## I Introduction

The emerging paradigm of massive machine-type communications (mMTC) is identified as an indispensable component for enabling the massive access of machine-type devices (MTDs) in the emerging Internet-of-Things (IoT) [1]. In stark contrast to conventional human-centric mobile communications, mMTC focuses on uplink-oriented communications serving massive MTDs and exhibits sporadic tele-traffic requiring low-latency and high-reliability massive access [1].

The conventional grant-based access approach relies on complex time and frequency-domain resource allocation before data transmission, which would impose prohibitive signaling overhead and latency on massive mMTC

[1]. To support low-power MTDs at low latency, the emerging grant-free approach has attracted significant attention for massive access, since it simplifies the access procedure by directly delivering data without scheduling [2, 3, 1, 4, 5, 6]. Specifically, by exploiting the block-sparsity of mMTC, the authors of [2] and [3] proposed compressive sensing (CS) solutions for joint active device and data detection, while a maximum a posterioriprobability based scheme was proposed in [1] for improving performance. Furthermore, MTDs having slow-varying activity tend to exhibit partially block sparsity, hence a modified orthogonal matching pursuit solution was conceived in [4], beside a modified subspace pursuit algorithm was proposed in [5]. It was shown that the previous detected results can be exploited for enhancing the following detection. However, the contributions [2, 3, 1, 4, 5] only consider single-antenna configurations at both the MTDs and the BS. To achieve higher efficiency and more reliable detection, multi-antenna at MTDs using spatial modulation (SM) and massive multi-input multi-output (mMIMO) were considered in [7, 6] at the BS, where a two-level sparse structure based CS (TLSSCS) detector and a structured CS detector was proposed in [6] and [7], respectively. However, the increased data rate of SM by one bit requires doubling the number of antennas [8, 9], which violates the low-cost requirement of MTDs. To improve the uplink (UL) throughput at a low cost and power-consumption, authors of [10, 11] proposed to employ media modulation at the MTDs, where an iterative interference cancellation detector and a CS detector was employed for multi-user detection in [10] and [11], respectively. However, they have not considered the active device detection.Against this background, we propose to adopt media modulation at the MTDs for improving the UL throughput and to employ a mMIMO scheme at the BS. Moreover, a CS-based active device and data detection solution is proposed by exploiting both the sporadic traffic and the block-sparsity of mMTC as well as the structured sparsity of media modulated symbols. Specifically, we first propose a block sparsity adaptive matching pursuit (BSAMP) algorithm for active device detection, where the block-sparsity of UL access signals across the successive time slots and the structured sparsity of media modulated symbols are exploited. Additionally, a successive interference cancellation based structured subspace pursuit (SIC-SSP) algorithm is proposed for demodulating the detected active MTDs, where the structured sparsity of media modulated symbols in each time slot is exploited for enhancing the decoding performance. Finally, our simulation results verify the superiority of the proposed scheme over cutting-edge benchmarks.

Notation

: Boldface lower and upper-case symbols denote column vectors and matrices, respectively. For a matrix

, , , , , , denote the transpose, Hermitian transpose, inverse, pseudo-inverse, Frobenius norm, the -th row and -th column element of , respectively. () is the sub-matrix containing the rows (columns) of indexed in the ordered set . is the -th column of . For a vector , , , and are the norm, -th element, -th to -th elements, and entries indexed in the ordered set of , respectively, and is the index set of the modulus largest elements of . For an ordered set and its subset , , , and are the cardinality of , -th element of , and complement of subset in , respectively. is the set .## Ii System Model

We first introduce the proposed media modulation based mMTC scheme and then focus on our massive access technique relying on joint active device and data detection at the BS.

