Internet of things (IoT), which refers to the connected future world in which every mobile device and machines are linked to the internet via wireless link, has received attention from both academia and industry in recent years . IoT enables a wide range of unprecedented services such as autonomous driving, smart home/factory, and factory automation, just to name a few . Massive connectivity is one of the most important requirements of a fully connected IoT society [3, 4]. In accordance with this trend, the international telecommunication union (ITU) defined massive machine-type communication (mMTC) as one representative service category.111Three representative service categories include enhanced mobile broadband (eMBB), ultra-reliable and low latency communication (uRLLC), and massive machine-type communication (mMTC) . In mMTC networks, data communications may occur between an MTC device and a server or directly between MTC devices . It is of considerable importance to support high connection density with limited resources because the number of devices is at least two orders of magnitude higher than current human-centric communication.
From a technological standpoint, enormous number of devices in mMTC networks can be used to exploit full benefit of multiuser MIMO. It is essential to have high-resolution channel state information (CSI) at the access point (AP) to exploit multiuser diversity gain [7, 8]. In most current cellular systems relying upon frequency division duplexing (FDD), the quantized CSI is communicated to the AP via a rate-constrained feedback link [9, 10, 11]. One challenge of feedback-assisted multiuser systems is that low-resolution CSI overrides the multiuser diversity gain because the signal-to-interference-plus-noise ratio (SINR) is limited due to the channel quantization error [12, 13]. In the feedback-assisted multiuser systems, the rate-constrained feedback mechanism is the biggest obstacle to supporting a massive number of devices on an MTC network.
Antenna combining techniques, e.g., quantization-based combining (QBC) , has been proposed to obtain high-resolution CSI. A key feature of the QBC is that receive antennas are combined to generate an effective channel that can be quantized accurately. Employing more antennas would enhance the quantization performance. However, direct application of antenna combining techniques for mMTC is infeasible since it is difficult to employ multiple antenna elements due to the strict budget constraints on small-scale devices. In this paper, we develop a cooperative feedback strategy to obtain an additional spatial dimension for the antenna combining process without imposing an additional burden on mMTC devices.
Recently, multiuser systems incorporating user cooperation algorithms have been proposed [15, 16]. In , the user in the cooperative link helps other adjacent users by forwarding adjacent users’ information while achieving its own quality of service (QoS). In , the users in the cooperative link exchange their CSI via device-to-device (D2D) communications. The users can compute a more appropriate precoder at the user side because CSI exchange allows users to obtain the global CSI. However, since the number of users222The users can be any kinds of machines, devices, and mobile users. for the mMTC network is much larger than that of current human-centric communication, it is not feasible to exchange CSI with all the other users. Therefore, it is important to develop solutions with minimal overhead for feedback and/or cooperative links.
The aim of this paper is to develop user cooperation strategies for an mMTC network allowing only point-to-point CSI exchange between close-in users. In order to obtain high-resolution CSI with a minimal burden on the user cooperation framework, few bits are exploited to exchange CSI. To the best of our knowledge, a user cooperation strategy designed to reduce channel quantization error has been proposed here for the first time. The main contributions of this paper are summarized as follows:
Cooperative limited feedback: Adjacent users are connected to a cooperation link and these users are considered one cooperation unit (CU). Each user in CU shares the other user’s local channel information (i.e., local channel direction information (CDI) and channel quality indicator (CQI)). CSI sharing is only allowed between users in a CU. Each user generates the global channel information required for downlink transmission (i.e., global CDI and CQI) using its own channel information and the local channel information received from an adjacent user. After exchanging each other’s global CQI, the user having larger global CQI is assigned as the main user (MU) and the other user is assigned as an assistant user (AU). The AU acts as an assistant for MU by allowing MU to use its receive antennas to construct the global CDI more precisely. The MU only feeds back the global CSI so that the AP perceives the MU as the sole active user, while the AU is transparent to the AP. In the data transmission phase, both the MU and AU receive data information from the AP and then the AU forwards the received signal to the MU. The channel feedback accuracy of the MU is improved due to the virtue of exploiting AU resources.
