## 1 Introduction  
In the recent years, an explosive growth in mobile communication networks has been observed, which has led to a boom of new applications and data services. This growth has emerged as a global challenge for service providers and researchers to meet the capacity demands of the emerging 5 th generation (5G) of wireless communication networks. In this context, the extension and efficient-use of usable frequency spectrum is believed to be of vital importance. Expansion of usable frequency spectrum to higher bands of frequencies, i.e., millimeter-wave (mmWave), is thought to be a potential research direction to address the capacity demands. Accurate understanding of radio propagation channel characteristics helps in devising efficient signal processing algorithms and designs for receivers to meet the capacity demands of emerging wireless communication networks. Analysis of angular spread and second-order fading statistics (SOFS) of land-mobile radio cellular communication channels is thoroughly studied in the literature, e.g., [1,2]. For different scenarios of terrestrial communications, such studies investigate the characteristics of the channel in angular, Doppler and delay domain. Several studies [3, 4, 5, 6, 7, 8] have been presented in the literature to study the channel characteristics for mmWave band, mainly at 28 GHz and 38 GHz. In [3], measurements are presented which were conducted for outdoor cellular propagation environments at 28 GHz in New York City; where Path loss, angular statistics, and delay statistics are studied. In [4], channel measurements are presented for outdoor urban environment at 38 GHz. Angle-of-arrival (AoA) analysis is presented for different locations of receiver (Rx) and transmitter (Tx) with antennas of different gains. A study presented in [5], provides an analytical relationship for SOFS of mmWave communication channels. In [6], spatial and temporal characteristics of indoor radio channels for 28 GHz mmWave band are studied; particularly for an indoor office environment. Similarly, in [7], channel measurements are conducted in an indoor corridor radio propagation environment for mmWave range at 19 GHz, 28 GHz, and 38 GHz bands. Various dynamic challenges in addressing the demands of emerging 5G communication networks, demand conduction of an intensive research to study both the large- and small-scale fading statistics of both indoor and outdoor mmWave radio propagation channels. Mobility of mobile user terminals and the spread of energy in angular domain determines Doppler spread, which further has a direct relationship with the rate of fluctuations in the received signals envelopes. These fluctuations at small and large scale in the received signal's envelope affect the performance of error-correction algorithms, modulation schemes, equalization, diversity, and channel coding techniques. Therefore, it is imperative to have a comprehensive understanding of the dispersion of energy in angular domain, which further helps in characterization of SOFS of the channels. A theory of multipath shape factors (SFs) is proposed by [PERSON] et al. in [9,10] which provides a direct analytical method for quantification of the dispersion of energy along azimuth AoA. The proposed SFs are named as, angular constriction, angular spread, and direction of maximum fading. Moreover, novel analytical relationships of these SFs with SOFS of the radio propagation channels are also proposed. These SOFS quantifiers are spatial auto-covariance (ACV), coherence distance (CD), average fade duration (AFD), and level-crossing-rate (LCR). Modeling the AoA in 3D domain is of high significance. Many studies proposed in literature [11, 12, 13] present different methods for determining the arrival angles and their intensity. In [14,15], the characterization of angular spread in 3D scenarios is presented in terms of SFs. In [16,17], a new angular spread quantifier, named true standard deviation, is proposed; moreover, a new definition of SFs is also provided.