### Ii-a Proposed Media Modulation Based mMTC Scheme

As illustrated in Fig. 1, we propose that all MTDs adopt media modulation for enhanced UL throughput and the BS employs mMIMO using receive antenna elements for reliable massive access. In the UL, each symbol consists of the conventional modulated symbol and of the media modulated symbol, and each MTD relies on a single conventional antenna and extra radio frequency (RF) mirrors [10, 11, 12]. By adjusting the binary on/off status of the RF mirrors, we have mirror activation patterns (MAPs), and the media modulated symbol is obtained by mapping bits to one of the MAPs. Therefore, if the conventional -QAM symbol is adopted, the overall UL throughput of an MTD is bit per channel use (bpcu). To achieve the same extra throughput, media modulation requires a single UL transmit antenna and a linearly increasing number of RF mirrors, but SM requires an exponentially increasing number of antennas [10, 8, 9, 11, 12]. Clearly, media modulation is more attractive for mMTC owing to its increased UL throughput at a negligible power consumption and hardware cost [10, 11, 12]. Moreover, using a mMIMO UL receiver is the most compelling technique. By leveraging the substantial diversity gain gleaned from hundreds of antennas, the mMIMO BS is expected to achieve high-reliability UL multi-user detection, in the context of mMTC. By integrating the complementary benefits of media modulation at the MTDs and mMIMO reception at the BS into mMTC, we arrive at an excellent solution.

### Ii-B Massive Access of the Proposed mMTC Scheme

As shown in Fig. 1, we assume that the activity patterns of the MTDs remain unchanged in a frame, which consists of successive time slots. Hence we only focus our attention on the massive access for a given frame. Specifically, the signal received at the BS in the -th time slot, denoted by , can be expressed as

(1) |

where the activity indicator is set to one (zero) if the -th MTD is active (inactive), while , , and are the conventional modulated symbol, media modulated symbol, and equivalent UL access symbol of the -th MTD in the -th time slot, respectively. Furthermore, is the multi-input multi-output (MIMO) channel matrix associated with the -th MTD,

is the noise with elements obeying the independent and identically distributed (i.i.d.) complex Gaussian distribution

, while and are the aggregate MIMO channel matrix and UL access signal in the -th time slot, respectively.Note that for any given and , only one of its entries is one and the others are all zeros, i.e.,

(2) |

where is the support set of its argument. Furthermore, we consider the Rayleigh MIMO channel model, hence the elements in for follow the i.i.d. complex Gaussian distribution . We assume that the channels remain time-invariant for a relatively long period in typical IoT scenarios, hence

can be accurately estimated at the BS via periodic updates.

## Iii Proposed CS-Based Massive Access Solution

In typical IoT scenarios, the MTDs generate sporadic tele-traffic [1, 2, 3, 4, 5, 6], which indicates that is a sparse vector and . Moreover, this activity pattern exhibits the block-sparsity, since typically remains unchanged in successive time slots within a frame [2, 3, 1, 6]. Furthermore, for exhibits the structured sparsity [10, 11], due to the sparse nature of media modulated symbols’ feature as illustrated in (2). The block-sparsity and structured sparsity of the UL signals inspire us to invoke CS theory to detect the active devices and demodulate the data at the BS.

To exploit the block-sparsity of active MTD patterns, we first rewrite the received signals within a frame as

(3) |

where we have , , , and . Thus the massive access problem can be formulated as the following optimization problem

(4) |

In the following subsections, we will first utilize the proposed BSAMP algorithm to determine the indices of active devices. On that basis, the associated data is further detected based on the proposed SIC-SSP algorithm.

### Iii-a Proposed BSAMP Algorithm for Active Device Detection

The proposed BSAMP technique formulated in Algorithm 1, is developed from the sparsity adaptive matching pursuit (SAMP) algorithm of [13]. Specifically, line 1 calculates the sum correlation associated with all MAPs in time slots for each MTD; line 1 combines (i.e., the most likely active MTDs) with to extract the preliminary support set ; in line 1, the coarse signal estimate is obtained by the least squares (LS) algorithm; lines 11 exploit the structured sparsity of media modulated symbols to re-calculate for improved robustness to noise, and then the fine signal estimate is obtained in lines 11. If the residual becomes bigger, we increase , otherwise the iteration continues with a fixed . The loop stops when the stopping criterion in line 1 is met.

