# Design, Analysis, and Performance of a Noise Modulated Covert Communications System

- Jack Chuang
^{1}, - Matthew W. DeMay
^{1}and - Ram M. Narayanan
^{1}Email author

**2008**:979813

**DOI: **10.1155/2008/979813

© Jack Chuang et al. 2008

**Received: **10 March 2008

**Accepted: **22 July 2008

**Published: **18 August 2008

## Abstract

Ultrawideband (UWB) random noise signals provide secure communications because they cannot, in general, be detected using conventional receivers and are jam-resistant. We describe the theoretical underpinnings of a novel spread spectrum technique that can be used for covert communications using transmissions over orthogonal polarization channels. The noise key and the noise-like modulated signal are transmitted over orthogonal polarizations to mimic unpolarized noise. Since the transmitted signal is featureless and appears unpolarized and noise-like, linearly polarized receivers are unable to identify, detect, or otherwise extract useful information from the signal. The wide bandwidth of the transmitting signal provides significant immunity from interference. Dispersive effects caused by the atmosphere and other factors are significantly reduced since both polarization channels operate over the same frequency band. The received signals are mixed together to accomplish demodulation. Excellent bit error rate performance is achieved even under adverse propagation conditions.

## 1. Introduction

The primary objectives of today's wireless secure communications systems are to simultaneously and reliably provide communications that are robust to jamming and provide low probability of detection and low probability of intercept in hostile environments. Spread spectrum techniques, such as direct-sequence spread-spectrum systems and frequency-hopping spread-spectrum systems, have been widely used in wireless military applications for many years. Such systems have the ability to communicate in the presence of intentional interference and also permit transmission with a very low-power spectral density by spreading the signal energy over a large bandwidth to thwart detection [1, 2]. Thus, spread spectrum techniques offer both security and low probability of detection features. However, statistical processing techniques, such as triple correlation [3, 4], autocorrelation fluctuation estimators [5], and multihop maximum likelihood detection [6] have been developed which exploit the statistical properties of the pseudonoise sequences used in direct-sequence spread-spectrum systems and the pseudorandom frequency-hopping sequences used in frequency-hopping spread-spectrum systems, thereby permitting third parties to detect the hidden message signal. Further research has revealed that the chaotic and ultrawideband (UWB) noise waveforms are ideal solutions to combat detection and exploitation since the transmitted signals have unpredictable random-like behavior and do not possess repeatable features for signal identification purposes [7–9].

Digital communication systems utilizing wideband carriers require a coherent reference for optimal data processing. This reference may be either locally generated or transmitted simultaneously with the data. The transmitted reference (TR) technique was initially explored as a means for establishing communication when there are critical unknown properties of the transmitted signal or channel [10, 11]. This scheme completely avoids the synchronization problem of locally generated reference systems but performance will be worse than the locally generated reference systems at the same signal-to-noise ratios (SNRs) because the noise-cross-noise term will appear at the output of correlator [12].

The purpose of this new polarization diversity system is to be able to conceal a message from an adversary and to avoid jamming countermeasures while maintaining an acceptable performance level. A band-limited true Gaussian noise waveform is used to spread the signal's power into large bandwidth. Thus, an extremely large processing gain is achieved and the system can operate in a noisy and jammed channel. The primary reason of choosing the UWB noise waveform is because it provides covertness. In the time domain, the transmitted signal appears as unpolarized noise to the outside observer while the spectrum hides under the ambient noise in the frequency domain. However, the drawback of this noise modulated UWB TR system is the increased system complexity compared with the pulse-based UWB TR system introduced in [13, 14]. Since a continuous wave signal is used, the time separation structure introduced in [14] cannot be used because eight interference terms will be generated after the mixing process in our receiver. A solution is simultaneously transmitted the reference signal and message signal on orthogonal polarization channels and only three interference terms will be generated after mixing process. However, the system which may confront polarization mismatch will be discussed in Section 5, and the rotation angle between transmitter's and receiver's antenna needs to be estimates to compensate performance degrading causing by polarization mismatch. On the other hand, this noise modulated UWB TR system also requires adding extra circuit to alleviate BER degradation in multipath environment while the pulse-based UWB TR system can directly operate in multipath environment.

In our earlier publications, simulation results demonstrate that the noise modulated covert communication system maintains good performance in white Gaussian noise channels, and indoor experiments prove that the system can retrieve messages in interference-free channels [15, 16]. In this paper, a theoretical performance metric is derived and compared with simulations, for both single-user and multiuser environments, that demonstrate the system's ability to operate in a noisy channel. We also present preliminary field test results with the baseband processing implemented in a software defined radio architecture that clearly validates that the system concepts.