Automatic role assignment: Identification of the MU and AU is an important issue since only the spectral efficiency of the MU can be increased by sacrificing the resources of the AU. In the proposed algorithm, the cooperation process between users is designed to occur without transmitter intervention (i.e., a grant-free environment) through an active decision process. An important issue behind this active decision process is the motivation for participating in cooperative communication as the AU.333One possible option can be the social relationship between users 
. If users have a close relationship in the social domain, users can readily help each other by using their own resources for cooperative feedback. Other possible scenario can be the cooperation between different devices in each user. Alternatively, an artificial intelligence (AI)-based and/or game-theoretic approach can be applied in identifying the MU and AU and this would be an interesting future research topic.Under a grant-free environment, the AP regards the MU as the sole user and this identification process is transparent to the AP.
Adaptive cooperative feedback: If cooperative feedback is activated, the number of active users is reduced by half because two users are combined as a single CU to obtain high-resolution CSI. Unless a massive number of users are active in the mMTC network, the cooperative feedback strategy might not be an effective solution because the multiuser diversity gain is highly limited in a small-user regime. For this reason, effective allocation of limited multiuser resources is required to obtain accurate CSI without loss of multiuser diversity gain. We analyze the sum-rate throughput of the multiuser MIMO systems relying upon the proposed cooperation algorithm. Based on the analytical studies, we develop cooperation mode switching criteria to activate/deactivate the cooperation mode according to channel and network conditions.
In Section II, we briefly introduce a multiuser MIMO system and review a user selection algorithm. In Section III, we present the proposed cooperative feedback algorithm. An adaptive cooperation algorithm is developed based on analytical studies on sum-rate throughput in Section IV. In Section V, we present numerical results to verify the performance of the proposed scheme. We conclude the paper in Section VI.
Throughout this paper, denotes the field of complex numbers,
denotes the complex normal distribution with mean
and variance, is the
all zeros matrix,is the all ones matrix, is the identity matrix,
is the Chi-squared random variable,
is the Beta-distributed random variable,is the Beta function, is the gamma function, is the binomial coefficient, is the Pochmann symbol, is the ceiling function, is the expectation operator, is the indicator function, is the -norm, and is the
-th element of the column vector. Also, , , , , and denote -th column vector, pseudo-inverse, conjugate transpose, trace, and -th entry of the matrix , respectively.
Ii System Model and Background
We briefly review the FDD-based multiuser MIMO systems. We first present the system model and then discuss antenna combining-based limited feedback. An overview of conventional multiuser MIMO systems is depicted in Fig. 1(a).
Ii-a System Model
We consider multiuser MIMO systems employing transmit antennas at the AP and receive antennas at each of users. Assuming a block-fading channel, an input-output expression for the -th user444The user index is subscripted and the set of user indices in the network is written by . is defined as
where is the received baseband signal, is the signal-to-noise ratio (SNR), is the unit-norm combiner,
is the MIMO channel matrix, is the channel vector between the AP and the -th receive antenna consisting of independent and identically distributed (i.i.d.) entries following , is the transmit signal vector (with the power constraint ), and is the additive noise vector with entries following .
We consider a single layer data transmission for each user. The transmit signal vector is rewritten as , where
is the precoder and is the transmit symbol vector. Note that and denote the transmit beamformer and the data stream for the -th scheduled user with the power constraints and .
In FDD-based cellular systems, an AP obtains channel information through receiver feedback from each user. In feedback-assisted MIMO architectures, channel vectors are quantized using the predefined codebook
where is the number of codewords in the global codebook. To facilitate the multiuser signaling framework, the quantized channel information is fed back to the AP via a rate-constrained -bit feedback link.
, exploiting more sets of unitary matrices (i.e., oversampled discrete Fourier transform (DFT) codebook) enables the AP to obtain high-resolution CSI. However, an ultra low-latency requirement for MTC services restricts the use of large codebooks. Assuming an intensely rate-constrained feedback link, we considercodewords for channel feedback and beamforming, meaning that the number of codewords equals to the number of transmit antennas. If only
codewords are allowed for CSI quantization, it would be optimal to consider a set of orthonormal vectors for random beamforming
. We use a single unitary matrixfor defining codewords according to .
