GNSS spoofing is a type of attack that aims to deceive GNSS receivers by transmitting fake signals that imitate the authentic ones. To detect such attacks, a possible solution is to calculate the double difference (DD) of carrier phase measurements between two antennas of two separated receivers. This DD measurement represents the angle of arrival (AoA) information of the signal. In the case of authentic signals, each signal comes from a different satellite, so the AoA values are different for each satellite. However, in the case of a spoofing attack, all the counterfeit signals from the same broadcaster come from the same direction, and thus the AoA values are the same for all DD measurements. Sum of Squares (SoS) detector and Dispersion of Double Difference (D3) detector are known as simple but effective methods for spoofing detection. However, these detectors are not robust in some special regions where cycle slips are large and vary rapidly. This paper proposes a new method for detecting GNSS spoofing by using carrier phase double difference measurements to generate a feature vector as a descriptor for each satellite in a set of observed satellites. The feature vectors are formed by statistical parameters of a series of consecutive double difference values computed for each reference satellite. Our proposed feature descriptor has been evaluated on a dataset containing both real and fake signals using an SVM classifier. The study shows that the proposed feature descriptor is highly effective in detecting spoofing satellite signals.