## 2. Rf System Overview

### 2.1. Transmitter

### 2.2. Receiver

where is the attenuation factor ( ) causing by propagation and is Doppler shift due to moving transmitter or receiver. In general, can be considered as constant when the distance between transmitter and receiver is small (a few km) under clear atmospheric conditions but will be a frequency-dependent when the distance becomes larger or unfavorable atmospheric conditions, such as heavy rain exists [18]. The performance will indeed degrade when the spectrum of received signal is not flat [15]. To overcome this problem, the communication link should ideally estimate attenuation information based on local climatology and compensate for it at the transmitter, especially when the system is used for operation over large distances. Without loss of generality, therefore, we assume that . We also assume perfect carrier synchronization at receiver side, and therefore can be considered to be zero without affecting the following analysis.

The signal is amplified and passed through a delay line with the exact same delay time as introduced in the transmitter (for the horizontal channel). It is then mixed with the signal in the mixer, which acts as a correlator. This brings the two channels in synchronization. If this delay does not exactly match the corresponding transmit delay, no message can be extracted from the mixed signal. Only a friendly receiver knows the exact value of this delay, and thus an unfriendly receiver will not be able to perform the proper correlation to decode the hidden message.

where is filter impulse response. Since binary modulation is used and the term is always positive, the transmitted bit sequence can be successfully retrieved from .

## 3. System Performance Modeling

In wireless communications, the bit error rate (BER) is an important metric which is used to gauge and compare the system performance. Since this noise modulated covert communications system is a new architecture, the theoretical BER performance in an additive white Gaussian noise channel is derived and compared with simulation results in this section. Unlike other single-channel spread spectrum systems, the low-pass equivalent model can directly be used to model the system behavior in the Gaussian channel. The spreading and dispreading process of our system is accomplished at the RF front-end. The noise floor at the antenna output is not the same as that at the output of the first mixer, and the noise terms within the system are generated by mixing of two zero mean independent Gaussian random variables. Thus, the system behavior needs to be modeled based upon the relationship between the SNR at the output of receiver antenna and the probability of bit error. In this section, we will demonstrate that the mixed noise can be approximated as Gaussian after passing through a narrow-band filter, and the BER equation can be expressed using the *Q*-function. The bandwidths of the signal, antenna, low-pass filter, and the SNR at the output of receiver's antenna are the parameters which dominate the BER when the bit rate is fixed.

where and are the polarization dependent random Rayleigh-distributed amplitude and uniformly-distributed phase terms, respectively. The power of and is equal to their variance since they are zero-mean random variables and these are denoted as and , respectively. We further assume that the powers of and , both of which are zero-mean band-limited Gaussian processes, are the same, and each is denoted as . The corresponding SNR values at the output of vertical and horizontal polarized antennas are and respectively, and are denoted as and . In reality, the bandwidth of is slightly greater than that of due to the modulation induced on it. However, the bandwidth of is very small compared with . We assume that the signal bandwidth of and (hence the bandwidth of and ) is , and that the bandwidth of and is (equal to the receive antenna bandwidth). Usually, is almost the same as in order to avoid receiving additional interference.

In the real system implementation, the bandpass filter is used to capture just the sum frequency signal centered at (3 GHz) containing the information message, while discarding all difference frequency signals contained in is discarded as noise. Let denote the bandpass filtered output of the signal The bandpass filtered noise signals are denoted as , and , where , and . Generally, the probability density function of the noise needs to be found in order to calculate the BER. Since the probability density function of the product of two independent zero-mean normal distributions is approximated by a modified Bessel function of the second kind, the closed form probability density function for the sum is extremely difficult to derive. Because the bandwidth of filtered noise is much smaller than before filtering, the noise spectrum following the filter is relatively flat compared to the sum frequency noise. Thus, we can approximate the filtered noise as a Gaussian variable. For convenience, we assume that the bandwidth of the bandpass filter is twice that of the low-pass filter following the second down-conversion, since the low-pass filter is the key component dominating the received noise spectrum before the decision circuit. Later in this section, we will compare the theoretical results with simulation results to show that our derivation by applying this assumption also works when the bandwidth of bandpass filter is much greater than bandwidth of low-pass filter.

where is impulse response of bandpass filter [19]. Similarly, the mean values of and are both zero.