Ii-B QBC-based Limited Feedback for Multiuser MIMO
One major issue of the feedback architecture using codewords is that the channel quantization performance is expected to be poor in a single receive antenna scenario. When multiple receive antennas are available, antenna combining techniques can be applied to enhance the channel quantization performance [14, 21]. In this paper, we consider a QBC-based antenna combining algorithm . The objective of the QBC algorithm is to compute an effective channel vector that can be quantized accurately using a small-sized codebook. For a given target codeword , the receive combiner is computed such that a cross-correlation between the effective channel
and the target codeword is maximized. As discussed in , the effective channel that maximizes the cross-correlation is obtained by projecting onto the channel subspace such that
where is the orthonormal basis that spans . Using the QBC algorithm, the receive combiner , which satisfies , can be computed by multiplying the pseudo-inverse of the channel matrix such as
Finally, the unit-norm combiner is computed according to
Assuming the user is scheduled to use the -th beamformer (codeword), the received signal is written by
because the -th beamformer is identical to the -th codeword such that in our random beamforming architecture. Notice that denotes the combined noise. The SINR of the -th user is then defined by555In our beamforming scenario exploiting a single unitary matrix, the SINR can be computed at the receiver side because the -th user knows all the transmit beamformers, i.e., , assigned for other users. The SINR can be regarded as CQI that quantifies the quality of each transmission layer.
From among beamformers , each user (e.g., -th user) selects a single beamformer
that maximizes the SINR according to , where the index of the selected codeword is , and the selected combiner is666For the sake of simplicity, the index of the selected codeword is dropped for the rest of the sections. . We call the selected beamformer global CDI and the selected SINR global CQI. In this paper, we focus on quantizing the CDI and refer to  and the references therein for quantizing the CQI. We assume that the index of the quantized CDI is fed back via an error-free -bit feedback link and the unquantized CQI can be communicated to the AP.
Finally, we refer to the user selection algorithm in  to schedule/select users from among users such that
where denotes the scheduled user exploiting the -th codeword . The -th scheduled user is given by
where denotes the set of indices of users who choose as their global CDI. It should be noted that the multiuser diversity gain from user selection plays a significant role in improving the sum-rate throughput and it grows like under the perfect CSI assumption at the AP [7, 23].
Despite the advantage, it has some obstacles that hinder the direct application of conventional multiuser systems to mMTC. First, the channel quantization error overrides the multiuser diversity gain. In feedback-assisted FDD architectures, multiuser systems become interference-limited due to unsuppressed quantization error. The sum-rate is thus upper bounded even though the SNR goes to infinity [12, 13]. Second, a large number of devices imposes a heavy burden on the initial access architecture of cellular networks. In 5G new radio (NR), there are a limited number of physical-layer cell identities . Since there is no specific collision avoidance procedure, a massive number of access attempts can cause severe congestions that accompany the increase in transmission latency . Even assuming congestion-free scenarios, the sum-rate growth in a large-user regime has slowed because the sum-rate grows in a double-logarithmical fashion [24, 23].
Iii Cooperative Limited Feedback Architecture
One of the key challenges in developing feedback-assisted multiuser systems for mMTC is to obtain accurate CSI at the AP while overcoming the following restrictions:
Ultra low-latency requirement for mMTC restricts the use of large codebook and this make it difficult to achieve robust channel quantization performance.
Considering the strict budget constraints of small-scale devices, it is not practical to employ a multitude of antenna elements for the antenna combining.
In QBC, the resolution of an effective channel increases as the spatial dimensions of a channel matrix for an antenna combining increases . In this paper, we propose user cooperation strategies to obtain high-resolution CSI while limiting the number of antenna elements at the receiver. The main feature of the proposed algorithm is that users in a CU employ an additional spatial dimension for the antenna combining by allowing a limited amount of CSI exchange. The key difference between the conventional system in Fig. 1(a) and the proposed system in Fig. 1(b) is the existence of the cooperation link. We assume that the quantized version of CSI can be exchanged between close-in users by using the Wi-Fi peer-to-peer sidelink, as presented in .
Before presenting the cooperative limited feedback algorithm, we pause to provide supporting details behind the variables in the proposed cooperative feedback architecture:
The term global is used to designate the variables and signal processing operations within CU, while the term local is used to designate the variables and signal processing operations within AU.
