/1099-4300/20/4/269/s1)).  
**Acknowledgments: We would like to thank [PERSON] for aid in producing datasets for this paper. We would also like to thank [PERSON] for his comments and corrections. Support by [PERSON] offered by AFOSR under grant FA 9550-15-1-0351. DISTRIBUTION STATEMENT A: Approved for Public Release, Distribution Unlimited. This work was sponsored in part by Defense Advanced Research Projects Agency under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government.**  
Figure 5: Average rate at which each helper forwards to base in distributed compression (Theorem 7) versus \(K\)-factor (scattered-to-direct-path received signal power ratio). Four helpers with 0 dB average receive SNR and a LAN constraint of \(L=5\) bits per channel use of side information the helpers share to inform the base of their observations. Averaged over 1000 channels with gains \(\sim\mathcal{CN}(0,I)\). Interferer present at each receiver with a uniform random phase and specified INR. As the proportion of line-of-sight path power increases, the need for receive diversity increases and the base draws information from more helpers. This does not occur when the base has its own observation, when presumably it is used as an estimate of the interferer to be mitigated from a compression of the highest-SNR helper’s observation.  
**Author Contributions:** [PERSON], [PERSON] and [PERSON] developed the theoretical work in the paper. [PERSON] and [PERSON] performed the simulations. [PERSON] wrote the paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.