The next step is to calculate the variance of the filtered noise, which is equal to its power. Clearly, the power of , and can be calculated by integrating the power spectrum of the sum frequency noise of , and within the bandpass filter frequency range.

Let the power spectral density of the sum frequency noise of be denoted as . The average power of the sum frequency noise needs to be found first in order to find the mathematical expression for . We know that for a given ergodic random process , its autocorrelation function and its power spectral density form a Fourier transform pair, that is, . Furthermore, the average power of such a random process is the value of the autocorrelation function at zero lag, that is, equal to .

*k*th moment of a Rayleigh distributed random variable is noted as [19]

The
term is mixed with the 3-GHz carrier and down to the baseband with a power that is equal to
. Since the baseband noise is zero-mean Gaussian and binary modulation is used, the BER equation for the optimal receiver can be expressed by the *Q*-function with two parameters: the spectrum magnitude of the noise
and the bit energy
[20, 21].

## 4. Multiuser Modeling

*i*th user, the received signals in the vertically and horizontally polarized antennas in an additive white Gaussian noise channel are given by

when there are
users in the channel. The
term in (27) is the specific delay time assigned to the *i* th user, and the receiver already knows this information. Since the output signals of different noise generators are independent of each other, the
terms are independent to each other and so are the
terms.

*i*th user, the delay line with the delay between vertical polarization antenna and the first mixer in the receiver is activated. Then, the signal at the output of the first mixer can be written as

## 5. Comprehensive Experimental Results

The zero crossings show up when the channel is not clean but the message can still be retrieved. Although not shown, when both tone interferences are located within the narrow frequency range
in the low-SIR channel, the bit stream is ruined because of high-power tone interference at the output of low-pass filter generated by the sum frequency signal of the tone interference in the *V*-channel mixed with the tone interference in *H*-channel. Usually, this problem can be solved by adding a digital filter in the baseband signal processing design.

*V*-channel and

*H*-channel to the first mixer at the receiver side can then be expressed as

where
is the delay time of the delay line (
in the system implementation),
is the received leakage from the transmit *H*-channel into the receive *V*-channel, and
is the received leakage from the transmit *V*-channel into the received *H*-channel. The terms
and
are the square root of polarization loss factor with value depending on the rotation angle. They are within the range [
] and
[22]. For perfect antenna alignment,
and
, and there is no polarization leakage.

and
are as shown in (18), (19), and (31). Comparing (35) with (23), nonperfect antenna alignment will degrade system performance because it generates extra interference terms and decreases the power of desired received signal. A method for measuring the rotation angle is to send a pilot tone from one of the dual-polarization channels and use the power ratio between received *V*-channel signal and received *H*-channel signal to determine the rotation angle. To simplify the structure, better estimation technique should be developed for measuring rotation angle without using a pilot.

## 6. Conclusions

A spread spectrum technique using noise-modulated waveforms is proposed for covert communications. The featureless characteristics of the transmitted waveform in the noise modulated covert communication system ensure the security of communications. By using a band-limited true Gaussian noise waveform to spread the signal's power into a large bandwidth, an extremely large processing gain is achieved and the system can operate very well in a low SNR or SIR channel. Based on our current research, the "cross-multiplication" method could alleviate performance degradation caused by multipath. The underlying concept of this method is to synchronize the *n* th path in the *V*-channel with the *m* th path in the *H*-channel instead of directly synchronizing the received *V*-channel and *H*-channel signals. Without considering system complexity, combining a pseudonoise sequence with our method can show better performance than a RAKE receiver since more diversity can be used. For example, if each channel contains
multipath terms, there are
diversity that can be used by the RAKE receiver but
diversity can be used by our method.

The performance of this noise modulated covert communication system in a single and multiuser environment is properly modeled and compared with simulations. The bandwidth of the transmitted signal and antenna controls the BER performance when the SNR at the output of antenna and bit rate is fixed. The field tests demonstrate that the concept can be realized, and the system can operate in an additive white Gaussian noise channel with negative SNR.

## Declarations

### Acknowledgments

This work is supported by the Office of Naval Research (ONR) under Contract no. N00014-04-1-0640. The authors appreciate fruitful discussions with Mr. John Moniz and Mr. Timothy Wasilition of ONR. They thank Dr. Sven Bilen of The Pennsylvania State University for supplying the two-field programmable gate array boards for the experiments. Moreover, they also thank Star-H Corporation, Pa, USA , for providing the location for the field tests and Arhan Gunel, Keith Newlander, and Paul Bucci for their help in the field testing.

## Authors’ Affiliations

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