VirtualMIMO feedback and transmission for wireless ad hoc networks
 Sungyoon Cho^{1},
 ByoungYoon Min^{1},
 Kaibin Huang^{2} and
 Dong Ku Kim^{1}Email author
https://doi.org/10.1186/s1363801607573
© The Author(s) 2016
Received: 19 October 2015
Accepted: 17 October 2016
Published: 4 November 2016
Abstract
Ina wireless ad hoc network, singleantenna nodes can cooperate in their transmissions to create a virtual multipleinput multipleoutput (MIMO) channel for maximizing the spatial multiplexing gain. However, implementing virtualMIMO transmission can result in overwhelming overhead, such as channel state information (CSI) feedback and local data exchange, as the number of cooperating nodes increases. To suppress this overhead, we apply the principle of virtualMIMO transmission to CSI feedback and design a novel framework for supporting parallel feedback streams, called virtualMIMO feedback. Building on this feedback framework, we optimize virtualMIMO transmission techniques and quantify their throughput gains in the presence of CSI and localexchange overhead. To be specific, the outage capacities of these virtualMIMO techniques are analyzed, and the corresponding bandwidth allocation for local data exchange and longrange transmission is optimized in a way to maximize overall spectral efficiency. Finally, the improvement of spectral efficiency in proposed virtualMIMO feedback and transmission is demonstrated by the simulation results.
Keywords
1 Introduction
The multipleinput multipleoutput (MIMO) technology was a breakthrough in wireless communication as it improved the capacity of wireless system without increasing bandwidth and transmission power [1]. In singleuser MIMO system, the spatial degrees of freedom (DoF) have been utilized to attain diversity and array gains by either maximum ratio combining (MRC) or spacetime codes [2]. Moreover, MIMO techniques have been developed to achieve the full multiplexing gain in multiuser system by using space division multiple access (SDMA) schemes [3]. In practice, linear precoding schemes such as zeroforcing (ZF) and block diagonalization have been studied in imperfect channel state information (CSI) at transmitters and their matching scheduling algorithms achieving multiuser diversity gain have been proposed in [4–7]. Also, various existing studies in MIMO systems have been considered where a transmitter acquires CSI from receivers through the finite rate feedback by quantizing the estimated channel vectors; these studies show that the required number of feedback bits for each channel vector should be scaled with the number of antennas and transmit power to compensate for the rate loss due to limited feedback [4].
In modern cellular systems such as LTEadvanced, cooperative MIMO transmission schemes have been proposed to mitigate the othercell interference in cellular networks. By allowing that the neighboring base stations (BSs) share both user data and CSI via highcapacity backhaul links, cooperative MIMO creates a multiuser MIMO system with one BS equipped with a large number of antennas, called network MIMO or coordinated multipoint transmission and reception (CoMP) in Third Generation Partnership Project (3GPP) standardization. In network MIMO, a joint transmission between BSs is performed to send the desired data to the corresponding users, which provides a considerable performance gain in multicell interference channels [8, 9]. However, the network MIMO requires a huge amount of CSI feedback for all direct and interfering links as well as the desired data exchange through the backhaul links between BSs, which makes practical implementation difficult.
The cooperative MIMO system in a cellular network has been explored in the context of collaboration between singleantenna nodes in order to exploit spatial DoF in wireless ad hoc networks, called virtualMIMO (VMIMO). In [10, 11], a singlesource node broadcasts its desired signal to neighboring nodes in the same cluster with which they form the spacetime block coding (STBC) towards its corresponding destination node, which achieves the diversity gain in the distributed network. Similar studies in [12, 13] show that the cooperative beamforming provides the power gain at the desired receiver as well as interference avoidance at the unintended receivers. Recently, the efficient clustering algorithm with neighboring nodes for constructing VMIMO and the design of cooperative precoding that maximizes data rate are proposed in [14, 15]. However, these existing studies of VMIMO are limited to singlesource to singledestination link and employ the localexchange overhead that linearly increases with the number of cooperative nodes [10–15].
In an effort to improve the spectral efficiency in VMIMO systems, the optimal channel and power allocation between local and longrange transmission between transmitter and receiver clusters was proposed to minimize the outage capacity in [16]. In [17, 18], algorithms for efficient local data exchange were proposed, where multiple sources broadcast their desired signals over the same spectrum with simple signaling and perform the corresponding beamforming that maximizes the system performance. However, previous literature showed that CSI feedback of all channel links between receiver cluster and transmitter cluster are required to realize the cooperative beamforming, which significantly degrades the spectral efficiency as the number of nodes participating in the cooperation increases.

