In this article, we present a new scenario of direction of arrival estimation using massive multiple-input multiple-output receive array with low-resolution analog-to-digital convertors (ADCs), which can strike a good balance between performance and circuit cost. Based on the linear additive quantization noise model, the inpact of low-resolution ADCs on methods, such as Root-MUSIC, is analyzed. Also, the closed-form expression of Cramer–Rao lower bound (CRLB) is derived to evaluate the performance loss caused by the low-resolution ADCs. The simulation results show that the Root-MUSIC methods can achieve the corresponding CRLB. Furthermore, adopting ADCs with 2–3 b is an efficient choice for most applications if 1 dB performance loss is acceptable.

High hardware cost and high power consumption of massive multiple-input and multiple output (MIMO) are two challenges for the future wireless communications including sixth generation (6G). Adopting the low-resolution analog-to-digital converter (ADC) is viewed as a promising solution. Additionally, the direction of arrival (DOA) estimation is an indispensable technology for beam alignment and tracking in massive MIMO systems. Thus, in this letter, the performance of DOA estimation with mixed-ADC structure is firstly investigated. The Cramér-Rao lower bound (CRLB) for this architecture is derived based on the additive quantization noise model. Eventually, a performance loss factor and the associated energy efficiency factor is defined for analysis in detail. Simulation results show that the mixed-ADC architecture can strike a good balance among performance loss, circuit cost and energy efficiency. More importantly, just a few bits (up to 4 bits) of low-resolution ADCs can achieve a satisfactory performance for DOA measurement.

To reduce the signal-to-interference-plus-noise ratio (SINR) loss of analog directional modulation (DM) with finite radio frequency (RF) phase shifters (PSs), a hybrid analog and digital (HAD) DM with mixed PSs is proposed. Using the law of large numbers, the closed-form expressions of SINR performance loss (PL), secrecy rate (SR), and bit error rate (BER) are derived. In accordance with the closed-form expression of SINR loss, it is clear that the SINR PL at desired receiver (Bob) gradually decreases as the fraction $\eta$ of the low-resolution phase shifter decreases, where $\eta$ is defined as the ratio of the number of low-resolution shifters to the total number of shifters. The simulation results show that the SINR PL, SR PL, and BER gradually decrease as the number of quantization bits increases. When the fraction of low-resolution shifters is equal to 50%, 2 bits is sufficient for low-resolution shifters to achieve a SINR PL less than 0.5 dB and a negligible BER degradation. Also, when the number of quantization bits of low-resolution shifters is equal to 2, the SR PL is about 0.3 bits/s/Hz. Thus, compared with analog DM, the HAD DM structure strikes a good balance between PL and circuit cost.

As an excellent aided communication technology, intelligent reflecting surface (IRS) can make a significant rate enhancement and coverage extension. In this paper, we present an investigation on beamforming in an IRS-aided directional modulation (DM) network. To fully explore the advantages of IRS, two beamforming methods with enhanced secrecy rate (SR) performance are proposed. The first method of maximizing secrecy rate (Max-SR) alternately optimizes confidential message (CM) beamforming vector, artificial noise (AN) beamforming vector and phase shift matrix. The first optimization vector is directly computed by the Rayleigh ratio and the last two are solved with generalized power iteration (GPI). This method is called Max-SR-GPI. To reduce the computational complexity, a new method of maximizing receive power with zero-forcing constraint (Max-RP-ZFC) of only reflecting CM and no AN is proposed. Simulation results show that the proposed two methods harvest about 30 percent rate gains over the cases of random-phase IRS and no IRS, and the proposed Max-SR-GPI performs slightly better than the Max-RP-ZFC in terms of SR, particularly in the small-large IRS.

Massive multiple input multiple output (MIMO) antenna arrays eventuate a huge amount of circuit costs and computational complexity. To satisfy the needs of high precision and low cost in future green wireless communication, the conventional hybrid analog and digital MIMO receive structure emerges a natural choice. But it exists an issue of the phase ambiguity in direction of arrival (DOA) estimation and requires at least two time-slots to complete one-time DOA measurement with the first time-slot generating the set of candidate solutions and the second one to find a true direction by received beamforming over this set, which will lead to a low time-efficiency. To address this problem, a new heterogeneous sub-connected hybrid analog and digital (H ² AD) MIMO structure is proposed with an intrinsic ability of removing phase ambiguity, and then a corresponding new framework is developed to implement a rapid high-precision DOA estimation using only single time-slot. The proposed framework consists of two steps: 1) form a set of candidate solutions using existing methods like MUSIC; 2) find the class of the true solutions and compute the class mean. To infer the set of true solutions, we propose two new clustering methods: weight global minimum distance (WGMD) and weight local minimum distance (WLMD). Next, we also enhance two classic clustering methods: accelerating local weighted k-means (ALW-K-means) and improved density. Additionally, the corresponding closed-form expression of Cramer–Rao lower bound (CRLB) is derived. Simulation results show that the proposed frameworks using the above four clustering can approach the CRLB in almost all signal to noise ratio (SNR) regions except for extremely low SNR (SNR< −5 dB). Four clustering methods have an accuracy decreasing order as follows: WGMD, improved DBSCAN, ALW-K-means and WLMD.

Due to the power consumption and high circuit cost in antenna arrays, the practical application of massive multiple-input multiple-output (MIMO) in the sixth generation (6G) and future wireless networks is still challenging. Employing low-resolution analog-to-digital converters (ADCs) and hybrid analog and digital (HAD) structure is two low-cost choices with acceptable performance loss. In this paper, the combination of the mixed-ADC architecture and HAD structure employed at receiver is proposed for direction of arrival (DOA) estimation, which will be applied to the beamforming tracking and alignment in 6G. By adopting the additive quantization noise model, the exact closed-form expression of the Cramér-Rao lower bound (CRLB) for the HAD architecture with mixed-ADCs is derived. Moreover, the closed-form expression of the performance loss factor is derived as a benchmark. In addition, to take power consumption into account, energy efficiency is also investigated in our paper. The numerical results reveal that the HAD structure with mixed-ADCs can significantly reduce the power consumption and hardware cost. Furthermore, that architecture is able to achieve a better trade-off between the performance loss and the power consumption. Finally, adopting 2-4 bits of resolution may be a good choice in practical massive MIMO systems.