Detection and estimation of improper complex random signals
Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen-Loeve (K-L) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It pro...
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| Veröffentlicht in: | IEEE transactions on information theory 2005-01, Vol.51 (1), p.306-312 |
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| creator | Schreier, P.J. Scharf, L.L. Mullis, C.T. |
| description | Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen-Loeve (K-L) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It produces two sets of eigenvalues and improper observable coordinates. We then use the K-L expansion to solve the problems of detection and estimation of improper complex random signals in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. In particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and mean-squared error (MSE), respectively, can be as large as a factor of 2. In a communications example, we show how this finding generalizes the result that coherent processing enjoys a 3-dB gain over noncoherent processing. |
| doi_str_mv | 10.1109/TIT.2004.839538 |
| format | Article |
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Since the Karhunen-Loeve (K-L) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It produces two sets of eigenvalues and improper observable coordinates. We then use the K-L expansion to solve the problems of detection and estimation of improper complex random signals in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. In particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and mean-squared error (MSE), respectively, can be as large as a factor of 2. 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Since the Karhunen-Loeve (K-L) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It produces two sets of eigenvalues and improper observable coordinates. We then use the K-L expansion to solve the problems of detection and estimation of improper complex random signals in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. In particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and mean-squared error (MSE), respectively, can be as large as a factor of 2. In a communications example, we show how this finding generalizes the result that coherent processing enjoys a 3-dB gain over noncoherent processing.</description><subject>Additive white noise</subject><subject>Applied sciences</subject><subject>Australia</subject><subject>Codes</subject><subject>Coherence</subject><subject>Deflection</subject><subject>Detection</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Eigenvalues</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Error analysis</subject><subject>Error detection</subject><subject>estimation</subject><subject>Exact sciences and technology</subject><subject>Gain</subject><subject>Gain measurement</subject><subject>Gaussian</subject><subject>improper complex random signal</subject><subject>Information technology</subject><subject>Information, signal and communications theory</subject><subject>Karhunen-LoÈve (K-L) expansion</subject><subject>nonstationary process</subject><subject>Object detection</subject><subject>Particle measurements</subject><subject>Performance gain</subject><subject>Probability</subject><subject>Random signals</subject><subject>Signal analysis</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal, noise</subject><subject>Telecommunications and information theory</subject><subject>widely linear transformations</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kM9LwzAUx4MoOKdnD16KoJ665WeT4Enmr8HAyzyHNH2VjrapzQb635vawcCDp8cjn_fyfR-ELgmeEYL1fL1czyjGfKaYFkwdoQkRQqY6E_wYTTAmKtWcq1N0FsImtlwQOkH3j7AFt618m9i2SCBsq8b-tr5MqqbrfQd94nzT1fCV9JHxTRKqj9bW4RydlLHAxb5O0fvz03rxmq7eXpaLh1XqmCLbNM-1tIV1mhROZrnIcmypA-ZKSmQhCklYbkFjVTAsseCYgXSSlYxmkBVOsCm6G_fGNJ-7GNE0VXBQ17YFvwtG6YwyLpSK5O2_JFXxcEEG8PoPuPG7fjjKEC10zKGGf-cj5HofQg-l6fpop_82BJvBuYnOzeDcjM7jxM1-rQ3O1mX05apwGMs4lwzTyF2NXAUAh2cmpcCK_QDiW4ki</recordid><startdate>200501</startdate><enddate>200501</enddate><creator>Schreier, P.J.</creator><creator>Scharf, L.L.</creator><creator>Mullis, C.T.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Since the Karhunen-Loeve (K-L) expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It produces two sets of eigenvalues and improper observable coordinates. We then use the K-L expansion to solve the problems of detection and estimation of improper complex random signals in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. In particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and mean-squared error (MSE), respectively, can be as large as a factor of 2. In a communications example, we show how this finding generalizes the result that coherent processing enjoys a 3-dB gain over noncoherent processing.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2004.839538</doi><tpages>7</tpages></addata></record> |
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| subjects | Additive white noise Applied sciences Australia Codes Coherence Deflection Detection Detection, estimation, filtering, equalization, prediction Eigenvalues Eigenvalues and eigenfunctions Error analysis Error detection estimation Exact sciences and technology Gain Gain measurement Gaussian improper complex random signal Information technology Information, signal and communications theory Karhunen-LoÈve (K-L) expansion nonstationary process Object detection Particle measurements Performance gain Probability Random signals Signal analysis Signal and communications theory Signal processing Signal, noise Telecommunications and information theory widely linear transformations |
| title | Detection and estimation of improper complex random signals |
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