VMIMO technique is proposed for CSI feedback, where the receivers simultaneously transmit their CSIs to the associated transmitters, which are cooperatively decoded at the transmitter cluster. The proposed feedback scheme provides a significant increase of total feedback bits by exploiting the spatial multiplexing gain over the orthogonal feedback channel access of traditional MIMO system which separately allocates the feedback channeluse to each receiver [4, 5]. Based on VMIMO feedback, we analyze the optimal resource partitioning between VMIMO feedback and data transmission channels that maximizes the spectral efficiency of cooperative ZF beamforming in a distributed ad hoc network. As the proposed VMIMO feedback method improves feedback channel capacity, it provides the increase of achievable MIMO transmission rate under optimal resource partitioning.

In the presence of CSI feedback and local data exchange overhead, we analyze the outage capacity of VMIMO transmission due to the discrepancy between localexchange and longrange data transmission channel quality. To meet the outage capacity, the optimal number of VMIMO nodes that maximizes the spectral efficiency is derived as a function of the distance between nodes, transmit power, and target data rate between transmitter and the corresponding receiver.
The remainder of this paper is organized as follows. The system model is introduced in Section 2, and the cooperative CSI feedback using VMIMO is described in Section 3. In Section 4, the cooperative ZF transmission is proposed and the corresponding performance gain and the resource optimization between local data exchange and longrange transmission are analyzed in a wireless ad hoc network. Section 5 provides simulation results, and the concluding remarks are followed in Section 6.
Notation: Bold upper case and lower case letters denote matrices and vectors, respectively. (·)^{ T }, (·)^{ † }, and ∥·∥ represent the transpose, Hermitian transpose, and the Frobenius norm of a matrix, respectively. \(\Gamma (a, x)=\int _{x}^{\infty } t^{\alpha 1}e^{t}dt\) is the complementary incomplete gamma function. \(\mathbb {E} \{\cdot \}\) and Q(x) denote the expectation over the random channel realizations and Qfunction of x, respectively.
2 System model
where \(P_{o}=P_{T}\, d_{o}^{\alpha }\) and d _{ o } is the distance between transmitters and receivers, satisfying \({{\textbf {h}_{i}^{T}}{\textbf {v}_{j}}}=0, i \ne j\).
where \(\hat {\textbf {v}}_{i}\) is the normalized ith column vector of \(\hat {\textbf {H}}^{\dag }(\hat {\textbf {H}}\hat {\textbf {H}}^{\dag })^{1}\) given \(\hat {\textbf {H}}=[\hat {\textbf {h}}_{1},...,\hat {\textbf {h}}_ M]\) and \(\hat {\textbf {h}}_{i}\) is quantized by a Bbit random codebook that minimizes the chordal distance, for analytical simplicity^{1}. The residual interference is bounded as \({\mathbb E}\left [ \textbf {h}_{i} \hat {\textbf {v}}_{j} ^{2}\right ] \le 2^{{B\over M1}}\) [4, 5].
3 VirtualMIMO feedback
Note that total available bandwidth W is partitioned into W _{ f } for CSI feedback and W _{ d } for data transmission to implement VMIMO transmission, where W _{ f }+W _{ d }=W. In this section, we propose a novel method of realizing collaborative spatial CSI feedback channels, called VMIMO feedback. VMIMO feedback allows the system bandwidth to be more efficiently partitioned and utilized for data transmission and feedback as well.
3.1 VirtualMIMO feedback: algorithm and performance
where \(\bar {P}_{o}=P_{R} \, {d_{o}}^{\alpha }, P_{R}\) is the transmission power at receiver cluster and \(({\bar{\mathbf{r}}_{\text{ZF}}^{i}})^{\dag }\) is the ith row vector of \({\bar {\textbf {R}}_{\text {ZF}}}= (\textbf {G}^{\dag }\textbf {G})^{1}\textbf {G}\). For simplicity, we denote that the expected achievable rate of feedback channel between the ith receiver and transmitters as \(R_{m}={\log _{2}(e)e^{1/{\bar {P}_{o}\over M}} { \Gamma \left (0,{M \over { {\bar P}_{o}} }\right)}}\).

