Statistical Device Activity Detection for OFDM-Based Massive Grant-Free Access

MLE-based Device Activity Detection for Grant-free Massive Access under Rician Fading

“…as N, L, M → ∞, same as the one in [29] and higher than the one in [7], i.e., O(NL 2 ), as 9 It is still unknown how to analyze the number of iterations required to reach certain stopping criteria. Therefore, we provide only per-iteration computational complexity analysis to reflect the computation cost to some extent as in [5], [7]- [10], [15], [16], [23], [25]. Later in Section V, the overall computation time will be evaluated numerically.…”

“…Thus, in asynchronous case-i, we can view Ŝi,n as the set of data-embedding pilots maintained at device n in massive grant-free access with data embedding, view the device activity detection for asynchronous cases as the joint device activity and data detection in the synchronous case in [16], and treat Problem 2 as the MLE problem for joint device activity and data detection in [16]. However, different from the MLE problem in [16], Problem 2 for asynchronous case-i has discrete variables (a, x i ), whose number does 10 If an = 0, no matter which value xi,n takes in Xi, the objective function fi(a−n, an, x−n, xi,n) of Problem 2 does not change.…”

“…Specifically, in Steps 5-7, besides computing Σ −1 i,n and Y i,n based on Σ −1 i and Y i , respectively, as in Steps 5 and 6 of Algorithm 2, we compute Φ i,n based on Φ i by matrix manipulations and the methods for calculating Σ −1 i,n and Y i,n ; in Step 8, we compute α i,n , β i,n , and η i,n according to their equivalent forms given by Lemmas 1-3; in Steps 10-12, we compute Σ −1 i , Y i , and Φ i based on Σ −1 i,n , Y i,n , and Φ i,n , respectively, similar to the updates of Σ −1 i,n , Y i,n , and Φ i,n in Steps 5-7. For all n ∈ N , the computational complexities of Steps 5,6,7,9,10,11,and 12…”

“…The AMP-based algorithms are computationally efficient but the activity detection and channel estimation accuracies degrade significantly if the number of active devices is larger than the pilot length [7]. Besides, leveraging statistical estimation techniques, [7]- [10] formulate device activity detection as maximum likelihood estimation (MLE) problems [7]- [9] and maximum a posterior probability estimation (MAPE) problems [9], [10] under flat [7]- [9] and frequency selective [10] Rayleigh fading and tackle the non-convex problems using the coordinate descent (CD) method. The statistical estimation approaches generally outperform the CS-based approaches in activity detection accuracy at the cost of computation complexity increase [8] and have fewer restrictions on the system parameters.…”

“…13 In the simulation, we adopt Gaussian pilot sequences (i.e., p n , n ∈ N are i.i.d. generated according to CN (0, I L )) [5], [7]- [10], [12], [13], [15]- [17], [20]- [26]. Set h n = (e j(m−1)φn ) m∈M [34],…”