The bar symbol will be used to highlight variables corresponding to the global signal processing operation.
The tilde symbol will be used to highlight variables corresponding to the downlink transmission.
We present the details of the cooperative feedback algorithm based on the assumption that two close-in users have already been combined as a single CU777Developing a user grouping algorithm for holding two users together to form CU and/or considering a coalition of more than two users in a CU would be an interesting future research topic. according to .
Iii-1 Local CSI acquisition
An aim of this step is to compute local CSI that will be used to increase spatial dimensions of the partner’s channel matrix. The quantized version of local CSI is transferred to its partner via a cooperation link.
One viable approach to achieve reduction of both local CSI quantization error and cooperation link overhead is to share only a single effective channel vector that is combined based on the QBC algorithm . The combined channel is quantized using the random vector quantization (RVQ) codebook
which consists of codewords. The distance of the cooperation link is much shorter than that of the feedback link. The cooperation link would be subject to less stringent overhead constraints compared to that for the feedback link such that .
First, user in the CU computes a virtual vector
that can be quantized more accurately using a target codeword , where the local combiner and the projected codeword , needed for the local channel combining, are computed using similar method in (5) and (6).
Second, each user selects a local codeword that maximizes the cross-correlation of the normalized virtual channel vector and the codeword, i.e.,
where is the difference in angle. We call the selected codeword local CDI and its corresponding cross-correlation coefficient local CQI. The local CDI and CQI are given by
where the index of the selected codeword is
Under the assumption the index of the selected codeword is dropped, the selected local combiner, the virtual channel vector, and the difference in angle can be rewritten as
The quantized virtual channel vector is then defined with the local CDI and CQI according to
Finally, users in the CU exchange the local CDI and CQI, i.e., quantized virtual channel vector in (15), with its cooperation partner via a -bits cooperation link. The local CDI and CQI will be included in a global channel matrix of its cooperation partner. The local combining and quantization processes are depicted in the left side of Fig. 2.
Iii-2 Global CSI acquisition Role assignment
An aim of this step is to compute global channel information and to assign the role of MU and AU. The global CSI will be fed back to the AP.
First, each user constructs a global channel matrix
which includes one’s own channel matrix and the quantized virtual channel vector from a cooperation partner, where . Each user regards the virtual channel vector as an additional channel vector between the AP and the virtual antenna element at the receiver. Assuming oneself is selected as MU, each user computes the global effective channel vector
that can be quantized accurately with a target codeword . The global combiner is computed using the combining method in (5) and (6). The difference with the combining process in (11) is that the rank of the channel matrix and the dimension of the combiner are increased to .
Second, each user selects a single global codeword that maximizes the SINR
We call the selected codeword global CDI and its corresponding SINR global CQI. The global CDI and CQI are
where the index of the selected codeword is . Assuming the index of the selected codeword is dropped, the selected global combiner and the effective channel vector are rewritten according to
Third, users in the CU exchange their global CQIs with cooperating users via a cooperation link to determine who’s best for maximizing the data-rate throughput. The user having a larger CQI is assigned to MU and the unselected user is assigned to AU. The role assignment are made at the beginning of the transmission frame and will continue for the duration of the channel coherence time. We assume that the
-th (odd number indexed) user is assigned to MU and the-th (even number indexed ) user is assigned to AU. The set of indices of MUs is then written by .
Finally, MU only transmits the global CSI to the AP via a feedback link. The number of active users in the network is thus reduced by half . The global combining and quantization processes are depicted in the right side of Fig. 2.
Iii-3 User scheduling
After collecting global CDI and CQI from MUs, the AP schedules MUs such that
where denotes the scheduled MU exploiting the -th codeword . The -th scheduled MU is given by
where denotes the set of indices of MUs who choose as their global CDI.
Iii-4 Post-signal processing
An aim of this step is to decode the received signals888A memory in the receiver allows retention of received signals. The post-signal processing has no effect on a variation of the sum-rates because this process is conducted using the received signals stored in memory.
