01-12-2019 | Research | Issue 1/2019 Open Access

# Deterministic pilot pattern allocation optimization for sparse channel estimation based on CS theory in OFDM system

## 1 Introduction

## 2 CS-based channel estimation optimization problem

_{P}are chosen as transmitting pilot in OFDM systems. The allocation position of the pilot pattern is \( K=\left({k}_1,\cdots, {k}_{N_p}\right)\kern0.5em \left(1\le {k}_1\le \cdots \le {k}_{N_p}\le N\right) \). The relationship between the received pilot and transmitted pilot is expressed as

^{T}is of the length of N, among which the first L elements contain multipath energy. \( {W}_{N_P}={\left[W\left({k}_1\right),W\left({k}_2\right),\cdots, W\left({k}_{N_P}\right)\right]}^T \) is the Gaussian white noise in the frequency domain. \( {F}_{N_P} \) is a N

_{P}× N partial Fourier matrix, whose N

_{P}row is extracted from the N × N standard Fourier matrix by the pilot pattern K, and defined as

^{−j2π/N}. We further denote

_{m}, a

_{n}〉| denotes the inner product between the mth column and the nth column of the sensing matrix A. Substituting (3) to (5) can be obtained

_{i})| = 1 (i = 1, 2⋯N

_{p}). Letd = n − m, and Ω = {1, 2, ⋯N − 1}. Then (6) can be rewritten as

## 3 Method: MAGA-based pilot pattern optimization

### 3.1 MAGA

_{avg}is the population average fitness, η

_{max}is the population maximum fitness, and η is the individual fitness. The crossover probability minimum value is P

_{c1}= 0.1, and the maximum value is P

_{c2}= 0.9. The mutation probability minimum value is P

_{m1}= 0.01, and the maximum value is P

_{m2}= 0.1.

_{m}and the crossover probability P

_{c}of the largest fitness individuals are not zero in the MAGA, and these values are increased to P

_{c1}and P

_{m1}respectively. The modified algorithm ensures that the optimization process will not stop in the early stage of evolution, which can avoid solutions falling into local optimum.

### 3.2 MAGA-based pilot pattern optimization method

_{P}subcarriers from the N subcarriers as pilots, then possible pilot patterns will be \( \left(\begin{array}{l}N\\ {}{N}_P\end{array}\right) \). It is very difficult to obtain all the pilot patterns for selecting the optimal. Here, we present a method to globally search for a near-optimal deterministic pilot pattern allocation by MAGA. This scheme is universal for OFDM system with getting the optimized sensing matrix by minimizing the MC, and the specific execution is demonstrated in Fig. 2.

^{(0)}, which consists of randomly obtained N individuals, starts the execution of the work. The ith generation of the evolutionary population is expressed as

^{(i)}generation to the P

^{(i + 1)}generation. The probability that an individual of the population will be selected for the next generation is defined as

## 4 Results and discussion

_{P}), where L is the channel length, D is the number of iterations, and N

_{P}is the number of pilots. The channel model is channel 3 of mode B in the DRM standard [14], and the related parameters are displayed in Table 1.

Parameters | Value |
---|---|

OFDM sample period | T = 83.3 μs |

OFDM symbol period | T _{u} = 21.33 ms |

Guard interval | T _{g} = 5.3 ms |

FFT length | N = 256 |

Number of channel multipath | S = 4 |

Modulation | 4QAM |

Number of pilot | M = 26 |

SNR | 0–30 dB |

Type | MC | Running time (s) | Optimized pilot pattern |
---|---|---|---|

Random | 0.2045 | 570.65 | 4, 9, 20, 25, 34, 38, 65, 70, 75, 83, 91, 104, 125, 130, 135, 149, 171, 178, 187, 188, 194, 202, 211, 219, 226, 248 |

GA | 0.1812 | 140.53 | 20, 26, 42, 53, 56, 64, 72, 77, 79, 85, 101, 107, 114, 119, 128, 146, 151, 156, 160, 173, 197, 208, 216, 223, 228, 244 |

MAGA | 0.1399 | 310.41 | 4, 16, 31, 39, 46, 54, 61, 75, 92, 100, 107, 113, 135, 142, 160, 168, 176, 183, 191, 197, 205, 211, 221, 229, 246, 253 |