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Ion-irradiating technology for high temperature superconducting integrated circuits is a very promising approach for many implementations because of possibility to design the schemes with a high density of arbitrary situated Josephson elements. Recently developed in our group, a technological process [1] demonstrated ability to produce high quality Josephson junctions, particularly suitable for mixing and heterodyne detecting in sub-THz and THz frequency range [2,3]. One of well known problems for many potential applications of HTS Josephson junctions is their excessive noise level (and consequently broad generation linewidth) which are often higher than the ones theoretically expected [4,5]. Unlike the other types of HTS junctions, which noise characteristics were extensively investigated previously, there is lack of experimental as well as theoretical results reported on the ion-irradiated devices. We present the results of our experimental and numerical investigation on noise characteristics of ion-irradiated Josephson junctions and arrays and discuss the results in the context of their potential implementation for heterodyne THz detecting. [1] N Bergeal et al. “Using ion irradiation to make high-Tc Josephson junctions”, J. Appl. Phys. 102, 083903 (2007) [2] M Manlou et al. “Toward terahertz heterodyne detection with superconducting Josephson junctions”, Appl. Phys. Lett. 101, 233505 (2012) [3] M Manlou et al. “High-Tc superconducting Josephson mixers for terahertz heterodyne detection”, J. Appl. Phys. 116, 074505 (2014) [4] Yu Divin et al. “Linewidth of Josephson oscillations in YBa2Cu3O7-x step edge grain boundary junctions”, Future directions in nonlinear dynamics in physical and biological systems, NATO ASI Series Volume 312, 1993, pp 343-346 [5] G Kunkel et al. “Millimeter-wave radiation in high-Tc Josephson junctions”, IEEE Trans. Appl. Supercond., 7, 3339-3342 (1997)