LLRs for active nodes fast turn negative, while the remaining activity LLRs turn positive. Additionally, we see that the evaluation of the activity LLRs is rather stable with increasing number of iterations. This behavior is not true with short spreading yielding to a non changing composite signature matrix. Here all activity LLRs are subject to strong variations, yielding a high uncertainty about the node activity. Consequently, we observe that the frame BP yields huge performance gains with changing signature matrices.
Multiuser Energy Detection
5.1 Overview
The previous two chapters focused on optimally detecting activity and data in CS-MUD. Both chapters showed that exploiting knowledge about frame activity yields performance gains in the detection. However, especially the optimal activity detection concepts presented in Chapter 3 suffered from the bias contained in the activity LLRs for frame-based transmissions. Further, the algorithms presented were optimized for finite alphabet source data which requires perfect Channel State Information (CSI) which may be an issue in a practical system with a massive number of nodes only sporadically transmitting data. Another point is the complexity while K-Best detection is a viable approach for decreasing the complexity of tree search algorithms, the frame BP shown had a tremendous complexity due to the iterative message exchange.
For addressing the detection in systems with a massive number of nodes, these points have to be taken into regard, therefore raising demand for low-complexity and robust algorithms with practical applicability. The aim of this chapter is to focus on these points and to close the gap between theory and practice by formulating low-complexity and robust algorithms that can be implemented in a system, thereby, leveraging the formulation of a practical system based on CS-MUD as presented in Chapter 6.
We therefore consider separate activity and data detection in a two stage setup. The idea followed in this chapter is to focus on activity detection algorithms for frame-based systems by looking at the received energies of
the nodes. This is facilitated by looking at the receive covariance matrix at the base-station and goes back to the concept of energy detection which is a commonly known concept with wide applicability. The main idea of energy detection is to estimate the presence of unknown signal from a noisy observation. Thus, the idea followed here is to apply this concept to CS-MUD to estimate the node activity by estimating the presence of a node.
However, the straightforward application of the energy detection concept to CS-MUD is not possible due to the under-determined multiuser system.
To still enable energy detection in CS-MUD it is necessary to estimate all energies for all nodes in the system from a superimposed multiuser signal.
To address this task, the heart of the energy detector for CS-MUD is a block that estimates the individual node energies from the receive covariance matrix at the base-station. Subsequently, we call this block multiuser energy estimator. The multiuser energy estimator estimates the support set SX
based on the receive covariance matrix. This estimated support set is then forwarded to a data detector, thereby, following a two step activity and data detection.
Applying energy detection concepts for CS-MUD has several advantages.
First, we have a direct estimation of the frame support SX without looking at the multiuser symbols X. This renders the underlying estimation problems for the multiuser energy estimation task simple as we only have to estimate N energies instead of N ×LF multiuser symbols. Second, energy detection based on the receive covariance matrix averages out the noise. This yields an SNR enhancing effect depending on the length of the time duration the receive covariance matrix is estimated. This has tremendous impact already with short frames of a few hundred symbols. Further it makes activity error rate control superfluous as the activity detection is already sufficiently good at very low SNR regions where data detection is not feasible. Third, as shown in this chapter, energy detection can even be applied in systems where the instantaneous receive power is not fully known to the base-station. This enables robust activity detection in setups with imperfect power control or fast fading.
We start by reviewing the general concept and the application of energy detection in Section 5.2. Further, in Section 5.4 we consider three different algorithms tailored for the energy estimation task in AWGN and the fading channel. Starting with a novel low complexity greedy Matrix Matching Pursuit (MMP) that is motivated by the well known OMP we investigate the performance of the well known MUSIC algorithm for the multiuser energy estimation task. Finally, we also consider solving the MAP optimization problem which incorporates the particular fading environment as prior probability. The MAP problem for the AWGN channel is a finite alphabet
problem and solvable by non-linear tree search approaches such as K-Best.
However, for fading channels approximations have to be made in order to enable a convex problem formulation that can be solved by state-of-the-art solvers.
Section 5.5 contains the numerical evaluation via simulations. For the AWGN channel, we will show that MAP estimation allows for reliable multiuser energy estimation with M = √
N observations only, which is a remarkable result. However, especially in fading channels, the MAP approach sacrifices optimality due to approximations made during the derivation.
Surprisingly, the MUSIC algorithm performs well in fading and in AWGN channels yielding a good trade-off between robustness and optimality. The introduced MMP suffers optimality in the fading channel and can only be applied for AWGN channels. Further, it can be shown that the SNR enhancing effect outperforms state-of-the-art algorithms such as the GOMP.
The results and schemes for the AWGN channel introduced in this chapter have been published in [MBD14]. Augmenting these concepts to the fading channel is a novel contribution solely contained in this thesis.