The technique of SNR estimation is one of the key technologies in adaptive frequency hopping system. The methods of channel quality estimation for non-linear continuous phase modulation (CPM) signals have some limitations. Therefore, the algorithm of channel quality estimation for CPM signals is worthy of further study. Some similar phase characteristics between sampling CPM and MPSK motivate us to propose a channel estimation algorithm with applications to nonlinear CPM using linear modulation signal processing. A comprehensive analysis of LDPC-CPM schemes using proposed algorithm is presented, and simulation results indicate that the proposed method can not only estimate channel quality well but also make the normalized MSE (NMSE) of SNR estimate close to/less than 0.1 dB at SNR of 4 dB using short block codes. It shows that the algorithm in this paper is effective enough to estimate the signal to noise ratio (SNR). Meanwhile, the algorithm in this paper reduces the complexity of computation compared with other traditional algorithms.
Adaptive frequency hopping is the core technology in modern military ultra- short electric wave communication. Channel quality evaluation is the core of adaptive frequency hopping system. According to the signal received from hopping channels, we can use the real-time channel quality judgment rules to analyze the quality of the channel, then we can determine whether the jump frequency is interfering the normal communication [
CPM is a constant envelope modulation since the phase changes continuously, and it overcomes the phase mutation occurred when symbols convert mutually. At the same time, the waveform has good roll-off characteristics. Because of its characteristics of continuous phase, we can use the similar characteristics of CPM carrier phase with MPSK at the final value
Now there are many ways of achieving wireless communication in signal to noise ratio estimation. Generally hopping systems adopt the following three classical algorithms to estimate SNR depending on their conditions: high-order cumulates estimator, data fitting estimator and eigenvalue decomposition of signal auto-correlation matrix estimator [
CPM is a constant envelope modulation, defined as
where
The carrier phase of continuous phase modulation is
where
The trajectory of the CPM phase can be represented as a tree phase. Using a tree to represent the phase trajectories can truly reflect from one state to another when the phase changes. The phase of CPM can also be used as a simple method of representation. For example, only considered to getting phase within the symbol duration time, the phase of CPM is changed. It can’t reflect the phase change between adjacent states truly, but we can simplify the analysis phase. Now we can derive the carrier phase in the case of the final value of time when
If we use REC pulse for CPM, the integration waveform
For complete response LRC pulse C PM signal satisfy the above derivation of integral waveform
non-final value time
The following discussion is limited to take the same modulation index h. The carrier phase of the CPM in final time is selected as
So we can see that in the final phase time
where
Hypothesis
We generally assumed that the transmission signal of each sequence is identically distributed and mutually independent, then we can get
Fourth-order copulation of complex Gaussian noise is identically zero, and it is independent of each other between signal and noise. So we can get the following formulas from above formulas and assumptions as
where
This SNR estimation algorithm flow is as follows:
1) Use the received signal sample sequence
2) Calculated variance estimates of noise component
3) Estimated energy of the transmitted signals
4) According to the formulas above to calculate the estimated value of SNR:
We judge the channel quality by the results of SNR estimation, and detect the frequency which is interfered and use a better quality of different frequencies to replace interfered frequency points respectively to achieve adaptive frequency hopping [
When M = 8 in CPM signal, the information block length N uses the value as 80, 160, 320 respectively, to get the mean and NMSE values of SNR estimate between 0 - 20 dB. We can see from
When information block length N is 320 for CPM signal, M uses the value as 2, 4, 8 respectively, h = 1/4, to get the mean and standard deviation values of SNR estimate between 0 - 20 dB.
of the modulation are almost consistent. Description of the algorithm for different decimal M for CPM modulation is insensitive, therefore, the algorithm is apply for different M.
Higher order statistical moments algorithm uses the relationship between the higher-order statistical moments to estimate the SNR. It uses the second moment and fourth moment in computation. The classic blind channel estimation methods are based on the data received from the correlation matrix (or cross- correlation matrix), such as subspace method (SS), Minimum Noise Subspace (MNS), using Singular Value Decomposition (SVD) or Eigenvaue Decomposition
(EVD) to achieve blind channel estimation method. The calculation complexity of SVD is
By analyze and derive the phase of CPM modulation signal, we find that the phase of CPM signal after sampling in the final time
This paper is funded by the International Exchange Program of Harbin Engineering University for Innovation-oriented Talents Cultivation, the Open Research Fund of State Key Laboratory of Tianjin Key Laboratory of Intelligent Information Processing in Remote Sensing (Grant No. 2016-ZW-KFJJ-01), the National Natural Science Foundation of China (Grant No. 61403093), the Assisted Project by Heilongjiang Province of China Postdoctoral Funds for Scientific Research Initiation (Grant No. LBH-Q14048), and the Fundamental Research Funds for the Central Universities (Grant No. HEUCF160813).
Xue, R., Sun, B.B. and Zhu T.L. (2017) An Effective Method of SNR Estimation for LDPC-CPM. Int. J. Communications, Network and System Sciences, 10, 146-153. https://doi.org/10.4236/ijcns.2017.105B014