Joint User Activity and Non-Coherent Data Detection

Joint User Activity and Non-Coherent Data Detection in mMTC-Enabled Massive MIMO Using Machine Learning Algorithms Kamil Senel and Erik G. Larsson Department of Electrical Engineering (ISY) Link¨oping University, Link¨oping, Sweden Email: {kamil.senel, erik.g.larsson}@liu.se

Abstract—Machine-type communication (MTC) services are expected to be an integral part of the future cellular systems. A key challenge of MTC, especially for the massive MTC (mMTC), is the detection of active devices among a large number of devices. The sparse characteristics of mMTC makes compressed sensing (CS) approaches a promising solution to the device detection problem. CS-based techniques are shown to outperform conventional device detection approaches. However, utilizing CS-based approaches for device detection along with channel estimation and using the acquired estimates for coherent data transmission may not be the optimal approach, especially for the cases where the goal is to convey only a few bits of data. In this work, we propose a non-coherent transmission technique for the mMTC uplink and compare its performance with coherent transmission. Furthermore, we demonstrate that it is possible to obtain more accurate channel state information by combining the conventional estimators with CS-based techniques.

I. I NTRODUCTION Machine-type-communication (MTC) compels a paradigm shift in wireless communication due to the diverse data traffic characteristics and requirements in terms of delay, reliability, energy consumption, and security. A key scenario of MTC, referred as massive MTC (mMTC), corresponds to providing wireless connectivity to a massive number of low-complexity, low-power machine-type devices [1]. This massive number of devices is a result of various emerging smart services and applications such as healthcare, security, manufacturing, utilities and transportation [2]. Cellular networks are a potential candidate to accommodate the emerging MTC traffic thanks to the existing infrastructure and wide-area coverage [3]. However, previous generations of cellular systems are designed for human-type communication (HTC) which aims for high data rates using large packet sizes [4]. The integration of MTC along with HTC in cellular networks requires the handling of diverse communication characteristics. Moreover, unlike HTC, in MTC the data traffic is uplink-driven with packet sizes going down as low as a few bits [5]. An important example of singlebit transmission is the transmission of ACK/NACK bits [6]. This work was supported in part by ELLIIT and the Swedish Research Council (VR).

Massive MIMO (MaMIMO) is a key technology for 5G cellular networks, which exploits spatial multiplexing techniques to serve multiple users in the same time-frequency resource with the help of a large number of antennas at the base station (BS) [7]. MaMIMO technology is also a major enabler for the successful integration of mMTC services into the future cellular networks. Standard ALOHA-based approaches are not suitable for mMTC, as ALOHA suffers from low performance when the number of accessing devices is high [8]. A promising class of collision resolution methods, known as compressed sensing (CS) techniques, have been considered for device detection in mMTC [9]. With that approach, all active users transmit their unique identifiers concurrently, and the base station detects the set of active devices based on the received signal. Moreover, unique user identifiers can be utilized as a sensing matrix to estimate the channels along with the device detection [10]. The CS algorithms are shown to outperform conventional channel estimation techniques when the device activity detection is to be performed jointly with channel estimation [11]. However, conventional channel estimation techniques may also be employed once CS-based device detection has been accomplished. Under the assumption that perfect channel state information (CSI) is available, the channel states can be utilized as a sensing matrix and the joint active device and data detection problem can be tackled by CS-based techniques both for single-antenna [12], [13] and MIMO setups [14], [15]. In coherent transmission, the detection of active devices and the estimation of their channels is followed by payload data transmission. Coherent transmission in an mMTC setup has been investigated in [16] which proposes an approach that relies on pilot-hopping over multiple coherence intervals. A paper that investigates the spectral efficiency of a CS-based approach for mMTC setup is [17]. However, the acquisition of accurate channel state information is a challenging task, which prompted researchers to consider the possibility of non-coherent transmission schemes [18], [19]. Especially, for mMTC where devices usually transmit small packets intermittently, using resources to obtain CSI for coherent transmission may not be optimal.

