{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:41:21Z","timestamp":1760244081894,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2008,11,20]],"date-time":"2008-11-20T00:00:00Z","timestamp":1227139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider the problem of intercepting communications signals between Multiple-Input Multiple-Output (MIMO) communication systems. To correctly detect a transmitted message it is necessary to know the gain matrix that represents the channel between the transmitter and the receiver. However, even if the receiver has knowledge of the message symbol set, it may not be possible to estimate the channel matrix. Blind Source Separation (BSS) techniques, such as Independent Component Analysis (ICA) can go some way to extracting independent signals from individual transmission antennae but these may have been preprocessed in a manner unknown to the receiver. In this paper we consider the situation where a communications interception system has prior knowledge of the message symbol set, the channel matrix between the transmission system and the interception system and is able to resolve the transmissionss from independent antennae. The question then becomes: what is the mutual information available to the interceptor when an unknown unitary transformation matrix is employed by the transmitter.<\/jats:p>","DOI":"10.3390\/e10040722","type":"journal-article","created":{"date-parts":[[2008,11,20]],"date-time":"2008-11-20T07:24:42Z","timestamp":1227165882000},"page":"722-735","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Intercept Capacity: Unknown Unitary Transformation"],"prefix":"10.3390","volume":"10","author":[{"given":"John","family":"Kitchen","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, University of Melbourne, Australia"}]},{"given":"Bill","family":"Moran","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, University of Melbourne, Australia"}]},{"given":"Stephen D.","family":"Howard","sequence":"additional","affiliation":[{"name":"EWRD, DSTO, PO Box 1500, Edinburgh, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2008,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1023\/A:1008889222784","article-title":"On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas","volume":"6","author":"Foschini","year":"1998","journal-title":"Wireless Pers. Commun."},{"key":"ref_2","unstructured":"Telatar, E. (1995). Capacity of Multi-antenna Gaussian Channels, AT&T-Bell Lab. Internal Tech. Memo."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0165-1684(94)90029-9","article-title":"Independent Component Analysis, A new concept?","volume":"36","author":"Comon","year":"1994","journal-title":"Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1109\/18.256484","article-title":"Secret Key Agreement by Public Discussion From Common Information","volume":"39","author":"Maurer","year":"1993","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tse, D., and Viswanath, P. (2005). Fundamentals of Wireless Communication, Cambridge University Press.","DOI":"10.1017\/CBO9780511807213"},{"key":"ref_6","unstructured":"Papoulis, A. (1989). Probability, Random Varables, and Stochastic Processes, McGraw-Hill."},{"key":"ref_7","unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, John Wiley & Sons, Inc."},{"key":"ref_8","unstructured":"Wikipedia http:\/\/en.wikipedia.org\/wiki\/N-sphere."},{"key":"ref_9","unstructured":"Vesely, F. http:\/\/homepage.univie.ac.at\/franz.vesely\/sp.english\/sp\/sp.html."},{"key":"ref_10","unstructured":"Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I. (1986). Integrals and Series, Gordon and Breach Sci. Publ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1109\/18.746779","article-title":"Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading","volume":"45","author":"Marzetta","year":"1999","journal-title":"IEEE Trans. Inform. Theory"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/4\/722\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:21:10Z","timestamp":1760221270000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/4\/722"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,11,20]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2008,12]]}},"alternative-id":["e10040722"],"URL":"https:\/\/doi.org\/10.3390\/e10040722","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2008,11,20]]}}}