Crosslayered resource allocation in UWB noiseOFDMbased ad hoc surveillance networks
 Shrawan Chittoor Surender^{1},
 Ram M Narayanan^{2}Email author and
 Chita R Das^{1}
https://doi.org/10.1186/1687149920134
© Surender et al.; licensee Springer. 2013
Received: 23 May 2011
Accepted: 26 November 2012
Published: 4 January 2013
Abstract
Situational awareness in military surveillance and emergency responder scenarios requires detection of long range targets and secure communication of this information across a multisensor network. A potential approach towards this requirement is to harness the coexisting advantages of radar sensing and wireless communications. A multifunctional communicationsembedded radar design that implicitly develops into a crosslayered multiradar secure wireless ad hoc network is proposed to address this need. First, we demonstrate radar and communications coexistence through analysis of our novel composite orthogonal frequency division multiplexing (OFDM)embedded ultra wideband (UWB) noise waveform’s bit error rate and ambiguity function formulations. Second, to solve the medium access problem of allocating the multiple OFDM frequencies between different ad hoc radars nodes, we propose a simple yet fully distributed, channeldiversityaided algorithm. It constructs a contentionfree network, scaling logarithmically with the number of radar nodes, and analytically guarantees a provable fraction of the maximum throughput achieved by any optimal centralized allocation algorithm. Furthermore, our solution dynamically adapts with channel variations and topology changes. Working insync with the UWB noisebased single radio multichannel wireless platform, this distributed resource allocation builds a synergistic crosslayered ad hoc network of radars.
Keywords
Coexistence Radarcommunications UWB NoiseOFDM Multiradar Ad hoc networks Crosslayer Surveillance networks Distributed resource allocation1 Introduction
Recently, the wireless networks research community has taken considerable interest in concurrently utilizing the ultra wideband (UWB) spectrum with narrowband systems to architect coexisting and cognitive spectrum solutions [1, 2]. In parallel, multichannel multiradio wireless systems are being developed to achieve improved network capacity by exploiting nonoverlapping channel transmissions [3]. In this study, our motivation is to exploit the synergy between the above two approaches, in developing a multifunctional wireless system with significant support to applications of practical relevance. The goal is to provide a flexible framework for situational awareness in infrastructureless covert surveillance circumstances, such as hostage rescue, firstemergency response, natural disaster recovery, or military surveillance. The primary requirements for such applications are the capability for farfield sensing of phenomena, distributed computing, and secure multisensor networking. These situations are also characterized by the absence of any central infrastructure, limited spectrum availability, varying topological environments, and growing wireless security concerns [4].
An ad hoc network harnessing the combined advantages of UWB radarsensing [5, 6] and wireless communications is a viable solution to this requirement. This is accomplished through a unique multifunctional radar design, where we spectrally notch a UWB radar’s random noise transmit waveform and embed a secure spectrally equalized orthogonal frequency division multiplexed (OFDM) multicarrier message within the UWB spectrum. Thus, the composite transmit waveform is designed to simultaneously support farfield targetsensing and data communications, while possessing covertness and interference rejection properties owing to the transmission of a noiselike signal. This singleradio multichannel wireless radarcommunications system is what we call the UWB noiseOFDM radar [7]. Multiple such radars can then form an ad hoc communication network to provide significant benefits in target detection and recognition, by taking advantage of multiaspect and multilook fusion techniques [8, 9], and information dissemination through opportunistic routing [10]. Furthermore, by having multicarrier data communication within the same spectrum as the radar’s transmit signal, a substantial increase in network capacity and bandwidth efficiency can be achieved. This article, therefore, aims to transform a multifunctional UWB noiseOFDM radar into a coexisting, crosslayered, covert, and ad hoc network platform.
The two important parameters investigated for performance analysis are the bit error rate (BER) reliability measure for communications and the ambiguity function (AF) resolution measure for radar operations [11]. Furthermore, the presence of the OFDMbased multicarrier PHY and the absence of any coordinating central infrastructure necessitated access control to be exercised on the wireless medium in a distributed and efficient manner. Based on the available OFDM bandwidth and the modulation parameters, there exists a set number of orthogonal subcarriers available to each radar. All communications between radars are required to be channeled through these subcarriers only. This article presents a fully distributed contentionfree medium access strategy that simultaneously exploits channel diversity and maximizes data reliability. This strategy is also scalable and adaptable to changing network topologies and varying wireless channels. This problem is similar to the multiradio multichannel resource allocation problem considered in [3, 12, 13]; however, it is further constrained by the requirements of multifunctionality and covertness. In short, the key contributions of this study are as follows:

Through experimental simulations, we show that this radarembedded multiuser communication platform achieves a BER value better than 1×10^{−5} for an signaltonoise ratio (SNR) of 12 dB, thus forming a reliable physical layer for the wireless network of radars.

