This paper investigates the effect of various antenna array structures, i.e., uniform linear array (ULA), uniform rectangular array (URA), uniform circular array (UCA), and concentric circular array (CCA), on cluster index modulation (CIM) enabled massive multiple-input multiple-output (mMIMO) millimeter-wave (mmWave) communications systems. As the CIM technique indexes spatial clusters to convey additional information bits, the different radiation characteristics caused by different array structures can significantly affect system performance. By analyzing the effects of array characteristics such as radiation pattern, array directivity, half-power beam width (HPBW), and radiation side lobes on bit error rate (BER) performance, we reveal that URA achieves better error performance than its counterparts in a CIM-enabled mmWave system. We demonstrate that narrower beams alone cannot guarantee better BER performance in a CIM-based system. Instead, other radiation characteristics, especially radiation side lobes, can significantly influence system performance by entailing extra interference in the non-intended directions. Illustrative results show that URA owes its superiority to its lower side lobes. We also propose an algorithm to implement fixed phase shifters (FPS) as a hardware-efficient (HE) analog network structure (beamformer/combiner) to reduce cost and energy consumption in mmWave systems and investigate the effect of a non-ideal analog network on the BER performance for different array structures. It is demonstrated that HE systems with a few FPSs can achieve similar BER performance compared to the optimum (OP) analog network structure.