Summary
The era of sole human-oriented traffic disappears, thereby raising novel challenges on the design of future communication systems such as 5G and beyond. Among the demands, the aggregation of M2M is and remains one of the most challenging ones. Ranging from sporadic and short messages to high data-rate ultra-reliable communication, M2M can be seen as a diverse traffic source, whose aggregation requires carefully designed physical layer concepts. Especially, efficient aggregation of a massive amount of M2M devices with low overhead in terms of the medium access is a challenging task. To this end, the aim of this thesis is to address the physical layer aspects of the aggregation of sporadic M2M with a focus on low overhead.
InChapter 2, first an overview of sporadic M2M was given. The resulting system model encompasses the description of nodes that sporadically access the wireless channel to transmit small data packages to a central aggregation point. The medium access was closely aligned to CDMA and nodes spread their data to chips prior to transmission. The main difference to the classical application of CDMA is that the length of the spreading codes is much shorter than the number of nodes in the system, yielding overloaded systems.
Further it was shown that the base-station has to perform a joint activity and data detection. Hence, activity errors affect the performance of the communication. The corresponding error measures known as false alarm and missed detection were presented and it was shown that the system impact of both is fundamentally different. While false alarm errors result in a SNR loss at the data detection, missed detection errors lead to a loss of data.
Motivated by this observation, the aspect of sole activity detection with a subsequent data detection was presented in Chapter 3. Here the focus was to tackle the activity detection problem from a communication’s point of view
via soft information processing to control false alarm and missed detection rates. The basis for this chapter was the formulation of the activity LLR and corresponding decision rules. The eye opener was the fact that the typically optimal MAP decision rule yields undesirable activity error rates. Especially, the missed detection rate was shown to be very high when pursuing MAP estimation. Subsequently, two additional decision rules were introduced to enable controlling the activity error rates. First, the Bayes-Risk detection rule was shown to be a generalized MAP decision rule with an adjustable parameter Ω, determining the preference of the detector towards activity or inactivity. Preferring one direction automatically decreases one of the activity error rates while increasing the other rate. The Bayes-Risk decision rule allows overcoming the shortcomings of the MAP rule. However, the connection between Ω and resulting activity error rates has to be determined numerically. To enable full activity error rate control Chapter 3 introduced an adaptive threshold Neyman Person detector. This approach minimizes one activity error rate while bounding the other rate to a constant value. The results exemplary show that adaptive threshold Neyman-Pearson detection achieves a constant missed detection rate while simultaneously minimizing the false alarm rate.
Additionally, Chapter 2 addressed the implementation of upper decision rules. More specifically, the efficient calculation of the activity LLRs via Sphere Decoding was addressed. Here it was shown that the calculation of an activity LLR can be cast as a non-convex, penalized and underdetermined set of equations with a finite alphabet constraint. It was shown that this problem can implicitly be regularized by exploiting the penalty term. Results show that Sphere Decoding allows for optimal calculation of the activity LLRs at the cost of random complexity with exponential bound. Thus, K-Best detection is used as a sub-optimal approach which nearly achieves the performance of Sphere Decoding.
The joint activity and data detection was addressed in Chapter 3 via an all-encompassing detector involving knowledge about frame activity and channel coding. More specifically a message passing detector was formulated that accounts for a full soft estimation in frame based transmissions. This detector was shown to consist of three building blocks, a multiuser detector, a decoder and a frame activity estimator called SPE. The multiuser detector is based on recent advances from the field of message passing in Compressed Sensing and estimates the augmented symbols from the nodes. Combining several multiuser detectors to a bank lead to frame Belief Propagation.
Here messages are exchanged between a bank of decoders, a bank of SPEs and a bank of multiuser detectors. After some iterations this frame belief propagation algorithm yields the soft information for the information bits
and for the node activity states. The simulations have shown that the utilization of a low rate channel code allows to further decrease the spreading sequence length by decreasing the code-rate. Simulations were carried out using a repetition code, therefore it might be the case that more sophisticated channel codes even further decrease the spreading sequence length required.