By formulating and deriving the AF for the radar part of the noiseOFDM radar, we infer that if the fragmented spectral gap is less than 30%, then range and Doppler resolution, i.e., the radar performance, are essentially unaffected.

To have contentionfree medium access of this 30% available OFDM bandwidth among multiple radars, we propose a fully distributed Channeldiversityaided ProposeAcceptRejectConfirm (CPARC) resource allocation algorithm. Through simulations, CPARC is shown to scale logarithmically with the number of radars, and to adapt automatically to channel and topology variations.

We analytically prove that our resource allocation strategy guarantees a constant fraction of the maximum throughput region offered by any optimal centralized offline algorithm.

Finally, we highlight the improved performance of CPARC when compared with other related algorithms in the literature (centralized edgecoloring algorithm and distributed frequencyhopping OFDM technique).
The remainder of this article is organized as follows. Section 2 presents related work. System design of our secure wireless platform is briefly described in Section 3. In Section 4, we show its physical layer coexistence capability by investigating the performance of the communication and radar operations. To combine the individual radars into a multiradar multihop ad hoc communication network, Section 5 formulates the ad hoc multicarrier resource allocation problem, while Section 6 proposes a fully distributed channelsensing medium access solution. The throughput guarantee of our system is analyzed in Section 7. In Section 8, extensive numerical simulations are presented to validate the radar–communications coexisting spectrum access performance and to evaluate the expected performance of CPARC. We give our concluding comments in Section 9.
2 Related work
Compared to generic multistatic or netted radar systems [14], the UWB noiseOFDM radar is a distinct coexisting solution where the same transmit signal is simultaneously used for both radar and communication operations, and it is inherently secure. In [15], a comparable dualsystem is presented which uses UWB OFDM pulses for radar and communication. While this is indeed a viable alternative, immunity from detection requires random frequency hopping. Furthermore, the UWB OFDM pulses show greater range side lobes compared to Gaussian pulses and the communication system requires full synchronization between the platforms. Further examining the existing UWB radarcommunication systems, we observed that they are either not multiradar capable [16] or are easily jammed open communication systems [15]. In contrast, we present a multifunctional UWB netted radar with better coexistence of radar and communication abilities, along with inherent transmit waveform covertness and multiradar capability.
The current medium access protocols proposed for narrowband wireless systems such as carrier sense multiple access (CSMA), IEEE 802.11, IEEE 802.15.3, etc., are unsuitable for UWB systems such as ours, for a variety of reasons [17]. For instance, energybased clear channel assessment is necessary in CSMA/CA, however, UWB is defined to have lowenergy emissions. Furthermore, synchronization signaling overhead is very high in the above protocols, which UWB systems cannot handle. Next, among the solutions proposed for OFDMbased dynamic subcarrier allocation [18, 19], almost all of these techniques use a central coordinator or hierarchical coordinators to run the optimal/suboptimal subcarrier allocation algorithm and then flush the subcarrier allocations to all users (receivers) through a separate control channel. These typical downlinkbased cellulartype solutions [19] cannot, therefore, be applied to a system where there is no centralized infrastructure. However, [20] does present an interesting distributed spectrum access technique for OFDM systems.
Popular techniques in multihop distributed scheduling [13, 21] come close to satisfying our requirements. However, the approach presented in [21] is meant only for singlechannel systems. Lin and Rasool’s study [13] proposes a multichannel joint scheduling and channelassignment algorithm. It mainly depends on the channel queue length information being exchanged between interfering links, but it is assumed to be available to the distributed algorithm. In contrast, our strategy relaxes this assumption and includes channel diversitybased assignments, thereby, achieving a marginally better throughput guarantee than [13]. Dutta et al.’s study [12] solves the channel assignment problem, but it does not consider dynamic network topologies or channel variations and hence does not exploit channel diversity. Finally, a recent multiradio multichannel resource allocation based on a multidimensional conflict graph technique [3] is a novel approach, but it cannot be inherently applied to an ad hoc network. In contrast, our approach presented in Section 5 is a fully distributed channelaware solution appropriate for an ad hoc distributed computing environment.
3 Background: secure wireless platform design
The UWB noiseOFDM netted radar (in short, radar sensor) system architecture, performing: (1) radarspecific operations such as target detection, ranging, velocity (Doppler) estimation, and tracking, and (2) datanetworking with other radar sensors and the command center for distributed computing, consists of transmit and receive subsystems as summarized below.
3.1 Transmit subsystem
where u(t)=X_{ c }+j X_{ s } is the complex envelope and ∗ indicates the complex conjugation operation.
