GrantFree Massive MTCEnabled Massive MIMO: A Compressive Sensing Approach
Abstract
A key challenge of massive MTC (mMTC), is the joint detection of device activity and decoding of data. The sparse characteristics of mMTC makes compressed sensing (CS) approaches a promising solution to the device detection problem. However, utilizing CSbased approaches for device detection along with channel estimation, and using the acquired estimates for coherent data transmission is suboptimal, especially when the goal is to convey only a few bits of data.
First, we focus on the coherent transmission and demonstrate that it is possible to obtain more accurate channel state information by combining conventional estimators with CSbased techniques. Moreover, we illustrate that even simple power control techniques can enhance the device detection performance in mMTC setups.
Second, we devise a new noncoherent transmission scheme for mMTC and specifically for grantfree random access. We design an algorithm that jointly detects device activity along with embedded information bits. The approach leverages elements from the approximate message passing (AMP) algorithm, and exploits the structured sparsity introduced by the noncoherent transmission scheme. Our analysis reveals that the proposed approach has superior performance compared to application of the original AMP approach.
IEEEexample:BSTcontrol
I Introduction
Machinetypecommunication (MTC) compels a paradigm shift in wireless communication due to the diverse data traffic characteristics and requirements on 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 lowcomplexity, lowpower machinetype devices [deliverable2015d6]. These devices enable various emerging smart services in the fields of healthcare, security, manufacturing, utilities and transportation [ericsson].
Cellular networks are a potential candidate to accommodate the emerging MTC traffic thanks to the existing infrastructure and widearea coverage [centenaro2016long]. However, previous generations of cellular systems are designed for humantype communication (HTC) which aims for high data rates using large packet sizes [bockelmann2016massive]. 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 uplinkdriven with packet sizes going down as low as a few bits [boccardi2014five]. An example of a singlebit transmission is the transmission of ACK/NACK bits [larsson2012piggybacking]. In the mMTC context, the amount of signaling overhead per packet can become very significant compared to traditional setups with mainly humandriven traffic [dawy2017toward].
In mMTC, only a small fraction of the devices is active at a time. One reason for this sporadic traffic pattern is the inherent intermittency of the traffic (especially for sensor data), but the use of higherlevel protocols that generate bursty traffic also contributes. The setup of interest is depicted in Fig. 1. Here, a base station (BS) with antennas provides service to devices and among these devices, only are active at a given time. Our focus will be on systems with Massive MIMO technology such that is large. Massive MIMO is an important component of the 5G physical layer, as it enables the multiplexing of many devices in the same timefrequency resources as well as a range extension owing to the coherent beamforming gain [redbook].
The intermittency of mMTC traffic calls for efficient mechanisms for random access. Here we focus on grantfree random access, where devices access the network without a prior scheduling assignment or a grant to transmit. Owing to the massive number of devices, it is impossible to assign orthogonal pilot sequences to every device. This inevitably leads to collisions between the devices. Conventionally, such collisions are handled through collision resolution mechanisms [sesia2011lte, de2017randomM]. Standard ALOHAbased approaches are not suitable for mMTC, as ALOHA suffers from low performance when the number of accessing devices is large [boljanovic2017user]. A promising class of collision resolution methods, known as compressed sensing (CS) techniques, have been considered for device detection in mMTC [choi2017compressed]. With that approach, all active users transmit their unique identifiers concurrently, and the base station (BS) 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 [nan2015efficient]. The CS algorithms are shown to outperform conventional channel estimation techniques when the device activity detection is to be performed jointly with channel estimation [choi2015downlink]. However, conventional channel estimation techniques may also be employed once CSbased 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 CSbased techniques both for singleantenna [du2017efficient, wang2015compressive] and MIMO setups [gao2016compressive, garcia2015low].
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 [de2017random] which proposes an approach that relies on pilothopping over multiple coherence intervals. A paper that investigates the spectral efficiency of a CSbased approach for mMTC setup is [liu2017massive]. However, the acquisition of accurate channel state information is a challenging task, which prompted researchers to consider the possibility of noncoherent transmission schemes [liu2017novel, jing2016design]. 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 Massive MIMO 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 CSbased algorithms. We demonstrate that the minimummean square estimator, combined with CSbased techniques, can be utilized to obtain more accurate CSI. Furthermore, a novel noncoherent transmission technique is introduced. A comparison between coherent and noncoherent approaches reveals that noncoherent transmission can significantly outperform coherent transmission in mMTC setups. Comparisons of coherent and noncoherent transmission techniques in multipleantenna setups are available in the literature [zheng2002communication]. It is known that generally, noncoherent transmission outperforms coherent transmission. In this work, we provide a comparison under an mMTC setup with specific focus on the challenges that arise when joint device detection, channel estimation and data decoding must be performed with nonorthogonal pilots.
The specific contributions of our work are as follows:

