Generalized spatial representation for digital modulation and its potential application

数字信号调制的广义空间表征及其应用

Abstract

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 (f), in-phase component (I) and quadrature component (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.

创新点

信号的维度空间由频率和时间的乘积组成, 决定了数字信号调制的边界。针对每个给定的维度点, 通过二维星座图能够直观的表征出传统的数字信号调制如MPSK及MQAM的空间结构, 并借助于欧氏距离的定义量化了信号调制的误码率。然而传统的星座图表征无法衡量维度点之间调制的量化表征, 如频域MFSK调制,时域的CCSK调制等, 本文基于此, 初步提出了频域与传统IQ平面结合的广义空间表征及基于双缩四元数的数学表征, 并借助于广义欧式距离给出了MSK等固有信号空间的三维量化关系。最后借助于三维空间表征, 我们将OFDM调制映射为不同类型的拓扑图, 构建新型的空间结构关系。

This is a preview of subscription content, access via your institution.

References

  1. 1

    Proakis J G, Salehi M. Digital Communications. 5th ed. New York: McGraw-Hill, 2007. 227–229

    Google Scholar 

  2. 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

    MathSciNet  Article  MATH  Google Scholar 

  3. 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

    MathSciNet  Article  Google Scholar 

  4. 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

    MathSciNet  Article  MATH  Google Scholar 

  5. 5

    Saha D, Birdsall T G. Quadrature-quadrature phase-shift keying. IEEE Trans Commun, 2010, 37: 437–3409

    Article  Google Scholar 

  6. 6

    Kang S G. An OFDM with 3D signal mapper and IDFT modulator. IEEE Commun Lett, 2008, 12: 871–873

    Article  Google Scholar 

  7. 7

    Lee H, Paulraj A. MIMO systems based on modulation diversity. IEEE Trans Commun, 2010, 58: 3405–3409

    Article  Google Scholar 

  8. 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. 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

    Article  Google Scholar 

  10. 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

    Article  Google Scholar 

  11. 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

    Article  Google Scholar 

  12. 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. 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

    Article  Google Scholar 

  14. 14

    Ell T A, Sangwine S J. Hypercomplex Fourier transforms of color image. IEEE Trans Image Process, 2007, 16: 22–35

    MathSciNet  Article  MATH  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. 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

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hao Huan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huan, H., Shi, P., Yan, X. et al. Generalized spatial representation for digital modulation and its potential application. Sci. China Inf. Sci. 59, 122303 (2016). https://doi.org/10.1007/s11432-015-5493-5

Download citation

Keywords

  • quadrature frequency-phase shift keying (QFPSK)
  • chirp cyclic shift keying
  • spatial constellation mapping
  • image OFDM system
  • wireless communication

关键词

  • 正交相频联合调制
  • chirp循环移位调制
  • 空间星座图映射
  • OFDM调制图像化
  • 无线通信