In our simulations, we used a 1–2GHz frequency range of operation. Since the original UWB radar, which is already operational, was built in the 1–2GHz range, we continued to develop this system in the same range. Changing to FCC allowable ranges is trivial and the design can easily be adapted to it. For our system therefore, f_{ o }=1.5 GHz, f_{1}=1 GHz, and f_{2}=2 GHz. This is a UWB signal by definition since its fractional bandwidth (β/f_{ o }) is greater than 0.25. This bandlimited noise signal is then notchfiltered within the narrower range of 1.2–1.3 GHz (in general, this could be done over any range suitable for the application). The radar system therefore uses the full 1–2 GHz band, while the intrasensor communications operates over the 1.2–1.3 GHz subband. The Gaussian process X_{ N }(t) in the notched band has bandwidth β_{ n } and is centered at frequency f_{ n }, such that f_{ o }−β/2<f_{ n }<f_{ o }+β/2.
with ${s}_{k}={d}_{k}{e}^{j{\theta}_{k}}$ being the complex data symbols that are modulated onto the OFDM subcarriers and f_{ k }=f_{b}+k Δ f. Here, f_{b} is the base frequency, Δ f is the subcarrier spacing, and N is the total number of subcarriers. These parameters are appropriately selected so that the bandwidth of this OFDM signal exactly matches the notch bandwidth in X_{ N }(t).
3.2 Receive subsystem
4 Physical layer coexistence
To establish coexistence of communications with radar transmissions, the receive subsystem must be analyzed further to address two essential issues: (1) effect on communications performance due to the presence of UWB noise around the OFDM signal, and (2) effect on the radar’s range and Doppler estimation capabilities due to the presence of an OFDM spectrum embedded inside the UWB random noise transmit spectrum.
4.1 Noiseembeddedcommunications performance
where Y_{ l } is the received signal on the l th subcarrier, ε_{s,l} is the signal energy of the symbol being modulated onto the l th OFDM subcarrier, ν_{ l } is the FIR filter response’s magnitude ripple coefficient affecting the l th OFDM subcarrier, and ${\sigma}_{y,l}^{2}$ is the variance of the additive white Gaussian noise on the l th OFDM subcarrier. The model described by Equation (4) agrees with experimental simulations, as shown in [7]. We mention it here since it validates the multiuser BER versus SNR experimental simulations presented in Section 8.
4.2 Target detection performance
In this section, we examine the radar side of the coexisting system. The UWB noise radar has been shown to possess high range resolution and good velocity resolution capabilities [23]. Range resolution signifies the capability of the radar to distinguish between two closely separated targets. For a 1GHz bandwidth UWB noise radar, targets separated by 15cm spacing in the range dimension will correctly be detected as two separate targets. Velocity resolution represents the radar’s ability to estimate the speed of different moving targets whose velocities are closely separated. Since the transmit waveform of the noise radar was modified to embed a communication signal within, we investigate the UWB noiseOFDM radar’s range and velocity resolution performance by formulating its AF.
where h(t) is the integration filter impulse response, α is the delay rate associated with the target’s velocity, τ(t)=τ_{ o }−α t is the delay associated with the target’s range, and ${R}_{\mathit{\text{cc}}},{R}_{c{c}_{n}}$ are the autocorrelation functions of the UWB noise and notched noise, respectively.
Our simulations of this AF, in Section 8, clearly demonstrate that the OFDM data bandwidth can be as high as 30% of the complete UWB bandwidth available to the radar, without adversely affecting ranging or Doppler estimation performance and the noiselike properties of the radar transmit waveform.
5 Crosslayer problem formulation: multiuser resource allocation
Based on this available OFDM data bandwidth and the selection of the OFDM modulation parameters, there is a set amount of orthogonal subcarriers available to every radar in the system. In our case, we chose 3.125 MHz bandwidth for each subcarrier, thereby filling the 0.1 GHz notch band with 32 subcarriers. Individual radars can now use these subcarriers to concurrently communicate with their neighboring radars, while simultaneously performing radar functions, such as target detection. However, when a number of radars are deployed and all radars transmit on all 32 subcarriers, collisions on the channel will inhibit effective communication within the intended network. The goal therefore is to achieve medium access, i.e., to allocate these subcarriers in such a manner as to establish contentionfree communication links between every radar and its onehop neighbors. We call this radar pairing, i.e., every radar needs to be paired with each of its neighboring radars on a different subcarrier. All communication between the radar pairs must occur through these assigned subcarriers only. Furthermore, the allocation of these subcarriers between the radar pairs must be accomplished under changing radar topologies and the following unique constraints of an infrastructureless multiradar setup:

Multiecho issue: a radar receives signals not only from a transmitting radar in the neighborhood, but also the target echoes due to its own transmissions as well as the echoes due to transmissions of other radars in the vicinity, as depicted in Figure 5. Here, RS1 and RS2 transmit out their UWB NoiseOFDM signals ψ_{1} and ψ_{2}, respectively. RS2 being in the vicinity of RS1, receives ψ_{1} and primarily needs to extract data from it, but RS2 also receives the target echoes, ψ_{1e} and ψ_{2e}, which will lead to demodulation errors in the OFDM band. It is, therefore, important that the subcarriers, on which RS1 transmits data to RS2, are not affected by the corresponding subcarriers in the target echoes.

