CN110191430A - For the single-bit distribution sparse signal detection method of generalized Gaussian distribution situation - Google Patents

Abstract

The present invention proposes a kind of single-bit distribution sparse signal detection method for generalized Gaussian distribution situation, belongs to signal detection field.The distributed wireless sensor network comprising fusion center and multiple local nodes is arranged in this method in the detection area first；At any time, each local node exports corresponding analogue observation value according to whether receiving sparse signal, is quantified to obtain corresponding quantized result to analogue observation value and is sent to fusion center；Fusion center calculates the test statistics of local maxima gesture using all quantized values and calculates decision threshold；Finally, the size of comparing check statistic and decision threshold, exports the testing result at the moment.The present invention can be used as the important supplement for the single-bit distribution sparse signal detection method in the case of Gauss existing at present, can be adapted for the lower signal detection of a variety of noises/signal distributions situation, application value with higher.

Description

Single-bit distributed sparse signal detection method for generalized Gaussian distribution situation

Technical Field

The invention belongs to the field of signal detection, and particularly relates to a single-bit distributed sparse signal detection method aiming at generalized Gaussian distribution conditions.

Background

The compressive sensing technique aims at realizing the reconstruction of a high-dimensional sparse signal from a small amount of observation data. The compressed sensing technology also provides reference for sparse signal detection based on a distributed sensor network. In the distributed sensor network, each local sensor node (local node for short) only transmits a small amount of observation data to the fusion center, and the fusion center makes a judgment whether a sparse signal of interest exists. Under this framework, the transmission and processing of small amounts of data reduces the bandwidth and energy consumption of the distributed sensor network. In practice, the local nodes in the distributed sensor network will often perform single-bit quantization on the simulated observation information to be transmitted. The single-bit quantization is beneficial to further reducing the bandwidth required by the distributed sensor network, and the power consumption is low, thereby being beneficial to reducing the hardware complexity of the local node. Although single-bit quantization may lose amplitude information of data, it has been theoretically demonstrated at present that the detection performance loss caused by single-bit quantization can be compensated by increasing the number of sensors by a certain proportion.

Aiming at the problem of distributed sparse signal detection based on single-bit quantized data, the current method only aims at Gaussian signals and Gaussian noise scenes. In practice, however, non-gaussian signals and noise are prevalent. Generalized gaussian distributions are a common non-gaussian distribution and have gained wide attention in the fields of ship detection, speech and video processing. At present, a distributed single-bit sparse signal detection method aiming at the generalized Gaussian distribution condition does not exist.

Disclosure of Invention

The invention aims to fill the blank of the prior art and provides a single-bit distributed sparse signal detection method aiming at the generalized Gaussian distribution condition. The method can be used as an important supplement of the existing single-bit distributed sparse signal detection method under the Gaussian condition. Compared with the existing method, the detection method provided by the invention has wider application range, can be suitable for signal detection under various noise/signal distribution conditions, and has higher application value.

The invention provides a single-bit distributed sparse signal detection method aiming at a generalized Gaussian distribution condition, which is characterized by comprising the following steps of:

1) setting a distributed wireless sensor network comprising a fusion center and L local nodes in a detection area; setting false alarm probability 0 < P_FA< 1, variance of additive noiseAnd shape parameter β_w＞1；

2) At any moment, if the local node l receives the sparse signal, the local node linearly compresses the received sparse signal to obtain a corresponding sparse signalWherein x is_lFor sparse signals received by the local node l, h_lIs a compressed vector of the local node l, w_lAdditive noise at the L-th local node, L ═ 1,2, …, L; if the local node l does not receive the sparse signal, the local node l outputs the analog observation value y_l＝w_l，l＝1,2,…,L；

3) Each local node l utilizes a quantization threshold τ_lFor the analog observed value y_lQuantizing to obtain corresponding quantization result b_lAnd transmitted to the fusion center; b_lThe calculation expression of (a) is as follows:

b_l＝sign(y_l-τ_l)

wherein

4) The fusion center uses all quantized values b₁,b₂,…,b_LCompute test statistics of local maximum potentials:

wherein,

5) calculating a decision threshold:

wherein,

to representIs inverse function of and mu₀＝0，

6) Comparing the test statistic t (b) with the decision threshold η, and outputting the detection result at the moment:

if T (b) is not less than η, judging that sparse signals exist, and if T (b) is less than η, judging that sparse signals do not exist.

