This chapter analyzes the noise components impairing the coherent optical detection, comparing two receiver architectures, the dual-polarization quadrature coherent receiver and the single-coupler differential coherent receiver. There are noise components independent of both signal and LO power, other noise terms depend linearly on the signal or LO power, and other terms depend quadratically on the signal or LO power. These different dependencies are responsible for different compositions of the leading noise components, suggesting clear design optimization criteria to maximize the coherent receiver sensitivity in the given operating conditions. The noise analysis of the coherent optical receiver is essential to succeed in the optical sensitivity optimization and extended range performances of the LiDAR. The most relevant noise components of the coherent optical receiver are generated by the local oscillator laser (LO), in particular the LO shot noise, LO RIN and LO phase noise. The phase noise (PN) generated by the local oscillator (LO) is among the most relevant noise components affecting the coherent receiver sensitivity. In addition, the field of the local oscillator laser generates shot noise and RIN when it is converted into photocurrents by the photodetection process. Other noise components are generated by the beating process of the LO field with the received optical field. In particular, if the input section includes an optical amplification stage, either EDFA or SOA, the amplified spontaneous emission (ASE) noise field beats with the LO field and generates one of the largest noise components, depending on the OSNR of the optical amplifier. According to the classical model of the homogeneous line broadening, the phase noise is generated by instantaneous frequency deviations, modeled as a white noise process. The instantaneous frequency deviations of the laser light are generated by the spontaneously emitted photons inside the laser cavity that compete with the coherent stimulated emitted photons. Spontaneously emitted photons do not have the same cavity momentum and energy as the stimulated emitted photons, behaving as a noise perturbation added to the coherent photons population. The instantaneous frequency deviations generated by the randomly emitted spontaneous photons, and integrated in a given time interval, produce a random walk phase process, known as the integral phase process. When the integral phase process is added to the nominal monochromatic laser frequency, the resulting electric field includes the cosine (or sine) factor of the phase integral, known as the phase noise. The phase noise is the cosine of the integral phase process generated by the white noise instantaneous frequency deviation process when it is integrated in a given acquisition time interval. Additional noise components are produced by the photodiodes dark current and TIA thermal noise. The optical noise fields include amplitude and phase noises of the local oscillator laser, and eventually the amplified spontaneous emission (ASE) noise generated by the optical amplifier stages, either SOA or EDFA. Because of the electrical processing of signal photocurrents, the noise theory of the coherent optical receiver deals with the conversion of the optical noise fields into corresponding noise fluctuations of the detected photocurrents. This happens through the architecture of the coherent optical receiver implemented with the orthogonal polarizations and quadrature optical fields. Although the optical noise is generated by the fluctuation of the laser field, the ASE noise components are present whenever there are one or more optical amplifiers placed along the optical path. Optical amplifiers can be placed either at the transmitter port or at the receiver port, or at both terminations. In LiDAR applications, optical amplifiers are usually implemented by compact semiconductor optical amplifiers (SOA) to boost the transmitted power or increase the received optical power.