Ad hoc network: it is a multihop network of radars, with no single central coordinator to crunch an optimal or suboptimal resource allocation algorithm and disseminate the information to all radars in the system.

Channel diversity: due to terrain obstruction and other wireless channel issues, some subcarriers might not inherently be suitable for pairing a particular set of radars. Making such an allocation might degrade the data reliability of the system. Therefore, channel estimation is needed in exploiting channel diversity.
The overall problem is to minimize the number of subcarriers used for communication under the above constraints, which is analogous to maximizing subcarrier reuse in the overall system.
A naive solution is to statically assign subcarriers in the OFDM spectrum to different radar transmitter–receiver pairs. However, this does not permit exploitation of the benefits accruing from channel and spatial diversities. This static allocation will lead to disconnected radars and underutilization of the bandwidth spectrum especially when the radars are moving or when the radio channel changes.
6 A simple distributed channeldiversity approach
Our aim is to pair, i.e., to allocate OFDM subcarriers to different (source radar, destination radar) duple’s dynamically, so that collisionfree communication can occur simultaneously among the radars. A small subset of the available subcarriers in the OFDM spectrum is chosen as a control carrier set (CC), which is used by all the radars in the system as a broadcast channel for information exchange. All radars in the system will contend to use this channel for running their instance of our proposed CPARC distributed resource allocation algorithm. Initially, every radar will transmit predetermined data on all the OFDM subcarriers except CC. After the allocation of a subcarrier to a particular (source radar, destination radar) duple is complete and this information is broadcast to their onehop neighborhood, all neighboring radars of this radar pair will cease their transmission on this subcarrier. This technique will keep the OFDM subcarriers occupied and hence ensure a noiselike transmit waveform, even when the number of radars in the system is lower than the number of available subcarriers.
The following local and global data structures are maintained for state information: localallocationinformation (LAI) and neighborlist (N_{ l }) for radar nodespecific information, and globalallocationinformation (GAI) for systemwide information. The LAI is used by the CPARC algorithm running in a radar node to store information on this node’s pairing with its neighbors and the corresponding subcarrier(s), which were allocated to them. Whereas the GAI is indexed with all the available subcarriers in the system and every time a subcarrier is allocated, the GAI is updated and broadcast as globally available information. N_{ l } is used to record the nodes in the onehop vicinity of a given node. In all radar nodes, CPARC runs in an infinite loop. It performs a 4way handshake to complete pairing, by communicating through the following seven messages. Every radar node uses the following messages:

HELLO: to register itself with its neighbors,

PROPOSAL: to request for pairing with a particular neighbor in response to a HELLO,

ACCEPT: to send acceptance of pairing using a particular subcarrier in response to a PROPOSAL,

REJECT: to send rejection for pairing using a particular subcarrier in response to a PROPOSAL,

CONFIRM: to send an confirmation in response to a ACCEPT,

INFO: to broadcast the GAI to its onehop neighbors,

OFFLINE: to tell it does not need any pairing.
Further details follow in the description of CPARC given below.
CPARC Algorithm:
Input: Number of subcarriers available per radar node, Number of overall subcarriers available in the system, Incoming message.
Output: Pernode subcarrier allocation i.e., (transmit, receive) pairing.
6.1 CPARC: initialization
Radar node initializes LAI, GAI, and broadcasts a HELLO message with its identity, on the CC indicating that it would like to also share the communication medium. It then waits for any PROPOSAL it might receive from its neighbors.
6.2 CPARC: physical layer’s channeldiversity feedback
where ν_{ l } represents the magnitude scaling on the l OFDM subcarrier due to the receiving filter in the system, Q(.) is the tail probability of the standard normal distribution, ${\sigma}_{y,l}^{2}$ is the variance of the additive white Gaussian noise, and ε_{s,l} is the signal energy of the symbol being modulated onto the l th OFDM subcarrier. From this expression, it can be seen that the reliability of transmission, even for the noiseOFDM waveform, depends on the SNR at the receiving end. Therefore, between any pair of radar nodes, choosing a subcarrier that maximizes SNR thereby minimizing P_{ b }(Y_{ l }), is the key to exploiting channel diversity between them.
6.3 CPARC: received message processing

HELLO: Check in the LAI if it has already paired with this new neighbor. If yes, then ignore this message. Otherwise, based on the availability of free subcarriers (by checking the GAI), choose FS and send a PROPOSAL to the source of this message. If free subcarriers are not available, then the radar cannot pair with this new neighbor.