The invention has the characteristics and beneficial effects that:

the existing single-bit sparse signal detection method can only be applied to Gaussian scenes, but the single-bit distributed sparse signal detection method aiming at the generalized Gaussian distribution condition provided by the invention not only can be applied to Gaussian scenes, but also can be applied to various non-Gaussian scenes, and has wider application range. The method can be applied to a sparse signal detection part in a distributed communication and radar system, and especially can be applied to scenes with limited bandwidth and energy.

Detailed Description

The invention provides a single-bit distributed sparse signal detection method for generalized Gaussian distribution conditions, and the method is further described in detail below by combining specific embodiments.

The invention provides a single-bit distributed sparse signal detection method aiming at a generalized Gaussian distribution condition, which comprises the following steps of:

1) a distributed wireless sensor network comprising a fusion center and a plurality of sensors is arranged in a detection area (the network of the invention has no special requirement on the model of the sensors). In the network, each local sensor node (local node for short) L is 1,2, …, L (L represents the index number of the sensor, L represents the number of the sensors, and L > 1) is arranged at a plurality of positions of the detection area (the arrangement position of the sensor has no special requirement), and each local node communicates with the fusion center through a wireless channel. Setting false alarm probability 0 < P_FAVariance of < 1 and additive noiseAnd shape parameter β_w＞1。

2) At any moment, if the local node l receives the sparse signal, the local node linearly compresses the received sparse signal to obtain a corresponding analog observation valueWherein x is_lFor sparse signals received by the local node l, h_lCompressed vector (h) for local node l_lIs sampled from the standard normal distribution by the local node), w_lIs additive noise at the L-th local node, L ═ 1,2, …, L. If the local node l does not receive the sparse signal, the local node l outputs the analog observation value y_l＝w_l，l＝1,2,…,L；

3) Each local node l utilizes a quantization threshold τ_lFor the analog observed value y_lQuantizing to obtain corresponding quantization result b_lRepresents:

b_l＝sign(y_l-τ_l)

wherein

Then, each local node quantizes the value b_lIs transmitted to the fusion center,

4) the fusion center uses all quantized values b₁,b₂,…,b_LCompute test statistics of local maximum potentials:

wherein,

5) in the fusion center, a decision threshold is calculated:

wherein

To representIs inverse function of and mu₀＝0，

6) At the fusion center, the test statistic t (b) and the decision threshold η are compared, and finally, the detection result at the moment is output:

if T (b) is not less than η, judging that sparse signals exist, and if T (b) is less than η, judging that sparse signals do not exist.

Claims (1)

1. A single-bit distributed sparse signal detection method for a generalized Gaussian distribution situation is characterized by comprising the following steps:

1) setting a distributed wireless sensor network comprising a fusion center and L local nodes in a detection area; setting false alarm probability 0 < P_FA< 1, variance of additive noiseAnd shape parameter β_w＞1；

2) At any moment, if the local node l receives the sparse signal, the local node linearly compresses the received sparse signal to obtain a corresponding sparse signalWherein x is_lFor sparse signals received by the local node l, h_lIs a compressed vector of the local node l, w_lAdditive noise at the L-th local node, L ═ 1,2, …, L; if the local node l does not receive the sparse signal, the local node l outputs the analog observation value y_l＝w_l，l＝1,2,…,L；

3) Each local node l utilizes a quantization threshold τ_lFor the analog observed value y_lQuantizing to obtain corresponding quantization result b_lAnd transmitted to the fusion center; b_lThe calculation expression of (a) is as follows:

b_l＝sign(y_l-τ_l)

wherein

4) The fusion center uses all quantized values b₁,b₂,…,b_LCompute test statistics of local maximum potentials:

wherein,

5) calculating a decision threshold:

wherein,

to representIs inverse function of and mu₀＝0，

6) Comparing the test statistic t (b) with the decision threshold η, and outputting the detection result at the moment:

if T (b) is not less than η, judging that sparse signals exist, and if T (b) is less than η, judging that sparse signals do not exist.