In this work, we consider the uplink transmission between a large number of devices and a MaMIMO BS. The BS aims to detect the set of active devices and estimate their channels and decode a small amount of data transmitted by the active devices. The approaches in the literature employ coherent transmission based on estimates acquired from the CS-based algorithms. We demonstrate that the minimum-mean square estimator, combined with CS-based techniques, can be utilized to obtain more accurate CSI. Furthermore, a comparison between coherent and non-coherent approaches reveals that noncoherent transmission can significantly outperform coherent transmission in mMTC setups. This work extends our previous contribution presented in [20]. II. S YSTEM S ETUP We consider a MaMIMO system consisting of a single BS with M antennas and N single antenna devices. Non-line of sight communication is assumed and the channel between device k and the BS is modeled as p (1) gk = βk hk , ∀k = 1, . . . , N, where βk represents the large-scale fading and hk denotes the small-scale fading. The elements of hk are assumed to be i.i.d. CN(0, 1). The channel is constant and frequency-flat during τ samples called a coherence interval (CI). The largescale fading coefficients are assumed to be known at the BS and identical for all antennas whereas the small-scale fading coefficients, which change independently between CIs, are to be estimated in each CI. The active devices concurrently transmit τp -length pilot sequences which are used for both device detection and channel estimation. The remaining τ − τp symbols are utilized for data transmission. In traditional systems, an orthogonal pilot sequence is assigned to each device and this requires pilot sequences of length at least τp ≥ N . Such an approach is not feasible for mMTC where N is large. Therefore, we consider a setup with non-orthogonal pilot sequences which are generated by sampling an i.i.d. symmetric Bernoulli distribution. Let √ τp ϕk denote the pilot sequence of the kth device with p ϕk , [ϕ1,k , . . . , ϕτp ,k ]T ∈ Cτp ×1 where ϕl,k = (±1±j)/ 2τp and kϕk k2 = 1. The BS detects active users in a given CI based on the received composite signal, Y ∈ Cτp ×M which is defined as Y=

√

ρul τp

N X

αk ϕk gkT + Z,

(2)

k=1

where αk is the device activity indicator of user k with Pr(αk = 1) =  and Pr(αk = 0) = 1 − ; Z is additive white Gaussian noise with i.i.d. elements ∼ CN (0, σ 2 ). The transmission power of devices is denoted by ρul and is assumed to be identical for each device. Although power control can be employed to enhance the performance of the overall system, this requires further coordination between BS and the devices. We leave the investigation of power control and its effects on the overall system for future work.

TABLE I S IMULATION PARAMETERS Parameter Path and penetration loss at distance d (km) Bandwidth (Bw ) Cell edge length Minimum distance Total noise power (σ 2 ) UL transmission power (ρul )

Value 130 + 37.6 log10 (d) 20 MHz 250 m 25 m 2·10−13 W 0.1 W

Let Φ = [ϕ1 , . . . , ϕN ] ∈ Cτp ×N be the pilot matrix and X = [x1 , . . . , xN ]H ∈ CN ×M be the active channel matrix where xk = αk gk . (3) Then, (2) can be rewritten in vector notation as √ Y = ρul τp ΦX + Z.

(4)

Note that X has a sparse structure as the rows corresponding to inactive users are zero. The activity detection problem reduces to finding the non-zero rows of X. The problem considered in this work is finding efficient communication techniques for mMTC. The conventional techniques that rely on channel estimates and employ coherent transmission may not be suitable for mMTC for two critical reasons. First, the coherence interval length limits the number of available orthogonal pilots. Furthermore, utilization of higher frequency bands and relatively high mobility in some mMTC scenarios, e.g., vehicular sensing, makes the coherence interval length substantially smaller which compels different approaches for data transmission. Second, allocating orthogonal pilots to each device is suboptimal, if possible at all, due to the intermittent nature of mMTC as the devices transmit infrequently. III. D EVICE ACTIVITY D ETECTION Detecting the active devices is equivalent to finding the nonzero rows of X based on the composite received signal, Y and known pilot sequences, Φ. This problem can be modeled as a compressed sensing problem, as X have a row-wise sparse structure. In this work, a low-complexity CS algorithm called approximate message passing (AMP) [21], [22] is utilized to recover the sparse X. However, the ideas presented can be employed with any other CS-based device detection approach. Fig. 1 depicts the device detection performances of the conventional LMMSE and AMP algorithm for different M values. AMP clearly outperforms LMMSE in terms of device detection performance. This has also been reported in [9], [11]. Furthermore, the performance of AMP scales with M , although it has been observed that this scaling of detection performance with respect to M saturates [20]. The simulation parameters for the numerical analysis provided throughout the paper are summarized in the Table I. Similarly the comparison between the LMMSE and AMP algorithm for various values of τp , shown in Fig. 2, reveals a significant performance difference between the algorithms. Even though the performances of both algorithms scale with

Probability of Miss

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Probability of False Alarm Fig. 1. Device detection performance of AMP and MMSE with τp = 20 for N = 200 and  = 0.05.