INFO: Copy the GAI that has come in. This information will be used in FS/subcarrier selection. When a radar gets this messages, it checks to see if its LAI matches with the information that has come in. If yes, then allocations are consistent. If not, then this radar might have missed some ACCEPT or REJECT message due to collisions, so this radar will update its LAI.

PROPOSAL: Using the DFT performed in the receiving side and its PSD output, select the best subcarrier from the FS, and check in the LAI to see if this radar is already using this subcarrier. If yes, then further check if the corresponding source and destination pair are the same as is requested in this incoming proposal. If yes again, then this receiving radar’s earlier transmission of ACCEPT might have been lost. In that case, send ACCEPT again. However, if the subcarrier is being shared with some other radar, then send REJECT. Furthermore, if this subcarrier is not being used currently, then check for availability in GAI and quota of subcarriers: if OK, send an ACCEPT message.

ACCEPT: Check if the subcarrier for which this ACCEPT has come is already being used with some other radar, then send a REJECT message to the source. Otherwise, pair this radar with the source of the message and update the LAI, GAI. Send a CONFIRM message out to the source. If the CONFIRM is not for itself, then update the GAI about this new pairing.

CONFIRM: Update LAI, GAI, broadcast an INFO message containing the GAI to all radars in its onehop vicinity, to advertise this pairing. If the CONFIRM is not for itself, then use this message to update the GAI about this new pairing.

REJECT: Temporarily unmark this subcarrier for which the REJECT came, check for other available subcarriers in GAI, and send a PROPOSAL again. If quota for subcarriers is complete, then accept the REJECT message.