Low SNR: As \(\bar P_{o} \rightarrow 0 \), the number of average feedback bits in MRC based feedback is approximated as \(B_{\text {MRC}}^{i}\approx {{W_{f} \bar {P}_{o}} \over M} {\mathbb {E}}\left [{({\bar {\textbf {r}}_{\text {MRC}}^{i}})^{\dag } \textbf {g}_{i} ^{2}}\right ] \log _{2}e ={W_{f} \bar P_{o}} \log _{2}e\), while that of ZF based VMIMO is determined by \(B_{\text{ZF}}^{i}\approx {{W_{f} \bar P_{o}} \over M} {\mathbb {E}}\left [{({\bar {\mathbf{r}}_{\text{ZF}}^{i}})^{\dag } \mathbf{g}_{i} ^{2}}\right ] \log _{2}e ={{W_{f} \bar{P}_{o}}\over M} \log_{2}e\). Therefore, the cooperative decoding for CSI feedback under the bandwidth partitioning provides a higher performance gain than the VMIMO feedback scheme in the low SNR regime, where \(B_{MRC}^{i} = MB_{ZF}^{i}\).

High SNR: As \(\bar P_{o} \) increases, the average feedback bit in MRC based feedback method in (4) is approximated by$$\begin{array}{*{20}l} B_{\rm{MRC}}^{i} &\approx {{W_{f}}\over {M}} \cdot { {\mathbb E}\left [\log_{2}\left({\bar P_{o}} \left ({\bar{\textbf{r}}_{{\rm{MRC}}}^{i}})^{\dag} \textbf{g}_{i}\right^{2}\right) \right ]} \\ &= {{W_{f}} \over {M}}\cdot \left(\log_{2} \left(\bar P_{o} \right) + {\mathbb E}\left[ \log_{2} \chi_{2M}^{2} \right]\right). \\ \end{array} $$(5)Moreover, the average feedback bit in ZF based feedback method in (3) is approximated by$$\begin{array}{*{20}l} B_{\text{ZF}}^{i} &\approx W_{f} \cdot { {\mathbb{E}}\left[\log_{2}\left({{\bar{P}_{o}}\over M} \left ({\bar{\textbf{r}}_{{\text{ZF}}}^{i}})^{\dag} \textbf{g}_{i}\right^{2}\right) \right]} \\ &={{W_{f}}}\cdot \left(\log_{2} \left({\bar{P}_{o}}\over {M} \right) + {\mathbb{E}}\left[ \log_{2} {\chi_{2}^{2}} \right]\right)\\ \end{array} $$(6)
where the \(\left  ({\bar {\textbf {r}}_{{\text {MRC}}}^{i}})^{\dag } \textbf {g}_{i}\right ^{2}\) and \(\left  ({\bar {\textbf {r}}_{{\text {ZF}}}^{i}})^{\dag }\textbf {g}_{i}\right ^{2}\) follow the distribution of \(\chi _{2M}^{2}\) and \({\chi _{2}^{2}}\), respectively [22]. Therefore, we conclude that \(B_{\text {ZF}}^{i}= MB_{\text {MRC}}^{i}\) in the high SNR regime.
Throughout this paper, we consider ZFbased feedback scheme as the suggested VMIMO feedback scheme, since it provides better performance gain than that of MRC based feedback scheme over the operational threshold (i.e., relatively high SNR).
As shown in (8), the second term is negligible as SNR becomes large so that \(B^{i}_{\text {ZF}}={\bar {B}}^{i}_{\text {ZF}}\). This approximation is also verified by numerical results in Section 5. In practice, \(\lfloor B_{\text {ZF}}^{i}\rfloor \) bits are applied for the number of quantized VMIMO feedbacks since the feedbacks bits should be an integer to design a practical channel codebook, where ⌊·⌋ denotes the floor function.
3.2 VirtualMIMO feedback: bandwidth partitioning
VMIMO is performed by the following sequential procedures: (1) local data exchange between neighboring transmitters, (2) CSI feedback from the receiver to transmitter, and (3) cooperative transmission from the transmitter cluster to the corresponding receivers. For optimal bandwidth allocation for VMIMO, it is required for considering both bandwidth for local exchange and data transmission/CSI feedback. However, the corresponding optimization requires the super centralunit having all channel information over the network to control bandwidth allocation, which are impractical in the wireless ad hoc environment. Therefore, we investigate the optimal partition of the bandwidth W for both VMIMO transmission and feedback assuming that the local data exchange has been ideally performed prior to the data transmission. This assumption is followed by the network model in Section 2, where a local data exchange links between transmitters have much shorter propagation distances than the data transmission link between transmitters and receivers. As a result, the bandwidth required for local data (intracluster) exchanges would be much smaller than the bandwidth for longrange (intercluster) since the highspeed channel links are provided between transmitters.
