Spectral analysis of broadband RF signals in real time is of primary importance for numerous applications. So far, the instantaneous bandwidth of real-time spectrum analyzers based on conventional digital techniques is limited to a few GHz. This limitation is set by the clock jitter of the analog-to-digital converters, and by the processing capabilities in real time of digital electronics. On the contrary, analog architectures based on microwave photonics are not constrained by such limitations, and offer potentially a very high instantaneous bandwidth. However, they generally suffer from inherent limitations, such as large footprint and high complexity. Here, we propose a much simpler architecture of RF spectrum analyzer based on frequency-shifting loops. It utilizes only compact commercial telecom components, a single CW laser, and slow electronic resources (10 MSa/s). The probability of intercept is 100%, the instantaneous bandwidth reaches 16 GHz, and the spectral and temporal resolutions are respectively equal to 160 MHz and 50 µs. Our system is expected to open new avenues in embedded applications of microwave photonics.