τp , AMP benefits more from having longer pilots sequences in terms of device detection performance. The AMP algorithm provides an estimate of the channels, i.e., an estimate of X. However, once the set of active devices is determined (the non-zero rows of X), using the AMP estimates are strictly sub-optimal. Instead, a better estimate for device k can be obtained as follows, ! X √ T H H T yk = ϕk Y = ϕk ρul τp ϕk0 gk0 + Z , k0 ∈K

=

√

ρul τp gkT +

√

ρul τp

X

T 0 ϕH k ϕ k 0 gk 0 + z

(5)

k0 ∈K\{k}

where K is the set of active devices and z0 = ϕH k Z has i.i.d. CN (0, σ 2 ) components as kϕk k2 = 1. Then, the LMMSE estimate of gk is ˆk g

=

E{ykH gk } yk , E{ykH yk }

=

P

√

ρul τp

ρul τp βk y , H 2 2 k 0 k0 ∈K βk |ϕk ϕk0 | + σ

(6)

ρul τp

ρul τp βk2 , H 2 2 0 k0 ∈K βk |ϕk ϕk0 | + σ

P

which is assumed to be capable of affording the additional complexity. IV. DATA T RANSMISSION In this section, we provide a comparison of coherent and non-coherent transmission for an mMTC scenario. A. Coherent Transmission In coherent data transmission, the active users transmit their pilot sequences ϕk ∈ Cτp ×1 and the AMP algorithm is employed to detect the active devices and obtain their channel estimates. During data transmission, the BS receives X √ y = ρul gk sk + z (9) k∈K

where sk is the uncorrelated data symbol with |sk |2 = 1 and z is the AWGN with variance σ 2 . Let vk denote the combining vector for device k. Then, the processed signal for device k is ! X √ yk = vkH y = vkH ρul gk0 sk0 + z . (10) k0 ∈K

which is the true MMSE estimate were the pilot sequences and large-scale fading coefficients known at the BS. The estimate, ˆk has M i.i.d. elements and the mean square of the m-th g element is h i 2 γk = E |[ˆ gk ]m | , (7) =

Fig. 2. Device detection performances of AMP and LMMSE for different pilot sequence lengths, for N = 200 devices with  = 0.05 and M = 20.

(8)

where the expectation is with respect to the small-scale fading. Once the set of active devices are detected by the AMP, MMSE estimator can be utilized to obtain channel estimates. The increased complexity due to MMSE is less than one iteration of AMP and the computational burden is on the BS

Using the techniques in [7], an ergodic achievable rate for device k based on (10) is Rk = log2 (1 + Γk )

(11)

where Γk is the effective SINR given by
|E vkH gk |2

, Γk = P 2 E |vkH gk0 |2 + E (kvk k2 ) ρσul − |E vkH gk |2 k0 ∈K

(12) which heavily depends on the quality of the channel estimates. Although there are various ways of choosing the combining vector, we only consider maximum-ratio combining (MRC) in this work. Other techniques may potentially achieve higher

as the pilot sequence length is increased. Similarly, both techniques approach the perfect CSI case, since in the limit when τp → ∞, the effect of noise on the channel estimates vanishes and the pilot sequences becomes orthogonal.

3.5

3

B. Non-Coherent Transmission

2.5

2

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1

AMP AMP + MMSE Perfect CSI

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Fig. 3. Achievable rate comparison using different channel estimates obtained via AMP and MMSE under a setup with M = 50, N = 100 and  = 0.05.