An analysis of the AMP algorithm demonstrates that the gains from increasing the number of BS antennas is comparable to increasing pilot sequence length, making massive MIMO a key enabler for MTC applications. (Section LABEL:sec:DevDetAMP)

We investigate the effect of employing a power control approach suitable for mMTC setups, on device detection performance. The analysis reveals that power control provides significant improvement in terms of device detection. (Section LABEL:sec:PowerControl)

We present a scheme which combines conventional channel estimation techniques with CSbased device detection algorithms, and derive a closedform expression for the resulting achievable spectral efficiency. The proposed scheme significantly enhances the spectral efficiency for coherent transmission. (Section LABEL:sec:ChEstimation)

We introduce a novel noncoherent data transmission technique based on embedding information bits to the pilot sequences to be decoded during the user activity detection process. (Section LABEL:sec:noncoh)

We devise a new receiver based on approximate message passing that detects which devices are active, and detects their associated information bits, without using any prior information neither on the channel response nor on the user activity. (Section LABEL:sec:AlgDes)

We provide an extensive comparison between coherent and noncoherent transmission techniques and demonstrate that under mMTC setups, noncoherent transmission is more suitable for conveying small numbers of information bits. (Section LABEL:sec:CohVsNon)
The paper in hand goes beyond our previous conference papers [senel2017device, senel2017mMTCwsa], by considering power control, noncoherent transmission for multiple bits, detailing a new modified AMP algorithm for the multibit case, and providing several new experimental results and comparisons. Moreover, the analysis is carried out utilizing a novel receiver, which is designed for the proposed noncoherent scheme and provides additional performance gains compared to the original AMP algorithm.
Ii System Setup
We consider the uplink communication between a single base station with antennas and single antenna devices. Nonline of sight communication is assumed and the channel between device and the BS is modeled as
(1) 
where is the largescale fading and denotes the smallscale fading. The elements of are assumed to be i.i.d. . The channel is constant and frequencyflat for samples called coherence interval (CI). The largescale fading coefficients are assumed to be known at the BS and identical across antennas whereas the smallscale fading coefficients which change independently between CIs, are to be estimated in each CI.
During coherent transmission, each CI is utilized for both channel estimation and data transmission, i.e., each active device transmit length pilot sequences and the remaining symbols are utilized for data transmission. In order to accomplish coherent data transmission, BS must detect the active devices, estimate their channels, and decode the transmitted data based on the acquired channel estimates. In traditional networks, an orthogonal pilot sequence is assigned to each device which requires pilot sequences of length . Such an approach is not feasible for mMTC systems as the number of devices is large. Therefore, we consider a setup with nonorthogonal pilot sequences which are generated by sampling an i.i.d. symmetric Bernoulli distribution. Let denote the pilot sequence of the th device with where and . As a result of the Bernoulli distribution assumption, there are a finite number of unique pilot sequences and hence the probability that two devices have identical pilot sequences (called the “collision probability” here) is nonzero. If the sequences were generated by sampling an i.i.d. symmetric Gaussian distribution, the collision probability would be zero. However, as will be demonstrated later, pilot sequences based on Bernoulli distribution provide better performance. Let be the collision probability for a given number of devices, , and a pilot sequence length, . Then,
(2) 
In practice, the collision probability is negligible, for example, with devices and pilot sequences of length , the collision probability is .
In our setup, we assume that the pilot sequences associated with each device are known at the BS. The justification is that in practice the BS would have a list of devices that are associated with it, and their unique identifiers. The pilot sequences may then be created by a pseudorandom generator that uses the unique identifiers of the devices as seeds. Since these unique identifiers are known to the BS, the pilot sequence matrix is also known at the BS. Note that all devices are not necessarily active in each of the coherence intervals; only when they have data to transmit, they will communicate with the BS.
