Table 1 Theoretical value of cyclic spectrum at different frequency points of mixed double-signal.
From: Modulation recognition method of mixed signals based on cyclic spectrum projection
Serial number | Frequency point | Type | BPSK + QPSK | BPSK + OQPSK | QPSK + OQPSK | |||
|---|---|---|---|---|---|---|---|---|
1 | \(\alpha = \frac{{1}}{T}\) \(f{ = }f_{c}\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}{ + }{{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \({{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.81 | 1:1 | 0.41 | 1:1 | 1.00 | |||
1:4 | 1.00 | 1:4 | 0.20 | 1:4 | 0.25 | |||
4:1 | 0.51 | 4:1 | 0.41 | 4:1 | 1.00 | |||
2 | \(\alpha = \frac{{1}}{T}\) \(f{ = }f_{c} \pm \frac{\alpha }{{4}}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{{2}TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{QPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{QPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.54 | 1:1 | 0.27 | 1:1 | 0.67 | |||
1:4 | 0.67 | 1:4 | 0.13 | 1:4 | 0.17 | |||
4:1 | 0.34 | 4:1 | 0.27 | 4:1 | 0.67 | |||
3 | \(\alpha = \frac{{1}}{T}\) \(f{ = }f_{c} \pm \frac{\alpha }{{2}}\) | Theoretical value | 0 | 0 | 0 | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | 0 | |||
1:4 | 0 | 1:4 | 0 | 1:4 | 0 | |||
4:1 | 0 | 4:1 | 0 | 4:1 | 0 | |||
4 | \(\alpha = \frac{{1}}{T}\) \(f{ = }f_{c} \pm \frac{{{3}\alpha }}{{4}}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}{ + }{{{2}TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{QPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{QPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.32 | 1:1 | 0.16 | 1:1 | 0.40 | |||
1:4 | 0.40 | 1:4 | 0.08 | 1:4 | 0.10 | |||
4:1 | 0.20 | 4:1 | 0.16 | 4:1 | 0.40 | |||
5 | \(\alpha = \frac{{1}}{T}\) \(f{ = }f_{c} \pm \alpha\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.27 | 1:1 | 0.14 | 1:1 | 0.33 | |||
1:4 | 0.33 | 1:4 | 0.07 | 1:4 | 0.08 | |||
4:1 | 0.17 | 4:1 | 0.14 | 4:1 | 0.33 | |||
6 | \(\alpha = \frac{{2}}{T}\) \(f{ = }f_{c}\) | Theoretical value | 0 | 0 | 0 | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | 0 | |||
1:4 | 0 | 1:4 | 0 | 1:4 | 0 | |||
4:1 | 0 | 4:1 | 0 | 4:1 | 0 | |||
7 | \(\alpha = \frac{{2}}{T}\) \(f{ = }f_{c} \pm \frac{\alpha }{{4}}\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.27 | 1:1 | 0.27 | 1:1 | 0.67 | |||
1:4 | 0.33 | 1:4 | 0.33 | 1:4 | 0.42 | |||
4:1 | 0.17 | 4:1 | 0.17 | 4:1 | 0.42 | |||
8 | \(\alpha = \frac{{2}}{T}\) \(f{ = }f_{c} \pm \frac{\alpha }{{2}}\) | Theoretical value | 0 | 0 | 0 | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | 0 | |||
1:4 | 0 | 1:4 | 0 | 1:4 | 0 | |||
4:1 | 0 | 4:1 | 0 | 4:1 | 0 | |||
9 | \(\alpha = \frac{{2}}{T}\) \(f{ = }f_{c} \pm \frac{{{3}\alpha }}{{4}}\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{10\uppi }}^{2} }}} \right. \kern-0pt} {{{10\uppi }}^{2} }}{ + }{{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{{10\uppi }}^{2} }}} \right. \kern-0pt} {{{10\uppi }}^{2} }}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{10\uppi }}^{2} }}} \right. \kern-0pt} {{{10\uppi }}^{2} }}{ + }{{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{{10\uppi }}^{2} }}} \right. \kern-0pt} {{{10\uppi }}^{2} }}\) | \({{TE_{{{\text{QPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{QPSK}}}} } {{{10\uppi }}^{2} }}} \right. \kern-0pt} {{{10\uppi }}^{2} }}{ + }{{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{{10\uppi }}^{2} }}} \right. \kern-0pt} {{{10\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.08 | 1:1 | 0.08 | 1:1 | 0.20 | |||