Therefore, the amount of bandwidth for CSI feedback is increased with \(\mathcal {O} (M\log _{2}(M))\) and inversely proportional to the feedback channel rate R _{ m } achieved by VMIMO feedback.
4 VirtualMIMO transmission: cooperative zeroforcing precoding
In this section, we propose VMIMO transmission that enables the conventional ZF precoding for cooperative data transmission via the local data exchange and VMIMO feedback proposed in the preceding section. While the Section 3 focused on the optimality of bandwidth between data link and feedback link between transmitter and the receivers, we studied further effects on the local data exchange for constructing VMIMO transmitters and the analysis on the optimal node clustering to maximize the spectral efficiency throughout this section.

Step I: (Local data exchange) The ith transmitter broadcasts its desired signal to the (M−1) neighboring transmitters over β bandwidth. Since M data streams are exchanged between nodes over orthogonal bandwidth in FDMA manner, a total of β M bandwidth is used for local data exchange, to be transmitted towards the corresponding receivers.

Step II: (VMIMO feedback) Prior to the data transmission, each transmitter sends pilot signals to the receiver. Then, each receiver estimates CSI of channel links between all transmitters and the corresponding receiver. Finally, CSI is fed back to the transmitter through the reverse channel. All corresponding CSIs are obtained at all transmitters from joint VMIMO decoding suggested in Section 3.

Step III: (VMIMO transmission) Transmitter clusters design the cooperative ZF precoding to minimize the interuser interference then communicate with their corresponding receivers.
4.1 Local data exchange
4.2 Longrange data transmission
4.2.1 Infinite feedback channel
where R _{ sum }=M·R. Since β is proportional to d _{ l }, the spectral efficiency becomes higher when d _{ l } becomes smaller. Also, large P _{ o } increases the spectral efficiency as the outage probability approaches zero.
4.2.2 Limited feedback channel
where \(\gamma =P_{o}/M, \delta ={P_{o} \over M}\cdot 2^{ {B_{\text{ZF}}\over {M1}}}\), \(x \sim {\chi _{2}^{2}}\) and \(y \sim \chi _{2(M1)}^{2}\). Similar to the case of perfect CSI, the outage capacity of the ith transmitterreceiver link in the limited feedback is derived as follows.
Proposition 1
where t=2^{ R }−1 and \(I_{r}={\left (1 \over \delta \right)^{M1} \left ({t\over \gamma } +{1 \over \delta } \right)^{(M1)}}\)
Proof
See Appendix. □
From proposition 1, the large number of M degrades the system performance as it increases the outage probability of each transmitterreceiver link. Moreover, I _{ r } represents the effect of quantization error due to limited feedback, which follows I _{ r }≤1 in given \(B_{\text{ZF}}^{i}\) feedback bits. The degrading factor of the residual interference I _{ r } goes to one when \(B_{\text{ZF}}^{i}\) is large enough so that the result of (20) approaches the outage capacity in (17).
4.3 The optimal number of active transmitters
Solving the above equation with M>0, we obtain the following proposition.
Proposition 2

