Intelligent reflecting surfaces (IRSs) provide the ability to tune the wireless environments by introducing passive scattering elements between the base station (BS) or access points (APs) and users, and it is a promising technology for next-generation wireless networks. In this article, we consider joint activity detection and channel estimation in both centralized and distributed IRS-assisted Internet of Things networks. We determine the explicit distribution for the equivalent channel coefficients from the BS or APs to the users. It is shown that this distribution can be equivalently represented with a Gaussian scale mixture (GSM) model. With the generalized approximate message passing (GAMP) algorithm, the received pilot signals at the BS or APs are decoupled into scalar Gaussian noise corrupted versions of the effective channel coefficients. Subsequently, a minimum mean square error (MMSE) estimate of the effective channel coefficients and threshold detection rules is acquired. Finally, the optimal fusion rule is used to obtain the activity detection results of each user. As an additional low-complexity approach, we approximate the equivalent channel coefficients with a Gaussian approximation (GA) model. We derive the theoretical mean square error for the MMSE estimate of the effective channel coefficients using the GA model and the state evolution equations of the GAMP algorithm, under the assumption that the direct links from the BS to the users can be neglected due to unfavorable propagation conditions. Numerical results show that the GA for the distribution of the equivalent channel coefficients is accurate even for the moderate number of elements at the IRS. And the theoretical mean square error for the MMSE estimate of the effective channel coefficients under the assumption that direct link is negligible is shown to overlap with the corresponding numerical simulations.

Cell-free massive MIMO is one of the key technologies for future wireless communications, in which users are simultaneously and jointly served by all access points (APs). In this paper, we investigate the minimum mean square error (MMSE) estimation of effective channel coefficients in cell-free massive MIMO systems with massive connectivity. To facilitate the theoretical analysis, only single measurement vector (SMV) based MMSE estimation is considered in this paper, i.e., the MMSE estimation is performed based on the received pilot signals at each AP separately. Inspired by the decoupling principle of replica symmetric postulated MMSE estimation of sparse signal vectors with independent and identically distributed (i.i.d.) non-zero components, we develop the corresponding decoupling principle for the SMV based MMSE estimation of sparse signal vectors with independent and non-identically distributed (i.n.i.d.) non-zero components, which plays a key role in the theoretical analysis of SMV based MMSE estimation of the effective channel coefficients in cell-free massive MIMO systems with massive connectivity. Subsequently, based on the obtained decoupling principle of MMSE estimation, likelihood ratio test and the optimal fusion rule, we perform user activity detection based on the received pilot signals at only one AP, or cooperation among the entire set of APs for centralized or distributed detection. Via theoretical analysis, we show that the error probabilities of both centralized and distributed detection tend to zero when the number of APs tends to infinity while the asymptotic ratio between the number of users and pilots is kept constant. We also investigate the asymptotic behavior of oracle estimation in cell-free massive MIMO systems with massive connectivity via random matrix theory. Moreover, in order to demonstrate the potential performance loss of SMV based MMSE estimation, which does not employ the correlation between the received pilot signals at different APs, the multiple measurement vector (MMV) based MMSE estimation, i.e., joint MMSE estimation with pilot signals from all APs, is analyzed via numerical results. Numerical analysis shows that the theoretical analyze with our decoupling principle for the SMV based MMSE estimation of sparse signal vectors with i.n.i.d. non-zero components matches well with the numerical results.

In this paper, we investigate the performance of cell-free massive MIMO systems with massive connectivity. With the generalized approximate message passing (GAMP) algorithm, we obtain the minimum mean-squared error (MMSE) estimate of the effective channel coefficients from all users to all access points (APs) in order to perform joint user activity detection and channel estimation. Subsequently, using the decoupling properties of MMSE estimation for large linear systems and state evolution equations of the GAMP algorithm, we obtain the variances of both the estimated channel coefficients and the corresponding channel estimation error. Finally, we study the achievable uplink rates with zero-forcing (ZF) detector at the central processing unit (CPU) of the cell-free massive MIMO system. With numerical results, we analyze the impact of the number of pilots used for joint activity detection and channel estimation, the number of APs, and signal-to-noise ratio (SNR) on the achievable rates.

The sparse activity detection in intelligent reflecting surface (IRS) assisted wireless networks is investigated in this paper. With generalized approximate message passing (GAMP) algorithm, we first obtain the minimum mean square error (MMSE) estimates of the equivalent effective channel coefficients from the base station (BS) to the users, and convert the received pilot signals into additive Gaussian noise corrupted versions of the equivalent effective channel coefficients. Subsequently, multiple decisions on the activity of each user are made using the likelihood ratio test based on the Gaussian noise corrupted equivalent effective channel coefficients. At last, final decisions on the activity of all users are made with the optimal fusion rule, taking into account the previous decisions on the activity of each user and the corresponding reliabilities. Numerical results show that the average error probability of the sparse activity detection method proposed in this paper diminishes as the SNR, number of pilots, number of antennas at the BS or number of elements at the IRS increases.

In this paper, the minimum mean square error (MMSE) channel estimation for intelligent reflecting surface (IRS) assisted wireless communication systems is investigated. In the considered setting, each row vector of the equivalent channel matrix from the base station (BS) to the users is shown to be Bessel K distributed, and all these row vectors are independent of each other. By introducing a Gaussian scale mixture model, we obtain a closed-form expression for the MMSE estimate of the equivalent channel, and determine analytical upper and lower bounds on the mean square error. Using the central limit theorem, we conduct an asymptotic analysis of the MMSE estimate, and show that the upper bound on the mean square error of the MMSE estimate is equal to the asymptotic mean square error of the MMSE estimation when the number of reflecting elements at the IRS tends to infinity. Numerical simulations show that the gap between the upper and lower bounds are very small, and they almost overlap with each other at medium signal-to-noise ratio (SNR) levels and moderate number of elements at the IRS.

We investigate the sparse activity detection problem in cell-free massive multiple-input multiple-output (MIMO) systems in this paper. With the approximate message passing (AMP) algorithm, the received pilot signals at the access points (APs) are decomposed into independent circularly symmetric complex Gaussian noise corrupted components. By using the minimum mean-squared error (MMSE) denoiser during the AMP procedure, we obtain a threshold detection rule, and analytically describe the noise covariance matrix of the corrupted components via the state evolution equations, which is helpful for the performance analysis of the detection rule. Using the law of large numbers, it can be shown that the error probability of this threshold detection rule tends to zero when the number of APs, pilots and users tend to infinity while the ratio of the number of pilots and users is kept constant. Numerical results show that the error probability decreases while the number of APs increases, corroborating our theoretical analysis. In addition, we investigate the relationship between the error probability of the threshold detection rule and the number of symbols used for pilot transmissions during each channel coherence interval via numerical results.

This paper focuses on detection for multi-cell Massive MIMO network. As the column vectors are independent and identically distributed with each other, channel fast fading coefficient matrix is the eigenvector matrix for the covariance of received signal when the number of antennas at base stations (BSs) tends to infinity. Thus, we can get a set of normalized base vectors by eigenvalue decomposition of the covariance matrix for received signal. Based on this close relationship, an EVD (Eigenvalue Decomposition) based detection algorithm, which could solve the pilot contamination problem completely when the number of antennas at BS tends to infinity, is proposed. Simulation results show that the bit error rate (BER) could be reduced by two orders of magnitude when signal-to-noise ratio (SNR) is 40dB, with EVD-based detection algorithm, comparing with the traditional maximum-ratio combining (MRC) detection.