OFFLINE: Check if the source of this message is in the radar’s LAI, if so, then relinquish that subcarrier and update the GAI accordingly. Send an INFO message out to distribute this information.
The output of CPARC, therefore, is an allocation that shows the different subcarriers on which every radar is paired with its neighbors. This subcarrier set forms a dedicated contentionfree communication link between the radar duple. Since this algorithm runs in every radar and global allocation information is broadcast to just the onehop neighbors, subcarrier reuse will occur across nonoverlapping zones of the system, leading to efficient bandwidth utilization. The pseudocode for CPARC is shown in Appendix.
6.4 Discussion
Multiecho issue: with the output of CPARC and Figure 5 in reference, we observe that RS2 will not be paired with another radar on the same subcarrier that RS1 uses to talk to itself. This implies ψ_{2e} will no longer be a problem when RS2 tries to decode ψ_{1}. Furthermore, ψ_{1e} is basically a multipath signal for ψ_{1} and OFDM is inherently capable of overcoming this issue. Therefore, our OFDMbased CPARC solves the multiecho issue.
It is also to be noted that during the initial phase of sending a PROPOSAL, there is a possibility that multiple users may send symbols on the FS subcarriers at the same time. In this situation, the CC will itself result in a collision which implies the PROPOSAL will not be detected. So the receiving node will not look at the FS for the predetermined symbols at all. A node will scan the FS subcarrier’s spectral density only when the message comes through to it without any collisions, which implies that no other users interfered on the CC or the FS subcarriers. Hence, the channel estimation performance will not be affected. Furthermore, although the CC is a broadcast channel which is contentionbased and prone to collisions, redundancy builtin into CPARC using N_{ l } and the 4way handshake counteracts the loss of messages due to collisions and hence aids in scalability. A further improvement performed to decrease collisions on the CC is to allow a radar node to respond to a HELLO only if its identification number is smaller than that of the node which sent the HELLO message. This reduces the contention caused on the broadcast CC channel and leads to efficient packet transmissions.
7 CPARC throughput guarantee
Centralized algorithms with linear complexity have been designed for scheduling, channelassignment in multichannel, multihop networks [25], that attain the maximum achievable throughout region, Ω. It has been shown that such solutions cannot be implemented in a distributed manner or if so, are very inefficient [13]. The problem of distributed algorithms that solve the same is NPhard and hence relaxed throughputoptimality is aimed for. The following proposition shows that CPARC is a provably efficient distributed algorithm achieving a guaranteed fraction of Ω and tends to be marginally better than [13].
Proposition
For a network π and packet arrival rate vector $\overrightarrow{\lambda}$, if $\overrightarrow{\lambda}\in \Omega $ in π, then $\overrightarrow{\lambda}/\Lambda \left(\pi \right)\in {\Omega}^{\mathit{\text{CPARC}}}$ in π, i.e., the throughput region guaranteed by CPARC is 1/Λ of the maximum throughput region Ω[25], where Λ is the interference degree of the network.
Proof
The noiseOFDM radar being a multicarrier OFDM system inherently allows the radars to communicate simultaneously with more than one of its neighbors, although on separate subcarriers. Further, CPARC guarantees that a subcarrier set assigned to a radar pair will not be again used in pairing these constituent radars with their other neighboring radars. We call this a subcarrierexclusive spectrum sharing technique. Over this core subcarrier allocation strategy, we assume the use of a simple lowcomplexity distributed maximal scheduling flow strategy [26]. It basically ensures that if a transmitting radar r 0 has a packet to transmit to a receiving radar r 1, either (r 0,r 1) or a (transmitter, receiver) pair that interferes with (r 0,r 1) is scheduled for transmission; the scheduling is otherwise arbitrary. This is a valid assumption in CPARC, as the GAI developed by it in every radar has each of the neighboring radar’s subcarrier assignment information that is necessary to generate the required interference relations.
An interference relationship being defined as follows: For every radarpairing that CPARC performs using a particular subcarrier δ, there is a set of radar pairings Γ_{ δ } such that, a transmission on δ by the original radar pair and one of the pairs in Γ_{ δ } at the same time, will not result in any useful transfer of data. The strength of CPARC is that Γ_{ δ } will only consist of nodes which are onehop away from either of the constituent radars of the original pairing. A noninterfering subset of Γ_{ δ } is a subset of pairings ${\stackrel{\u0304}{\Gamma}}_{\delta}$ such that any two pairings in this subset do not interfere with each other. The interference degree Λ(δ) [26] of pairing δ is, therefore, defined as (i) the maximum size of the subset ${\stackrel{\u0304}{\Gamma}}_{\delta}$ if Γ_{ δ } is nonempty and (ii) 1 if Γ_{ δ } is empty. The interference degree of the whole network Λ is the maximum interference degree over all the pairings. The interference degree of the system is directly dependent on the physical interference model [13] and thus is independent of the exact network topology. Further, it is well known that the efficiency ratio of an algorithm is the largest number η such that this algorithm can stabilize the system under any load $\overrightarrow{\lambda}\in \mathrm{\eta \Omega}$. Given the above, and the pairwise interference relations developed from GAI, it follows directly from Theorem 1 in [26] that for our system π, if $\overrightarrow{\lambda}\in \Omega $ in π, then $\overrightarrow{\lambda}/\Lambda \left(\pi \right)\in {\Omega}^{\text{CPARC}}$ in π, i.e., CPARC can guarantee an efficiency ratio of 1/Λ, which is comparable to [13].
Furthermore, intuitively, the upper bound of Λ as mentioned in [26] will not be tight in our system, due to the OFDMbased multicarrier advantage. Using the subcarrierexclusive spectrum sharing technique, the common end point interference constraint no longer prevails. Due to this, Γ_{ δ } decreases, leading to a decrease in the upper bound of Λ, and hence an increase in the efficiency ratio of our algorithm. This makes CPARC marginally better than [13]. □
8 Simulation results and performance evaluation
