This study addresses the critical challenge of quickest mean-change detection (QMCD), which involves promptly detecting changes in the mean of a sequence of independent observations, particularly under the challenging condition where both pre-change and post-change distributions are unknown. A novel detector is proposed to tackle the QMCD problem. It recursively computes the backward sample average and checks whether the result escapes the forward confidence sequence, hence the name BAckward Recursive AVerage escapes Outside Confidence Sequence (BRAVO-CS). Rigorous analysis demonstrates that the proposed BRAVO-CS detector achieves an average detection delay that scales inversely with the magnitude of the mean shift-significantly better than the inverse quadratic scaling of current state-of-the-art approaches when the change is subtle. Furthermore, BRAVO-CS incurs linear time complexity, in stark contrast to the quadratic time complexity of state-of-the-art methods. Extensive simulations further confirm its robustness and efficiency across diverse scenarios, establishing BRAVO-CS as a compelling solution for real-time systems requiring rapid and reliable mean change detection.

In this paper, the heterogeneous distributed quickest change detection (HetDQCD) with 1-bit non-anonymous feedback is studied. The concept of syndromes is introduced and the family of syndrome-based fusion rules is proposed, which encompasses all deterministic fusion rules as special cases. Through the Hasse diagram of syndromes, upper and lower bounds on the second-order performance of expected detection delay as a function of average run length to false alarm are provided. An interesting instance, the weighted voting rule previously proposed in our prior work, is then revisited, for which an efficient pruning method for breadth-first search in the Hasse diagram is proposed to analyze the performance. This in turn assists in the design of the weight threshold in the weighted voting rule. Simulation results corroborate that our analysis is instrumental in identifying a proper design for the weighted voting rule, demonstrating consistent superiority over both the anonymous voting rule and the group selection rule in HetDQCD.

The heterogeneous distributed quickest change detection (HetDQCD) problem with 1-bit feedback is studied, in which a fusion center monitors an abrupt change through a bunch of heterogeneous sensors via anonymous 1-bit feedbacks. Two fusion rules, one-shot and voting rules, are considered. We analyze the performance in terms of the worst-case expected detection delay and the average run length to false alarm for the two fusion rules. Our analysis unveils the mixed impact of involving more sensors into the decision and enables us to find near optimal choices of parameters in the two schemes. Notably, it is shown that, in contrast to the homogeneous setting, the first alarm rule may no longer lead to the best performance among one-shot schemes. The non-anonymous setting is then investigated where a novel weighted voting rule is proposed that assigns different weights to votes from different types of sensors. Simulation results show that the proposed scheme is able to outperform all the above schemes and the mixture CUSUM scheme for the anonymous HetDQCD, hinting at the price of anonymity.

The problem of fully distributed sequential change detection (FDSCD) is studied, where a bunch of distributed sensors collaboratively detect the occurrence of an abrupt event without the help of a fusion center. Due to the distributed nature, each sensor determines whether the event has occurred according to their own observations and messages received from their neighbors through noiseless links with finite capacity. In this paper, a novel algorithm is proposed for FDSCD that views every sensor as a fusion center and mimics the behavior of the cumulative sum (CUSUM) algorithm that is optimal in the presence of fusion center. One crucial factor in the proposed algorithm is the weighting factors that reduce the influence of stale messages circulated in the network. Design of these weighting factors based on genetic algorithms is provided. Quantizer design is also studied to meet the finite capacity constraint. Two designs are proposed where the first one numerically maximizes the total output Kullback-Leibler divergence and the second one again exploits the genetic algorithms. Extensive simulations are conducted whose results show that the proposed algorithm outperforms the current state-of-art in terms of the tradeoff between expected delay and average run length to a false alarm.

Cooperative beamforming is a potentially useful technique for enhancing link reliability in modern wireless relay communications. To aid the beamforming design, the signal-to-noise ratio (SNR) of the source-to-relay (S-R) channel links must be known at the destination node. Abdallah and Papadopoulos in IEEE Trans. Signal Processing, vol. 56, no. 10, 2008, proposed a beamforming system with relay-assisted SNR acquisition; that is, the S-R link SNR is first quantized at each relay and is then forwarded to the destination. An optimal quantizer design problem was proposed in that paper, aiming at reducing the system bit error rate; however, only the binary quantization case was considered therein, with the quantization threshold computed by a suggested rule of thumb. In this paper, we study the aforementioned quantizer design problem in the general multiple-bit setting. We show that the solutions to the first-order necessary condition for optimality can be obtained as a fixed point of a certain nonlinear map over the feasible threshold set. The existence and uniqueness of the fixed point are established by using, respectively, the Brouwer's and Schauder's fixed point theorems. Finally, we show that the fixed point thus obtained yields the globally optimal set of quantization thresholds. To the best of our knowledge, this paper is the first which leverages fixed point theories to rigorously solve SNR quantization problems in the context of wireless relay communication.

Pilot contamination (PC) is known as a dominant factor for the performance of time-division duplex massive MIMO systems. Most of the existing studies of PC assumed perfect inter-cell synchronization, which is too costly to achieve or even impossible in practice. In this paper, we consider the unsynchronized scenario, in which the reused pilot signals from other cells are subject to timing misalignment, and propose a method for pilot sequence design for reducing the mean square error (MSE) of the linear least squares (LS) channel estimation. An analytic MSE formula is first derived, which is a very complicated function of the pilot coefficients. To ease analysis, an upper bound on the MSE is then derived. Through minimization of this upper bound, an analytic solution is obtained. Computer simulations are used to illustrate the performance of the proposed pilot sequence.