In this paper, an improved frequency offset estimation algorithm is proposed. It can effectively utilize pilot symbols in orthogonal frequency division multiplexing (OFDM) signals based on the Digital Radio Mondiale (DRM) system. In order to reduce the computational difficulty, the difference values of adjacent pilot symbols in the DRM system are sequentially combined into a pilot difference set. The pilot difference set is analyzed by inductive statistics so that the frequency offset estimator has higher calculation efficiency and accuracy. Through the induction statistics of multiple groups of symbols, the contingency of results can be effectively avoided. By comparing the performance of the proposed frequency offset estimator with that of the traditional estimators, the proposed algorithm has higher frequency offset estimation accuracy.

The system named as Digital Radio Mondiale (DRM) originally mainly used a digital radio broadcasting specification below 30 MHz [

The DRM system multiplexes three logical channels, that is, the fast access channel (FAC), the main service channel (MSC), and the service description channel (SDC) [

Due to its outstanding spectrum utilization efficiency, orthogonal frequency division multiplexing (OFDM) has been successfully adopted by multitudinous wireless communication systems on frequency-selective fading channels [

In terms of a receiver, frequency offset has a crucial impact on the quality of the audio. It has occurred due to the Doppler effect, multipath phenomena, and noise interference [

In general, carrier frequency offset estimation can be roughly divided into two parts: post-FFT integer frequency offset [

Aiming at the OFDM system of frequency-selective fading channels, Jiang et al. proposed a frequency offset estimator based on a frequency-domain training sequence [

Under the frequency-selective fading channel, the problem of sampling frequency offset estimation based on the OFDM broadcasting system was proposed by Jung and You [

In this paper, based on the received audio data, the method of estimating the integer frequency offset by using an inductive method and calculating the fractional frequency offset by using the correlation of the pilots has been presented. In order to prove the effectiveness of this method, the mean square error (MSE) of each method is calculated and compared. Based on theoretical analysis and simulation, the proposed scheme is verified and it is proven that compared with the original methods, the calculation difficulty in this paper is significantly reduced and the accuracy is higher.

The DRM transmitting signal consists of a series of OFDM symbols, each of which contains a guard interval and a useful part of the symbol. Each symbol is the sum of

Carrier numbers for each robust mode.

Robustness mode | Carrier | Spectrum occupancy (kHz) | |||||
---|---|---|---|---|---|---|---|

4.5 | 5 | 9 | 10 | 18 | 20 | ||

A | 2 | 2 | -102 | -114 | -98 | -110 | |

102 | 114 | 102 | 114 | 314 | 350 | ||

B | 1 | 1 | -91 | -103 | -87 | -99 | |

91 | 103 | 91 | 103 | 279 | 311 | ||

C | — | — | — | -69 | — | -67 | |

— | — | — | 69 | — | 213 |

Each transmission superframe consists of three transmission frames, including

For time references and frequency references in robust modes A, B, and C, the phases

Definition of phase parameters.

Robustness mode | Carrier index, | Phase index, |
---|---|---|

A | 18 | 205 |

54 | 836 | |

72 | 215 | |

B | 16 | 331 |

48 | 651 | |

64 | 555 | |

C | 11 | 214 |

33 | 392 | |

44 | 242 |

For gain references, the phases are specified.

Among them, the values of

Parameter definition of matrix

{512, | 0, | 512, | 0, | 512}, | |

{0, | 512, | 0, | 512, | 0}, | |

{512, | 0, | 512, | 0, | 512}} | |

{0, | 57, | 164, | 64, | 12}, | |

{168, | 255, | 161, | 106, | 118}, | |

{25, | 232, | 132, | 233, | 38}} |

Combining the above, the transmitted signal is represented by the following expression:

In this section, the traditional algorithms that use the characteristics of the pilot symbols in the DRM system to estimate integer frequency offset and the ML method to estimate fractional frequency offset are mainly described.

The conventional integral frequency offset estimation method utilizes the correlation between receiver symbols and time derivatives. The receiver uses frequency reference cells (FRCs) to detect the existence of the received signal and estimate its integer frequency offset. The frequency references can be used for various channel tracking processes [

A FRC is defined.

An integer frequency synchronization algorithm for the DRM system based on frequency references is proposed. The algorithm is introduced below [

Firstly, the algorithm needs Fast Fourier Transform (FFT) operation to estimate the power spectrum of receiver symbols.

In the case of frequency offset, the peak value of a pilot symbol will be offset. The integer frequency offset can be obtained by the displacement detection of the pilot symbols.

A very small residual frequency offset remains unchanged after the integer frequency offset is estimated by the pilot symbols inserted into the DRM signal subcarriers [

Assuming that integral frequency offset has been compensated, the remaining fractional frequency offset is temporarily set as

The estimated time delay is expressed as follows.

By this traditional algorithm, the fractional frequency offset is obtained.