To validate the concepts of the UWB noiseOFDM radar system presented above, simulations were performed for communications and radar performance using MATLAB ^{ â“‡ }, while CPARC was simulated using the OMNET++ simulation framework [27]. The UWB noise signal covered the 1–2GHz band, with the notch band over 1.2–1.3GHz. A 253tap finiteimpulseresponse (FIR) equiripple BPF with a transition region bandwidth of approximately 50 MHz and a passband magnitude ripple of ±0.5 dB was used in the receiver. The input parameters to these simulations are the number of subcarriers being used (which is 32 to cover a 100MHz notch), the number of symbols per carrier (which is 50 in our case), the bin length (1024), sample frequency of 5 GHz, and the channel SNR. Based on this required channel SNR, appropriate noise power was calculated and added to the transmitted signal.
8.1 Multiuser radarcommunications performance
8.1.1 Notch and BPF design
 1.
If the bandwidth of the BPF is greater than the OFDM signal’s bandwidth, then portions of the UWB noise waveform surrounding the OFDM signal is drawn into the OFDM demodulation process, thus causing unwanted additive UWB noise signal energy to be present in the demodulator output.
 2.
If the bandwidth of the BPF is less than the OFDM signal’s bandwidth, then the resulting truncation of the OFDM signal reduces the orthogonality of the OFDM subcarriers, causing ICI.
Therefore, if the BPF is designed appropriately such that the BPF’s bandwidth is larger than the OFDM signal’s bandwidth, then Case 1 mentioned above results. Due to the additive nature of the UWB noise, this does not affect the orthogonality of the subcarriers, hence causing no ICI in the system. Since the subcarriers on which data will be ported are known, the OFDM signal’s spectral bandwidth is also known. Therefore, a BPF that satisfies Case 1 mentioned above is appropriately designed for use in the receiver subsystem, ensuring no ICI is caused. Our earlier study [7] details these physical layers aspects of the noiseOFDM waveform with respect to spectral equalization, noiselike properties, reliability, and covertness.
In [7], we have also derived the BER for this radar–communications system theoretically. Our BER analysis is customized to the noiseembedded OFDM signal. This is a unique method, since the nonideal BPF in our receiver, based on its passband design, either truncates the OFDM signal or allows outofband noise signal causing errorfloor and magnitude ripple related issues in the demodulation process. And these effects are well modeled in the analysis. A close match between theory and simulations has also been shown. Based on the same validation of the simulation setup, we derive these further results for multiuser radar communications systems, which conclude to have a BER of 1×10^{−5} for SNR of 12 dB. Theoretical enhancement of the above derivation to a multiuser scenario is a future scope for this study.
8.2 Radar operations: range and doppler resolution
8.3 CPARC performance validation
8.3.1 CPARC distributed channelaware allocation
8.3.2 CPARC control channel performance
Here, we ran CPARC on an increasing network scale, nodes in the network increasing from 10 to 90. For every set of nodes, after CPARC produced the final set of subcarriers allocations for all the radar node pairs in the network, we collected statistics on the total number of packets that were generated, the total number of packets that collided and the total number of packets that were correctly received, overall in the entire network. The ratio of the correctly received packets to the number of packets transmitted gives us the packet delivery ratio and hence the success rate of the complete network. For every set of nodes, the results were averaged over 20 runs. An essential point to note is that instead of sending the packet at the next slot interval, we randomized the latency and based on a uniform probability distribution, every radar node will randomly delay its transmission (instead of using the next available slot for transmission, a random delay is observed and then the next available slot is used), so collisions can be minimized. The results are shown in Figure 14. When this latency per node was based off a uniform distribution from (0, 2), we observed good packet delivery ratios, as seen by the blue and red bars in the figure. However, when this random latency was reduced, to (0, 1.75), it can be observed that the packet delivery ratio reduced, as seen by the green and purple bars in the plot. This was quite drastic for node degree 4. From this figure, we can observe that success rate in this modified slotted Alohabased control channel is indirectly proportional to the latency that the nodes are allowed to carry, i.e., by introducing a random delay in selection of the next slot for transmission, packet delivery ratio is considerably high. As was mentioned in Section 2, contending for the channel or trying to sense the channel before transmission is not possible in the noiseOFDM waveform case. Therefore, this enhanced slotted Aloha technique is chosen as a base layer for the CC, over which CPARC is implemented. Of course, sending the message directly is basically setting this randomized delay to 0. But as seen from the plot above and our further simulations, reducing this delay does drastically decrease the success rate of the system and hence is not viable.
Another important inference that can be drawn from Figure 14 is that the success rate is almost constant with increasing number of nodes in the network, for any latency or node degree. Since the success rate is calculated after successful completion of subcarrier allocations across the entire network, this further goes to prove the distributed nature of CPARC and its ability to work on a multihopdistributed scenario.
8.3.3 CPARC dynamic subcarrier reallocation
In order to test performance in lieu of wireless channel failures, we introduced faults simulating channel (subcarrier) failures in our system. Using the abovementioned 16node square topology, after the initial allocation is complete, we simulated an event that subcarrier set 304 becomes unavailable. The resultant dynamic update produced by CPARC is shown in Figure 12b, where we now see that no radar pairs use 304. This holds true for multiple subcarriers and link failures too. Here, a subcarrier failure is the event that a particular subcarrier is unavailable to the whole system, whereas a link failure is the event that the specific pairing between any two given radar nodes fails due its associated subcarrier being unavailable locally.
8.4 Performance comparison of CPARC with centralized edgecoloring algorithm