The proposed BSAMP algorithm adaptively acquires the number of active MTDs without knowing . Compared to the classical SAMP algorithm, the proposed BSAMP achieves an improved detection performance by exploiting the block-sparsity and the structured sparsity of the UL access signals. Moreover, in contrast to the SAMP algorithm using the residual as the stopping criterion, we check whether the minimum average power of an MTD’s signal estimate is lower than a predefined threshold (line 1) to decide whether the loop should be terminated. If so, we use for the most recent past iteration rather than the current iteration as the output.

### Iii-B The SIC-SSP Algorithm Proposed for Data Detection

Based on the estimated active MTDs obtained from Algorithm 1, the data detection problem in formula (4) reduces to the same CS problem as in [7] (i.e., Eq. (10) for in [7]), which can be solved by the group subspace pursuit (GSP) algorithm of [7]. To further improve the performance, the proposed SIC-SSP algorithm, as listed in Algorithm 2, intrinsically integrates the idea of successive interference cancellation (SIC) with the GSP algorithm. Specifically, the outer for-loop recovers separately. For each with , the inner for-loop recovers a structured sparse signal with sparsity by performing () SIC operations. In contrast to the existing GSP algorithm, the inner for-loop of the proposed algorithm incorporates the SIC operation (line 22). Specifically, line 2 selects the index of the maximum element of the finely estimated signal and subsequently line 2 eliminates it from the measurement vector ; line 2 records the maximum element in () and reduces the size of the remaining set of active MTDs by 1, which corresponds to reducing the column dimension of the channel matrix in the next iteration for improving the data detection performance. Moreover, lines 2 and 2 improve the performance by exploiting the signal’s structured sparsity. Finally, the algorithm is terminated when is fully reconstructed.

## Iv Simulation Results

Let us now evaluate the probability of bit error rate () for the proposed CS-based massive access solution. Here , where is the number of active MTDs missed by activity detection, and are the total number of error bits in the media modulated symbols and conventional symbols for detected active MTDs within a frame, respectively, and is the total number of bits transmitted by active MTDs within a frame. In our simulations, the total number of MTDs is with active MTDs. Furthermore, each media modulation based MTD adopts RF mirrors and 4-QAM (), hence the overall throughput becomes bpcu. Finally, we set in the proposed BSAMP algorithm to 0.5.

For comparison, we consider the following 4 benchmarks. Benchmark 1: Zero forcing multi-user detector for the traditional mMIMO UL [7] with single-antenna users adopting 16-QAM to achieve the same 4 bpcu. Benchmark 2: TLSSCS detector from literature [6]. Benchmark 3: A modified BSAMP algorithm relying on the perfect knowledge of and on the existing GSP algorithm of [7], which are successively used to detect the active MTDs and the data. The modified BSAMP algorithm is initialized to and performs the iterations including lines 11 and 1 until . This scheme can be used for evaluating the reliability of the estimated for the proposed BSAMP algorithm. Benchmark 4: The proposed BSAMP algorithm and the existing GSP algorithm of [7] are successively used to detect the active MTDs and the data. Lastly, the Oracle LS based detector relying on the perfect known index set of active MTDs and the support set of media modulated symbols, is considered as the BER lower bound of the proposed mMTC scheme.

Fig. 2

-(c) compare the BER performance vs the signal-to-noise ratio (SNR), the frame length

, and the number of receive antennas , respectively. It is clear that the proposed mMTC scheme outperforms the traditional mMIMO UL for the same throughput, thanks to the extra bits introduced by media modulation. For the proposed mMTC scheme, we find that our “BSAMP+SIC-SSP” solution outperforms the TLSSCS detector, the “modified BSAMP+GSP” solution, and the “BSAMP+GSP” solution, which demonstrates the efficiency of the proposed solution. Moreover, the similar performance of Benchmarks 3 and 4 indicates the reliability of the -detection of our BSAMP algorithm. Furthermore, Fig. 2 indicates that except for the Oracle LS, the proposed “BSAMP+SIC-SSP” solution has the lowest BER floor, for sufficiently large . Finally, observe from Fig. 2 that the BER of the proposed “BSAMP+SIC-SSP” solution is better than that of the TLSSCS detector, the “modified BSAMP+GSP” solution, and the “BSAMP+GSP” solution when becomes large, which indicates the superiority of the proposed solution for mMIMO.## V Conclusions