SINRs [23], however the performance of different combining vectors is not the main focus of this work and MRC allows for closed-form expressions of the effective SINRs. Consider the maximum ratio combining (MRC) with the following combining vector, vk =

1 √ g ˆk . γk M

(13)

The spectral efficiency with MRC can be computed using the bounding techniques given in [7], and the following can be stated. Lemma 1: The achievable rate of device k is given by, τp (14) Rk = (1 − ) log2 (1 + Γk ) τ where Γk is the effective SINR given by M ρul

Γk = M

P

2 2 |ϕH k ϕk0 | ρul βk0 βk2

k0 ∈K\{k}

+

1 γk



 P

ρul βk0 + σ 2

k0 ∈K

(15) The rate that can be achieved with coherent transmission is limited by the non-orthogonality of the pilots, which creates coherent interference that scales with the number of antennas. Also note that (15) is valid for long block lengths while for control signaling tasks, probability of error is a more relevant performance measure. Nevertheless, the ergodic capacity gives an indication of how, qualitatively at least, the performance varies with the different system parameters. Fig. 3 illustrates how the quality of the channel estimates impacts the spectral efficiency. The estimates obtained via AMP, MMSE (after device detection is accomplished by AMP) are compared with the perfect CSI case. The curves depict the spectral efficiency of a single device which is known to be active; the remaining active devices are to be detected by AMP. The difference between AMP and MMSE estimates vanishes

In contrast to coherent transmission, explicit channel estimates are not required in non-coherent transmission. In order to convey r bits of data non-coherently, each device is allocated 2r pilot sequences and transmits one of these sequences based on the information bits. Here, the information is embedded into the pilot sequences and there is no need to allocate symbols for data transmission. Hence, τ symbols can be utilized for pilot sequences. Initial results on the special case of a single embedded bit (r = 1) were given in [20]. Here we extend the concept to multiple bits. ¯ k = [ϕk,0 , ϕk,1 , . . . , ϕk,2r −1 ] ∈ C(τ −r)×2r denote Let Φ the pilot sequences allocated for device k. This device transmits exactly only one of these pilot sequences, selected based on the information bits. Then, the composite received signal at the BS is √ ¯ + Z, ¯X (16) Y = ρul τp Φ ¯ = ¯ = [Φ ¯ 1, . . . , Φ ¯ N ] ∈ C(τ −r)×N 2r and X where Φ H ¯ ¯ ¯ [X1 , . . . , XN ] where Xk = [αk,0 gk , . . . , αk,2r −1 gk ] ∈ r CM ×2 . Here αk,l = 1 if device k is active and the lth-symbol is embedded. Recall that each device is active with probability  and ( r 2X −1 1, with Pr. , αn,i = ∀n = 1, . . . , N. (17) 0, with Pr. 1 − , i=0 Notice that with non-coherent transmission the BS must consider N 2r pilot sequences instead of N . However, the number of active users remains the same, i.e. the number of non¯ and X is equal. The active devices along zero rows of X with their embedded bits could in principle be detected by the AMP algorithm without any modification, implicitly assuming each pilot sequence belongs to a different, fictitious device. But such an approach is strictly sub-optimal, as the available ¯ is not utilized. A modified information about the structure of X AMP algorithm for the case of r = 1 was detailed in [20]. Its extension to the general r-bit case is conceptually similar, but for conciseness not presented here. Fig. 4 illustrates the performance of coherent and noncoherent transmission in terms of probability of error for 1bit and 4-bits transmission, for different coherence interval lengths. For 1-bit coherent transmission, first AMP is employed to detect the active devices and obtain the channel estimates. Then, a repetition code of length 3 with BPSK transmission is employed to convey the single bit of information. Hence, τp = τ − 3 and 3 symbols are utilized for data transmission with rate 1/3. For the 4-bit case, a (7, 4) Hamming code is utilized to convey 4 information bits. For the non-coherent transmission, AMP is employed to detect the transmitted pilot sequences among 2N = 200 candidates for the 1-bit case and 16N = 1600 for the 4-bit case. The results

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Fig. 4. Probability of error for 1-bit and 4-bits transmissions with respect to coherence interval length for M = 100 with N = 100 and  = 0.1.

show that non-coherent transmission not only outperforms coherent transmission but also scales better with the coherence interval length. An important point is that as the number of information bits increases, the performance difference between coherent and non-coherent transmission decreases. 10 0

Probability of Error

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5

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Fig. 5. Probability of error for a single information bit transmission for M = 100 with N = 200 and  = 0.1.