Scalability of resource allocation solutions is an important concern, especially in an ad hoc network setup, where the number of nodes deployed could vary hugely. In order to test the scalability of CPARC, we compared the runtime performance of CPARC (time taken to complete allocation) with a similar but centralized algorithm—the edgecoloring graph algorithm [29]. The edge coloring of a graph is the assignment of colors to the different edges such that no two adjacent edges are given the same color. This is similar to the subcarrier allocation problem, wherein no adjacent receiver–transmitter pairs should be allocated the same subcarrier. Furthermore, we also note that the edge coloring problem is constrained lesser than the problem that CPARC deals with since the former does not have to take care of the hidden terminal problem. Since CPARC was implemented on an eventdriven OMNET framework, the centralized edgecoloring algorithm was also implemented on the same framework. However, its running time was not measurable because the centralized algorithm did not produce any packettransmissions or networkbased events which were being used to record its running time. Therefore, we ran an efficient implementation of the edgecoloring algorithm separately on a simple UNIX machine and compared our distributed solution with it based on asymptotic order of growth analysis.
8.5 Improved performance of CPARC over distributed frequencyhopping OFDM
Here, we compare the performance of our distributed CPARC algorithm with another existing method in the literature, Frequencyhopping (FH) OFDM [30]. FHOFDM is a recent and promising technique used to achieve frequency diversity gain in OFDM subcarrier allocations. In this method, every radar can choose a random seed and inform its onehop neighbors of this seed. Then, based on this seed, it will randomly generate a sequence of subcarriers and transmit according to that sequence on consecutive time slots (assuming time is slotted). Since other radars in the vicinity know the seed of this pseudorandom sequence, they can follow along and receive the transmissions. This can happen in all the radars of the system. This method leads to good frequency diversity. This is because the radars are frequency hopping frequently, so they will not remain in any faded frequency for a long time.
However, for maintaining covertness, the radars in our system need to transmit on all the subcarriers, otherwise, the notch in the spectrum will easily be visible. So, a radar needs to be transmitting some random data on all the other 31 subcarriers, to maintain covertness. However, if it does do so, then it can bring about collisions on frequencies which are being used by neighboring radars. Although, initially, all the radars exchange their seed information with their neighbors, every radar will now need to maintain three things on a slotbyslot basis (i) the frequency that it needs to transmit on, (ii) the frequencies of its neighbors that it should not transmit on, and (iii) the frequencies of its neighbor’s neighbors (hidden terminal problem) it should also not transmit on. This third constraint above is motivated by the fact that if the 2nd hop neighbors change, then that information will not easily be known to the original radar, thereby, leading to potential collisions on the subcarriers.
8.6 CPARC spectrum utilization
9 Conclusions
This study targets the development of ad hoc radar networks as a solution to situations generally characterized by the absence of any central infrastructure, varying topological environments, and growing wireless security concerns. To address these needs, we have demonstrated that reliable multiuser data transmission/reception can occur simultaneously with highresolution target detection/ranging, leading to cooperative spectrum coexistence of communications and radar. We formulated the AF of the multifunctional noiseOFDM waveform and have shown that up to 30% of an UWB signal can be utilized for data communications, without adversely affecting the primary function of the radar. Furthermore, utilizing this 30% bandwidth, we extended the pointtopoint covert radar–communications platform to being a selforganized multihop crosslayered ad hoc radar network. This was achieved by developing a unique solution to the ad hoc OFDM multiuser multichannel resource allocation problem. The salient features are: (i) it is a fully distributed, channeldiversityaided multicarrier resource allocation strategy, with its simplicity leading to significant practical relevance, (ii) it automatically adapts to network topology changes and channel variations, and has an logarithmic growth rate runtime performance, (iii) it provides a provable throughput guarantee that is at least competitive to other algorithms in the literature, and (iv) it inherently presents physical layer security, since CPARC uses OFDM subcarriers that are embedded within UWB noise and hence the transmitted wireless signal appears random and noiselike to unintended receivers.
Employing a routing layer about CPARC’s contentionfree medium access layer will make this framework easily applicable to any mobile wireless platform. Towards this, and to exploit the multicarrier covert PHY, we explore modifying the ondemand routing protocols designed for mobile ad hoc networks (MANETs). We envisage to bring forward a second level of crosslayer information flow, which will enhance the routing protocol’s performance, especially security and scalability. Furthermore, promising and prospective candidates for implementing this system are softwaredefined radio techniques of softwarebased signal processing, hardware such as the universal software radio peripheral, and highspeed digitaltoanalog converters. This will allow the system parameters to be software configurable, hence making an flexible framework for covert infrastructureless surveillance networks.
Appendix
AF derivation for the UWB noiseOFDM radar
where k_{1} is the arbitrary amplitude constant representing target crosssection, antenna pattern, propagation factors, etc.
For evaluating ${s}_{1}{s}_{2}^{\ast}$, we make a reasonable assumption that identical data are transmitted over all subcarriers of the OFDM symbol. We then use the orthogonality principle for OFDM carriers and Equation (3) together, to finally show that $E\left\{{s}_{1}{s}_{2}^{\ast}\right\}=N{T}_{s}$, where T_{ s } is the symbol period.
Neglecting the phase terms, the expected values of the I and Q outputs of the I/Q integrating filters can therefore be symbolized as 〈Z_{ I }(α,τ,t)〉 and 〈Z_{ Q }(α,τ,t)〉.
Pseudocode for CPARC algorithm
Algorithm 1 CPARC(isc; osc; msg)
Declarations
Authors’ Affiliations
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