A media modulation based mMTC UL scheme relying on mMIMO detection at the BS was proposed for achieving reliable massive access with an enhanced throughput. The sparse nature of the mMTC traffic motivated us to propose a CS-based solution. First, a BSAMP algorithm was proposed to detect the active MTDs exhibiting block-sparsity and structured sparsity of the UL signals, which improved the performance. Furthermore, a SIC-SSP algorithm was proposed for detecting the data of the detected MTDs by exploiting the structured sparsity of media modulated symbols for enhancing the performance. Finally, our simulation qualified the benefits of the proposed solution.

## References

- [1] B. K. Jeong, B. Shim and K. B. Lee, “MAP-based active user and data detection for massive machine-type communications,” IEEE Trans. Veh. Technol., vol. 67, no. 9, pp. 8481-8494, Sept. 2018.
- [2] B. Wang, L. Dai, T. Mir and Z. Wang, “Joint user activity and data detection based on structured compressive sensing for NOMA,” IEEE Commun. Lett., vol. 20, no. 7, pp. 1473-1476, Jul. 2016.
- [3] Y. Du, C. Cheng, B. Dong, Z. chen, X. Wang, J. Fang and S. Li, “Block-sparsity-based multiuser detection for uplink grant-free NOMA,” IEEE Trans. Wireless Commun., vol. 17, no. 12, pp. 7894-7909, Dec. 2018.
- [4] B. Wang, L. Dai, Y. Zhang, T. Mir and J. Li, “Dynamic compressive sensing-based multi-user detection for uplink grant-free NOMA,” IEEE Commun. Lett., vol. 20, no. 11, pp. 2320-2323, Nov. 2016.
- [5] 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 J. Select. Areas Commun., vol. 35, no. 12, pp. 2812-2828, Jul. 2017.
- [6] X. Ma, J. Kim, D. Yuan and H. Liu, “Two-level sparse structure based compressive sensing detector for uplink spatial modulation with massive connectivity,” IEEE Commun. Lett., vol. 23, no. 9, pp. 1594-1597, Sept. 2019.
- [7] Z. Gao, L. Dai, Z. Wang, S. Chen and L. Hanzo, “Compressive-sensing based multiuser detector for the large-scale SM-MIMO uplink,” IEEE Trans. Veh. Technol., vol. 65, no. 10, pp. 1860-1865, Feb. 2017.
- [8] L. Xiao, P. Yang, Y. Xiao, S. Fan, M. Di Renzo, W. Xiang and S. Li, “Efficient compressive sensing detectors for generalized spatial modulation systems,” IEEE Trans. Veh. Technol., vol. 66, no. 2, pp. 1284-1298, Feb. 2017.
- [9] L. Xiao, Y. Xiao, P. Yang, J. Liu, S. Li and W. Xiang, “Space-time block coded differential spatial modulation,” IEEE Trans. Veh. Technol., vol. 66, no. 10, pp. 8821-8834, Oct. 2017.
- [10] L. Zhang, M. Zhao and L. Li, “Low-complexity multi-user detection for MBM in uplink large-scale MIMO systems,” IEEE Commun. Lett., vol. 22, no. 8, pp. 1568-1571, Aug. 2018.
- [11] B. Shamasundar, S. Jacob, L. N. Theagarajan and A. Chockalingam, “Media-based modulation for the uplink in massive MIMO systems,” IEEE Trans. Veh. Technol., vol. 67, no. 9, pp. 8169-8183, Sept. 2018.
- [12] A. K. Khandani, “Media-based modulation: A new approach to wireless transmission,” in Proc. IEEEInt. Symp. Inf. Theory, Jul. 2013, pp. 3050-3054.
- [13] T. T. Do, L. Gan, N. Nguyen and T. D. Tran, “Sparsity adaptive matching pursuit algorithm for practical compressed sensing,” in Proc. 42nd Asilomar Conf. Signal, Syst., Comput., Pacific Grove, CA, USA, Oct. 26-29, 2008, pp. 581-587.

Comments

There are no comments yet.