Chapter 2 and Chapter 3 addressed the optimal activity and the optimal joint activity and data detection. Results were promising and it was shown that knowledge about frame activity boosts the detection performance.
Chapter 4 goes away from optimal algorithms to low complexity algorithms for detecting frame activity. The idea followed there was to use the concept of energy detection for estimating node activity in CS-MUD. Here we showed that the individual receive energy for each node can be estimated from the estimated receive covariance matrix at the base-station. This concept leaves the assumption of having AWGN channels between the node and the base-station to fading channels ranging from Rician to full Rayleigh fading. The main advantage of using the receive covariance matrix is the SNR enhancing effect caused by the averaging carried out. The results showed that the algorithms developed in this chapter exhibit tremendous SNR gains for already for short frames. Further, three algorithms were introduced. First, a simple and heuristic matrix matching pursuit motivated by the well known OMP was presented. Here energies are estimated by correlating the receive covariance matrix with the columns of a dictionary to identify active nodes.
This algorithm was shown to be simple but sacrifices performance, especially in the fading channel where receive powers are unknown. Its application is restricted to the AWGN channel. Second, the well known MUSIC algorithm, based on the Eigenvalue decomposition of the receive covariance matrix was considered. Its application turned out to be quite powerful as MUSIC is able to estimate the activity in Rayleigh and Rician fading channels with good reliability. Finally, the MAP optimization problem for the powers denoted as MAP-E based on the receive covariance matrix was considered. Here it was shown that the particular fading can be subsumed into the prior power probability contained in the MAP. Depending on AWGN or Rayleigh fading channel, two versions of the MAP-E were formulated. In case of AWGN the optimization problem is over a finite alphabet allowing for non-linear algorithms such as Sphere Decoding. The results showed that the MAP-E algorithm achieves reliable activity detection with M = √
N observations only. Unfortunately, this is not true for the Rayleigh fading channel. Here the MAP-E showed performance losses and was even outperformed by MUSIC.
The last chapter of this thesis, Chapter 5 aimed at putting the advances of the preceding chapters into a practical system concept. The main focus was to identify certain key challenges that a practical system for M2M
has to address. Based on these requirements, the resulting MCSM system was defined. MCSM was shown to consist of three key technologies that hand in hand allow for the aggregation of sporadic M2M. First, a multi-carrier scheme was used to flexibly allocate time and frequency resources.
The MCSM system concept summarizes narrow-band systems that are simultaneously multiplexed to the bandwidth given. The assumption of narrowband systems lead to the second key technology component, being non-coherent receiver concepts driven by differential modulation. Due to the application of differential modulation the pilot overhead could be decreased down to a known starting phase. The third technology component was CS-MUD which is used on top of OFDM. Here the nodes multiplex their chips to the sub-carriers prior to transmission. This multiplexing was shown to be one of the MCSM specific design parameters that allow adapting the system to various channel conditions. In MCSM the activity detection schemes from Chapter 4 were used in combination with a least-squares data detector. The verification of the MCSM system was shown via an example parametrization simulatively and via a hardware demonstration platform. The concept shown can be seen as a candidate system for aggregating sporadic M2M uplink traffic in various scenarios. Depending on the propagation environment, the channel conditions and the requirements, MCSM allows adapting its parameters to match the requirements. This powerful property renders MCSM to be a candidate technology not only for 5G systems but also for M2M system in various other setups such as industrial applications.
Open Questions and Future Work
• The complexity of the frame BP was shown to be very high. Here recent research has shown that the complexity of the multiuser detector can be decreased by using second order approximations of the messages.
The resulting algorithm is known as AMP and has been published in [DMM09]. Applying these approximations may help to further decrease the performance.