M ^{∗} activate node selection: note that M nodes are distributed over transmitter cluster, where M ^{∗}<M. The node selection of M ^{∗} of M is performed by the roundrobin manner, where it provides the fairness of data transmission opportunity, implementable with low complexity. In a roundrobin approach, the selected nodes give a priority of data transmission to other idle nodes in a next transmission phase.

VMIMO transmission for M ^{∗}: the selected M ^{∗} transmitters only share the desired data streams \(\{s_{1}, s_{2},..., s_{M^{*}}\}\phantom {\dot {i}\!}\) over the M ^{∗} β bandwidth as each of the selected M ^{∗} nodes broadcasts its own data in β bandwidth. Then, (M−M ^{∗}) idle nodes, which are not allowed to transmit their own data, can help improving the achievable rate in (2) by providing array gain (see Fig. 3). In that case, h _{ i } v _{ i }^{2} follows a chisquare distribution with DoF of 2(M−M ^{∗}+1); then, the outage capacity is given by$$\begin{array}{*{20}l} {\tilde{R}_{\mathsf{opt}}}^{i} &= (1P_{\mathsf{out}})\cdot R \\ &=\left(1P\left(\mathbf{h}_{i}\mathbf{v}_{i}^{2} \le t \right)\right)\cdot R \\ &=\left(1P\left({\chi}_{2(MM^{*}+1)}^{2} \le t \right)\right)\cdot R \\ &= 1\left(1  {e^{ t}}\sum\limits_{i = 1}^{M  {M^{*}} + 1} {\frac{{{t^{i  1}}}}{{(i  1)!}}} \right) \cdot R \\ &= {e^{ t}}\sum\limits_{i = 1}^{M  {M^{*}} + 1} {\frac{{{t^{i  1}}}}{{(i  1)!}}} \cdot R. \end{array} $$(25)
where \(t={{M^{*}} \over {P_{o}}}\left (2^{R}1\right)\). Therefore, the large number of idle nodes can reduce the outage probability and \(\tilde R_{\mathsf {opt}}^{i}\) approaches R as M goes to infinity.
5 Simulation results
6 Conclusions
In this paper, an efficient feedback and data transmission scheme using VMIMO has been proposed in a wireless ad hoc network. We show that the cooperative feedback improves the accuracy of CSI compared with the orthogonal channel feedback and provides abundant channel resources for data transmission by reducing the use of channel resource for CSI feedback. Given the proposed feedback scheme, the outage capacity of ZF based VMIMO transmission under the transmitter cooperation is analyzed and the optimal number of active nodes that maximize the spectral efficiency is proposed for VMIMO based clustering. Future works will examine the design of VMIMO feedback and transmission in randomly distributed transmitter and receiver nodes and propose hierarchical clustering and cooperation with VMIMO feedback in the existence of multiple transmitter and receiver clusters. Moreover, we leave the analysis on stochastic geometric approach under VMIMO system, where it can represent the effectiveness of the proposed algorithms on more realistic environment.
7 Endnote
8 Appendix
8.1 Proof of proposition 1
Declarations
Acknowledgements
This research was supported by ICT R&D program of MSIP/IITP. (No. B0126151012, Multiple access technique with ultralow latency and high efficiency for tactile internet services in IoT environments)
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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