The traditional method mainly uses the power factor of the pilot symbols to calculate the correlation. Due to noise and multipath interference, the power factor of the pilot symbols is inevitably affected so that the correlation peak may be weakened. Combined with the above analysis, the implementation of this algorithm is complicated and unstable.

In the case of frequency selectivity, a pilot-assisted-based estimation method is proposed [

First of all, after FFT demodulation, the OFDM symbol received at the

The above method is used to estimate the frequency offset of the system as

Traditional algorithm C uses the correlation of pilots to construct an angle vector for frequency offset estimation [

The phase of the power spectrum is obtained.

Define the angle vector as

Thus, the frequency offset can be obtained.

Traditional method D proposes a scheme to estimate frequency offset by cyclic delay and pilot mode [

Supposing the channels

Then, use the GRC mode with the highest channel transfer function power to estimate the frequency offset.

The maximum value of the channel transfer function can be approximated as the following formula:

The frequency offset is estimated.

This method selects the time delay by looking for the delay that makes the channel transfer function power different. Then, the frequency offset is estimated once in the four repeated pilot symbols to maximize the power of the channel transfer function. Therefore, these conditions are used to improve the frequency offset synchronization performance.

In this part, an algorithm of frequency offset estimation based on inductive reasoning and correlation calculation of symbols is proposed. Among them, the integer frequency offset estimation is mainly based on the time reference values of the fixed positions in the standard. The fractional frequency offset is mainly estimated by the correlation of two adjacent symbols in the transmission frame.

First of all, the transmission signal with time reference values is called the first signal of the transmission frame. The first signal is locked by the timing synchronization precision method.

The length of a signal is intercepted from its maximum position. The signal removed the guard interval and FFT operation is performed.

Assume that

After integer frequency offset occurs,

Suppose that when

By this inductive statistical method, the integer frequency offset is estimated.

Based on the position of the first signal obtained in the above section, the angular difference of each position corresponding to the guard interval between adjacent signals will be obtained.

Through the above method, the frequency offsets obtained by estimating multiple groups of symbols are sequentially placed in the set

The previous algorithms only preserve the pilot phase factor in the correlation calculation. Considering the complexity of the algorithm, only a small number of continuous symbols are selected. The algorithm proposed in this paper integrates the differences between pilots into a set and estimates multiple groups of symbols, which greatly reduces the contingency of experimental results. With more continuous signals, the estimation accuracy is effectively improved.

In the case of a large calculation scale, the time complexity of the algorithm is calculated by

In this section, simulations of the MSE of the estimated frequency offset under the different SNR and channel conditions will be obtained. The different parameters of the four paths contained in each channel are shown in Table

The channel parameters.

Path | Property | Channel 1 | Channel 2 | Channel 3 |
---|---|---|---|---|

1 | Gain | 1 | 1 | 1 |

Delay (ms) | 0 | 0 | 0 | |

Df (Hz) | 0 | 0 | 0 | |

2 | Gain | 0 | 1 | 1 |

Delay (ms) | 0 | 2 | 2 | |

Df (Hz) | 0 | 0 | 1.2 | |

3 | Gain | 0 | 0 | 0.25 |

Delay (ms) | 0 | 4 | 4 | |

Df (Hz) | 0 | 2 | 2.4 | |

4 | Gain | 0 | 0 | 0.00625 |

Delay (ms) | 0 | 0 | 6 | |

Df (Hz) | 0 | 0 | 7.2 |

All frequencies mentioned in the simulation experiment are normalized frequencies [

Figure

Timing synchronization accuracy.

Define the MSE for the frequency synchronization as

By introducing Equations (

MSE of the conventional algorithms and the proposed algorithm in channel 1.

MSE of the conventional algorithms and the proposed algorithm in channel 2.

MSE of the conventional algorithms and the proposed algorithm in channel 3.

Figures

Through the above calculation method of MSE, Figure

MSE of the proposed algorithm in each channel.

It can be concluded from the simulation diagram that the channel environment has a significant influence on the accuracy of frequency offset estimation. Obviously, under the same SNR, the better the channel environment, the smaller the MSE of the frequency offset estimation, which proves that the channel environment with better quality can improve the accuracy of frequency offset estimation to a certain extent.

In this paper, according to the characteristics of the inductive statistics method and pilot symbols, a frequency offset estimation algorithm for the DRM system is proposed. Then, this algorithm effectively utilizes the pilot phase factor. In the correlation calculation of fractional frequency offset estimation, the structure of an angle vector availably reduces the influence of multipath and noise. By comparing the MSE between the proposed algorithm and the traditional algorithms, the simulation results show that the proposed algorithm can more effectively improve the accuracy of frequency offset estimation.

Upon reasonable request and with the permission of all authors, the data used to support the algorithm results of this article can be obtained from the corresponding authors.

The authors declare that there is no conflict of interest in the publication of this paper.

This work was funded by the Shaanxi Province Science and Technology Coordination and Innovation Project (Key Technology (Chain) for Resource-Oriented Industries): High-Efficiency Multistandard Digital Broadcasting Pointer (Project Number 2011KTCL01-10).