The results illustrated in Fig. 4 strongly suggest that noncoherent transmission is significantly better in terms of error probability. In order to further verify this result, the performance of coherent transmission using repetition codes of various lengths is illustrated in Fig. 5 for 1-bit transmission. The best performance is obtained with a length-15 repetition code, whereas lengths 9 and 21 provide similar performances. However, non-coherent transmission is significantly better than coherent transmission.

We investigated device detection and data transmission using the compressed sensing (CS) based algorithm AMP, in an mMTC setup where devices use non-orthogonal pilots. We considered both the probability of device detection, the channel estimation errors, and the resulting performance of coherent respectively non-coherent transmission. Non-coherent transmission was achieved by encoding the information to be transmitted into the choice of pilot sequence sent by the device, mapping r bits onto 2r possible pilots. In terms of device detection, CS-based approaches can outperform conventional approaches, and scale better with both the pilot sequence length and the number of BS antennas. We showed that once the active devices have been detected, it is possible to obtain more accurate channel estimates by using MMSE estimation, instead of relying on the estimates provided by the AMP. This in turn results in better data transmission performance. We also illustrated that for applications where the data to be transmitted comprises only a few bits (for example, for control plane signaling), non-coherent transmission can be better than coherent transmission in terms of error probability. R EFERENCES [1] METIS D6.6, “Final Report on the METIS System Concept and Technology Road map”, 2015. [2] Ericsson, “5G systems: Enabling the transformation of industry and society”, [Online], White paper. Available: https: //www.ericsson.com /assets/local/publications/white-papers/wp-5g-systems.pdf [3] Z. Dawy, W. Saad, A. Ghosh, J. G. Andrews, and E. Yaacoub, “Toward massive machine type cellular communications”, IEEE Wireless Communications, vol. 24, no. 1, pp. 120–128, 2017. [4] C. Bockelmann, N. Pratas, H. Nikopour, K. Au, T. Svensson, C. Stefanovic, P. Popovski, and A. Dekorsy, “Massive machine-type communications in 5G: Physical and MAC-layer solutions”, IEEE Communications Magazine, vol. 54, no. 9, pp. 59–65, 2016. [5] F. Boccardi, R. W. Heath, A. Lozano, T. L. Marzetta, and P. Popovski, “Five disruptive technology directions for 5G”, IEEE Communications Magazine, vol. 52, no. 2, pp. 74–80, 2014. [6] E. G. Larsson, and R. Moosavi, “Piggybacking an additional lonely bit on linearly coded payload data”, IEEE Wireless Communications Letters, vol. 1, no. 4, pp. 292–295, 2012. [7] T. L. Marzetta, E. G. Larsson, H. Yang and H. Q. Ngo, Fundamentals of Massive MIMO, Cambridge University Press, 2016. [8] V. Boljanovic, D. Vukobratovic, P. Popovski, and C. Stefanovic, “User Activity Detection in Massive Random Access: Compressed Sensing vs. Coded Slotted ALOHA”, [Online]. Available: https://arxiv.org/pdf/1706.09918.pdf [9] J. W. Choi, B. Shim, Y. Ding, B. Rao, and D. I. Kim, “Compressed sensing for wireless communications: Useful tips and tricks.”, IEEE Communications Surveys and Tutorials, vol. 19, no. 3, pp. 1527–1549, 2017. [10] Y. Nan, L. Zhang, and X. Sun, “Efficient downlink channel estimation scheme based on block-structured compressive sensing for TDD massive MU-MIMO systems”, IEEE Wireless Communications Letters, vol. 4, no. 4, pp. 345–348, 2015. [11] J. W. Choi, B. Shim, and S. H. Chang, “Downlink pilot reduction for massive MIMO systems via compressed sensing”, IEEE Communications Letters, vol. 19, no. 11, pp. 1889–1892, 2015. [12] Y. Du, B. Dong, Z. Chen, X. Wang, Z. Liu, P. Gao, and S. Li, “Efficient Multi-User Detection for Uplink Grant-Free NOMA: Prior-Information Aided Adaptive Compressive Sensing Perspective”, IEEE Journal on Selected Areas in Communications, 2017. [13] B. Wang, L. Dai, Y. Yuan, and Z. Wang, “Compressive sensing based multi-user detection for uplink grant-free non-orthogonal multiple access”, IEEE Vehicular Technology Conference, pp. 1-5, 2015.

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