The BS detects active devices in a given CI based on the received composite signal, which is defined as
(3) 
where is the device activity indicator for device with and ; is additive white Gaussian noise with i.i.d. elements . The transmission power is denoted by and it is identical for each device. In Section LABEL:sec:PowerControl, we investigate the performance when power control is employed.
Let be the pilot matrix and be the effective channel matrix where
(4) 
Then, (3) can be rewritten in vector notation as
(5) 
Note that, has a sparse structure as the rows corresponding to inactive users are zero. The activity detection problem reduces to finding the nonzero rows of .
The motivation of this work is based on finding efficient communication techniques for grantfree random access with small amounts of data in mobile systems. 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, the duration in which the channel can be assumed to be flat, limits the number of orthogonal pilots which in turn makes it harder to obtain accurate channel estimates. Second, allocating orthogonal pilots to each device is suboptimal, if possible at all, due to the intermittent nature of mMTC. Furthermore, utilization of higher frequency bands and relatively high mobility of devices in some mMTC scenarios, e.g. vehicular sensing, the coherence interval length is substantially smaller which compels different approaches for data transmission.
Iii Review of Approximate Message Passing
The problem of detecting active devices is equivalent to finding the nonzero rows of based on the noisy observations, and known pilot sequences, . This problem can be modeled as a compressive sensing problem, as has a rowwise sparse structure. For the single antenna setup, the problem reduces to the single measurement vector (SMV) reconstruction problem whereas with multiple antennas it becomes a multiple measurement vector (MMV) reconstruction problem. CSbased techniques are shown to outperform linear minimum mean square error (LMMSE) estimators in terms of device detection performance in various works [choi2017compressed, choi2015downlink]. In this work, a low complexity CS algorithm called approximate message passing (AMP) [kim2011belief, ziniel2013efficient] is utilized to recover the sparse . Next, we provide a brief review of the AMP algorithm.
Let denote the index of the iterations and let be the estimate of at iteration . Then, the AMP algorithm can be described as follows:
(6)  
(7) 
where is a denoising function, is the first order derivative of and is the residual at iteration [rangan2016vector]. The residual in (7) is updated with a crucial term containing , called the Onsager term, which has been shown to substantially improve the performance of the iterative algorithm [donoho2009message].
An important property of AMP is that in the asymptotic region, i.e., as while their ratios are fixed, the behavior is described by a set of state evolution equations [rangan2011generalized]. In vector form, the state evolution is given by [bayati2011dynamics]
(8) 
where ; is a complex Gaussian vector with unit variance and has the distribution
(9) 
Here, is the distribution of the channel vector of the active device and is the dirac Delta at zero corresponding to the inactive device channel distribution. The expectation in (8) is taken with respect to and allows performance analysis of the AMP algorithm as the update given by (6)(7) are statistically equivalent to applying a denoiser to the following [rangan2011generalized]:
(10) 
which decouples the estimation process for different devices. The state evolution is shown to be valid for a wide range of Lipschitz continuous functions [bayati2011dynamics]. For the multiuser detection problem, the following denoising function is used:
(11) 
where
(12)  
(13) 
The denoising function (11) is shown to be the MMSE for the equivalent system described by (10) in [kim2011belief]. Notice that, when the active device are to be detected the MMSE given by (11), is nonlinear.
Note that is a thresholding function based on the likelihood ratio which can be computed by considering two cases in (10), device is active, i.e., and when it is inactive. For the case when , i.e., every device is active, (11) reduces to the linear MMSE estimator.
Remark 1
State evolution provides an important tool to analyze AMP. However, the equations defined in (10), which decouple the estimation process for different devices, are only valid in the asymptotic region. More detail on the behavior of AMP in the asymptotic region is given in Section LABEL:sec:Asymp.
Parameter  Value 

Path and penetration loss at distance (km)  130 + 37.6 
Bandwidth ()  20 MHz 
Cell edge length  250 m 
Minimum distance  25 m 
Total noise power ()  2 W 
UL transmission power ()  W 