First, AU combines the received signal with the local combiner such as
where is the unquantized virtual channel vector in (14). Second, the combined signal is passed from AU to MU. Then, the MU constructs the global signal vector
where the global channel matrix corresponding to downlink transmission (downlink channel matrix) is defined by
and the global noise vector is . Finally, the MU combines the global signal vector with the global combiner according to
|CDI and CQI||(13)|
|CDI and CQI||(18)|
Iv Adaptive Cooperation Algorithm
The proposed cooperative feedback algorithm exploits some multiuser resources to improve channel quantization performance. High-resolution CSI can be obtained because more antenna elements (spatial dimensions) are used for global antenna combining. However, the proposed approach would restrict options that could be used to improve a network throughput due to the following reasons: First, the squared norm of the global effective channel vector decreases as the number of antennas used for a combining process increases [14, Lemma 3]. Second, the sum-rate grows like because user candidates are reduced by half.
In this section, we develop an analytical framework weighing the pros and cons of the proposed cooperative feedback algorithm. Based on the analytical framework, an adaptive cooperation algorithm is proposed in order to activate/deactivate the proposed cooperation strategy according to channel and network conditions.
Iv-a Loss in Local Channel Quantization
Before investigating the received signal of MU, we pause to analyze the channel quantization error induced in the process of local combining. As discussed in Section II-B, the channel quantization error between the normalized virtual channel vector and the target codeword is quantified by
random variable and its cumulative distribution function (cdf) can be approximated for small, with , according to
The local CDI is obtained by selecting the codeword corresponding to the smallest quantization error from among error terms . The channel quantization error corresponding to the local CDI can be studied by deriving the distribution of the smallest quantization error
where the index of the codeword in (13) is rewritten by
Based on the largest order statistics, we derive the expectation of the smallest quantization error in the following proposition.
The expectation of the channel quantization error corresponding to the local CDI is approximated by
Minimizing the quantization error is the same as maximizing the normalized beamforming gain
The cdf of the normalized beamforming gain is given by
where is derived because , , and is derived because when .
The normalized beamforming gain corresponding to the selected codeword (local CDI) is written as
The probability that the largest beamforming gain is smaller than an arbitrary numberis defined according to . Therefore, the cdf of is defined with the cdf of such as
Because is a non-negative random variable, the expectation of can be derived such that
where is derived based on [26, 6.6.8].
The expectation of the quantization error corresponding to the local CDI is approximated such that
because . This completes the proof.
Finally, the accuracy of the quantization error in Proposition 1 and the formulation in , i.e., , are evaluated by numerical results in Fig. 3. It is shown that our formulation in Proposition 1 shows better accuracy than the formulation in . Further, we point out that the quantization error is better fitted to the numerical results as the feedback bits increase because the cdf in (26) is valid for small .
Iv-B Received Signal of MU
We take a closer look at the received signal of MU in (24). Assuming MU is scheduled to use the -th beamformer (meaning that ), the received signal is written by
where is the global effective channel vector, and is the combined noise. In order to examine beamforming gain and interuser interference, we must investigate the cross-correlations between the global effective channel vector and codewords in .
The global effective channel vector is computed through two antenna combining processes (locally in AU and globally in MU) and each antenna combining process causes an individual quantization error. Before investigating both quantization errors jointly, we discuss each quantization error separately. First, we discuss the channel quantization error caused in the process of virtual vector quantization using local codebook . Note that the local quantization error is presented in Section III-1. As illustrated in Fig. 4(a), the virtual channel vector in (21) is divided into the quantized virtual channel vector in (15) and the local error vector according to
where quantifies the local quantization error. Second, we discuss the channel quantization error caused in the process of effective vector quantization using the global codebook . Note that the global quantization error is presented in Section III-2. As depicted in Fig. 4(b), the effective channel vector in (17) is divided into the target codeword and the global error vector such that
where quantifies the global quantization error.
We now consider both quantization errors jointly. When MU conducts post-signal processing, the global combiner is used to combine spatial dimensions of the global channel matrix in (23) for downlink transmissions. We call the downlink channel matrix. It should be noted that the downlink channel matrix includes the unquantized virtual vector in (14). However, the global combiner is computed using another global channel matrix in (16) including the quantized virtual vector in (15). The correspondence between the downlink channel matrix and the global channel matrix must be investigated because the combined quantization error occurs due to the difference between and .
where the effective channel vector is defined in (17) and the error vector is given by