• Further, the frame BP could be augmented to work within the MCSM system. This requires involving a differential demodulator within the frame BP. The connecting point would be the variable for the augmented symbol xn, whose prior probability summarized by fn would change. Therefore, the messages from the augmented symbol xn to the likelihood factor gm change. Here, the simple numeric calculation of mean and variance may not be possible anymore as xn is continuous-valued. The sole task of differential demodulation via belief propagation has been considered in [Bar10]. However, merging the results with the frame BP is still an open challenge.
• For multiuser energy estimation shown in Chapter 5 it was assumed that the base-station has instantaneous knowledge about the number of active nodes Nact. Here, future work can address the question of how this information is obtained. As stated within the corresponding chapter, existing works consider the Eigenvalue distribution of the covariance matrix [CW10].
• The MCSM system concept offers a wide field for possible future work.
Within this thesis we applied a least-squares data-detector, which is clearly not the best one can do. Thus, improved multiuser detection in MCSM is one possible direction of future research.
• The second point addresses the multi-carrier scheme applied. Here we used OFDM which comes at the cost of a cyclic-prefix. Further, it is well known that OFDM suffers performance in case of offsets such as Doppler impact. One idea would be to change the multi-carrier scheme to a generalized waveform accommodating these effects. The other side of the medal is that with non-orthogonal waveforms, more sophisticated multiuser detectors are required. A promising approach here is again to use message passing to detect the data of the nodes.
Appendix
A.1 Proof of the Bayes-Risk
The Bayes-Risk detector minimizes the Risk of an erroneous decision, where we can assign the weights CFA for false alarm and CMD for missed detection.
We hereby implicitly set the risks for correct decisions to zero. The risk can be formulated via
R = CFAPr (xn = 0)
ZA
py(y|xn = 0)dy+
CMDPr (xn ∈ A)
ZI
py(y|xn ∈ A)dy (A.1) Where ZI ∪ZA = Z are disjunct regions of the observation space Z which allows for reformulation of (A.1) according to
R = CFAPr (xn = 0)
ZZI
py(y|xn = 0)dy+
CMDPr (xn ∈ A)
ZI
py(y|xn ∈ A)dy. (A.2) With
Z
py(y|xn)dy = 1 ∀xn, (A.3) we can rewrite
ZZI
py(y|xn = 0)dy = 1−
ZI
py(y|xn = 0)dy ∀xn. (A.4)
Which allows to reformulate (A.2) to obtain R = CFAPr (xn = 0)
1−
ZI
py(y|xn = 0)dy
+ CMDPr (xn ∈ A)
ZI
py(y|xn ∈ A)dy. (A.5) Rearranging (A.5), yields
R = CFAPr (xn = 0) +
ZI
CMDPr (xn ∈ A)py(y|xn ∈ A)
I1
dy−
ZI
CFAPr (xn = 0)py(y|xn = 0)
I2
dy. (A.6)
Equivalently, we can rewrite the integration in (A.5) with respect to ZA and obtain for the risk
R= CMDPr (xk ∈ A) +
ZA
CFAPr (xn = 0)py(y|xn = 0)
I2
dy−
ZA
CMDPr (xn ∈ A)py(y|xn ∈ A)
I1
dy. (A.7)
With (A.6) and (A.8) the regions ZA and ZI are the free parameters that allow to minimize the risk. We see that the functionals below the integrals I1 and I2 are all positive and show up in both expressions. The risk can be minimized by estimating HI if I2 > I1 and HA if I1 > I2. This strategy results in a likelihood ratio test between the two hypothesis inactive and active. Note that the hypothesis for activity is a composite hypothesis which has to be evaluated over all possible sub-hypothesis yielding.
R = CMDPr (xk ∈ A) +
ZA
CFAPr (xn = 0)py(y|xn = 0)
I2
dy−
ZA
CMD
xn∈A
Pr (xn ∈ A)py(y|xn ∈ A)
I1
dy. (A.8)
Deciding in favor of I1 or I2 results in the LRT (3.20).