1:4 | 0.10 | 1:4 | 0.10 | 1:4 | 0.13 | |||
4:1 | 0.05 | 4:1 | 0.05 | 4:1 | 0.13 | |||
10 | \(\alpha = \frac{{2}}{T}\) \(f{ = }f_{c} \pm \alpha\) | Theoretical value | 0 | 0 | 0 | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | 0 | |||
1:4 | 0 | 1:4 | 0 | 1:4 | 0 | |||
4:1 | 0 | 4:1 | 0 | 4:1 | 0 | |||
11 | \(\alpha \ge \frac{{3}}{T}\) | Theoretical value | \(\ll {{TE} \mathord{\left/ {\vphantom {{TE} {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \(\ll {{TE} \mathord{\left/ {\vphantom {{TE} {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \(\ll {{TE} \mathord{\left/ {\vphantom {{TE} {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | << 0.1 | 1:1 | << 0.1 | 1:1 | << 0.1 | |||
1:4 | << 0.1 | 1:4 | << 0.1 | 1:4 | << 0.1 | |||
4:1 | << 0.1 | 4:1 | << 0.1 | 4:1 | << 0.1 | |||
12 | \(\alpha = {2}f_{c}\) \(f{ = 0}\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {4}}} \right. \kern-0pt} {4}}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {4}}} \right. \kern-0pt} {4}}\) | / | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 1.00 | 1:1 | 1.00 | 1:1 | / | |||
1:4 | 0.49 | 1:4 | 0.49 | 1:4 | / | |||
4:1 | 1.00 | 4:1 | 1.00 | 4:1 | / | |||
13 | \(\alpha = {2}f_{c} \pm \frac{{1}}{T}\) \(f{ = 0}\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}{ + }{{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \({{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.41 | 1:1 | 0.81 | 1:1 | 1.00 | |||
1:4 | 0.20 | 1:4 | 1.00 | 1:4 | 1.00 | |||
4:1 | 0.41 | 4:1 | 0.51 | 4:1 | 0.25 | |||
14 | \(\alpha = {2}f_{c} \pm \frac{{1}}{T}\) \(f{ = }\frac{1}{4T}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{{2}TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{OQPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{OQPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.27 | 1:1 | 0.54 | 1:1 | 0.67 | |||
1:4 | 0.13 | 1:4 | 0.67 | 1:4 | 0.67 | |||
4:1 | 0.27 | 4:1 | 0.34 | 4:1 | 0.17 | |||
15 | \(\alpha = {2}f_{c} \pm \frac{{1}}{T}\)\(f{ = }\frac{{1}}{{{2}T}}\) | Theoretical value | 0 | 0 | 0 | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | 0 | |||
1:4 | 0 | 1:4 | 0 | 1:4 | 0 | |||
4:1 | 0 | 4:1 | 0 | 4:1 | 0 | |||
16 | \(\alpha = {2}f_{c} \pm \frac{{1}}{T}\)\(f{ = }\frac{{3}}{{{4}T}}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}{ + }{{{2}TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{OQPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{OQPSK}}}} } {{{5\uppi }}^{2} }}} \right. \kern-0pt} {{{5\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.16 | 1:1 | 0.32 | 1:1 | 0.40 | |||
1:4 | 0.08 | 1:4 | 0.40 | 1:4 | 0.40 | |||
4:1 | 0.16 | 4:1 | 0.20 | 4:1 | 0.10 | |||
