SCIENCE CHINA Information Sciences, Volume 59, Issue 12: 122303(2016) https://doi.org/10.1007/s11432-015-5493-5

Generalized spatial representation for digital modulation and its potential application

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  • ReceivedAug 10, 2015
  • AcceptedOct 20, 2015
  • PublishedJun 12, 2016


Constellation mapping has provided a great convenience to measure the performance of digital signal modulation in Euclid space. However, traditional in-phase and quadrature (IQ) plane is difficult to express the frequency modulation scheme such as minimum shift keying (MSK) and the time domain modulation such as cyclic code shift keying (CCSK). How to represent the digital signal modulation visually through constellation mapping is an attractive problem. To address this issue, in this paper, the combined frequency and phase modulation are utilized to define a new kind of constellation mapping, where the phase and frequency are quantized to the same elements. The uniform geometric construction for combined phase and frequency modulation is redefined in the 3D cylindrical coordinate system based on frequency ($\bm{f}$), in-phase component ($\bm{I}$) and quadrature component ($\bm{Q}$). In the new coordinates, the quadrature frequency-phase shift keying (QFPSK) is produced by the QPSK with dimensional rotation matrix and denoted by the reduced dual quaternion. Furthermore, the spatial extension from QFPSK to chirp cyclic shift keying (Chirp CSK) is analyzed with bandwidth efficiency and energy efficiency. At last, the QFPSK is combined with the 2D OFDM, yielding the image OFDM system. Experimental results verify the effectiveness of QFPSK in the proposed system with the time-varying wireless channel and frequency selective fading channel respectively.



This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61501051, 61421001), and Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20121101130001).


[1] Proakis J G, Salehi M. Digital Communications. 5th ed. New York: McGraw-Hill, 2007. 227--229. Google Scholar

[2] Hu S, Bi G A, Guan Y L, et al. Spectrally efficient transform domain communication system with quadrature cyclic code shift keying. IET Commun, 2013, 7: 382-390 CrossRef Google Scholar

[3] Kang S G, Chen Z, Kim J Y, et al. Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN. IEEE Trans Signal Process, 2011, 59: 6267-6272 CrossRef Google Scholar

[4] Boutros J, Viterbo E. Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel. IEEE Trans Inf Theory, 1998, 44: 1453-1467 CrossRef Google Scholar

[5] Saha D, Birdsall T G. Quadrature-quadrature phase-shift keying. IEEE Trans Commun, 2010, 37: 437-3409 Google Scholar

[6] Kang S G. An OFDM with 3D signal mapper and IDFT modulator. IEEE Commun Lett, 2008, 12: 871-873 CrossRef Google Scholar

[7] Lee H, Paulraj A. MIMO systems based on modulation diversity. IEEE Trans Commun, 2010, 58: 3405-3409 CrossRef Google Scholar

[8] Cheng S, Seshadri R I, Valenti M C, et al. The capacity of noncoherent continuous-phase frequency shift keying. In: Proceedings of the 41st Annual Conference on Information Sciences and Systems, Baltimore, 2007. 396--401. Google Scholar

[9] Cheng S, Valenti M C, Torrieri D. Coherent continuous-phase frequency-shift keying: parameter optimization and code design. IEEE Trans Wirel Commun, 2009, 8: 1792-1802 CrossRef Google Scholar

[10] Shi P F, Huan H, Tao R. Waveform design for higher-level 3D constellation mappings and its construction based on regular tetrahedron cells. Sci China Inf Sci, 2015, 58: 082302-1802 Google Scholar

[11] Chen Z, Choi E C, Kang S G. Closed-form expressions for the symbol error probability of 3D OFDM. IEEE Commun Lett, 2010, 14: 112-114 CrossRef Google Scholar

[12] Liu W. Antenna array signal processing for a quaternion-valued wireless communication system. In: Proceedings of the IEEE Benjamin Franklin Symposium on Microwave and Antenna Sub-systems (BenMAS), Philadelphia, 2014. 1--3. Google Scholar

[13] Ma X, Wang S, Zhang S, et al. High bit rate pulse position modulation signal generation based on rare-earth-doped crystals. IEEE Commun Lett, 2015, 19: 179-182 CrossRef Google Scholar

[14] Ell T A, Sangwine S J. Hypercomplex Fourier transforms of color image. IEEE Trans Image Process, 2007, 16: 22-35 CrossRef Google Scholar

[15] Le B N, Sangwine S J, Ell T A. Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform. Signal Process, 2014, 94: 308-318 CrossRef Google Scholar

[16] Wang L F, Yu Z Y, Pan C H. A unified level set framework utilizing parameter priors for medical image segmentation. Sci China Inf Sci, 2013, 56: 110902-318 Google Scholar

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