17 | \(\alpha = {2}f_{c} \pm \frac{{1}}{T}\) \(f{ = }\frac{{1}}{T}\) | Theoretical value | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}{ + }{{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{TE_{{{\text{OQPSK}}}} } \mathord{\left/ {\vphantom {{TE_{{{\text{OQPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.14 | 1:1 | 0.27 | 1:1 | 0.33 | |||
1:4 | 0.07 | 1:4 | 0.33 | 1:4 | 0.33 | |||
4:1 | 0.14 | 4:1 | 0.17 | 4:1 | 0.08 | |||
18 | \(\alpha = {2}f_{c} \pm \frac{{2}}{T}\) \(f{ = 0}\) | Theoretical value | 0 | 0 | / | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | / | |||
1:4 | 0 | 1:4 | 0 | 1:4 | / | |||
4:1 | 0 | 4:1 | 0 | 4:1 | / | |||
19 | \(\alpha = {2}f_{c} \pm \frac{{2}}{T}\)\(f{ = }\frac{{1}}{{{4}T}}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{15\uppi }}^{2} }}} \right. \kern-0pt} {{{15\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{15\uppi }}^{2} }}} \right. \kern-0pt} {{{15\uppi }}^{2} }}\) | / | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.05 | 1:1 | 0.05 | 1:1 | / | |||
1:4 | 0.03 | 1:4 | 0.03 | 1:4 | / | |||
4:1 | 0.05 | 4:1 | 0.05 | 4:1 | / | |||
20 | \(\alpha = {2}f_{c} \pm \frac{{2}}{T}\)\(f{ = }\frac{{1}}{{{2}T}}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{3\uppi }}^{2} }}} \right. \kern-0pt} {{{3\uppi }}^{2} }}\) | / | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.27 | 1:1 | 0.27 | 1:1 | / | |||
1:4 | 0.13 | 1:4 | 0.13 | 1:4 | / | |||
4:1 | 0.27 | 4:1 | 0.27 | 4:1 | / | |||
21 | \(\alpha = {2}f_{c} \pm \frac{{2}}{T}\)\(f{ = }\frac{{3}}{{{4}T}}\) | Theoretical value | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{7\uppi }}^{2} }}} \right. \kern-0pt} {{{7\uppi }}^{2} }}\) | \({{{2}TE_{{{\text{BPSK}}}} } \mathord{\left/ {\vphantom {{{2}TE_{{{\text{BPSK}}}} } {{{7\uppi }}^{2} }}} \right. \kern-0pt} {{{7\uppi }}^{2} }}\) | / | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0.12 | 1:1 | 0.12 | 1:1 | / | |||
1:4 | 0.06 | 1:4 | 0.06 | 1:4 | / | |||
4:1 | 0.12 | 4:1 | 0.12 | 4:1 | / | |||
22 | \(\alpha = {2}f_{c} \pm \frac{{2}}{T}\) \(f{ = }\frac{{1}}{T}\) | Theoretical value | 0 | 0 | / | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | 0 | 1:1 | 0 | 1:1 | / | |||
1:4 | 0 | 1:4 | 0 | 1:4 | / | |||
4:1 | 0 | 4:1 | 0 | 4:1 | / | |||
23 | \(\alpha { < 2}f_{c} { - }\frac{{2}}{T}\)\(\alpha { > 2}f_{c} { + }\frac{{2}}{T}\) | Theoretical value | \(\ll {{TE} \mathord{\left/ {\vphantom {{TE} {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \(\ll {{TE} \mathord{\left/ {\vphantom {{TE} {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | \(\ll {{TE} \mathord{\left/ {\vphantom {{TE} {{\uppi }^{2} }}} \right. \kern-0pt} {{\uppi }^{2} }}\) | |||
Maximum normalized spectral value | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{QPSK}}}}\) | / | \(E_{{{\text{BPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | \(E_{{{\text{QPSK}}}} {:}E_{{{\text{OQPSK}}}}\) | / | ||
1:1 | \(\ll {0}{\text{.1}}\) | 1:1 | \(\ll {0}{\text{.1}}\) | 1:1 | \(\ll {0}{\text{.1}}\) | |||
1:4 | \(\ll {0}{\text{.1}}\) | 1:4 | \(\ll {0}{\text{.1}}\) | 1:4 | \(\ll {0}{\text{.1}}\) | |||
4:1 | \(\ll {0}{\text{.1}}\) | 4:1 | \(\ll {0}{\text{.1}}\) | 4:1 | \(\ll {0}{\text{.1}}\) | |||
