# A Real Orthogonal Space-Time Coded UWB Scheme for Wireless Secure Communications

- Yanbing Zhang
^{1}and - Huaiyu Dai
^{1}Email author

**2009**:571903

https://doi.org/10.1155/2009/571903

© Y. Zhang and H. Dai. 2009

**Received: **1 December 2008

**Accepted: **21 July 2009

**Published: **13 September 2009

## Abstract

Recent research reveals that information security and information-hiding capabilities can be enhanced by proper exploitation of space-time techniques. Meanwhile, intrinsic properties of ultra-wideband (UWB) signals make it an outstanding candidate for secure applications. In this paper, we propose a space-time coding scheme for impulse radio UWB systems. A novel real orthogonal group code is designed for multi-antenna UWB signals to exploit the full spatial diversity gain and achieve the perfect communication secrecy. Its performance in a frequency-selective fading channel is analyzed. The transmission secrecy, including low probability of detection (LPD), low probability of intercept (LPI), and anti-jamming performance, is investigated, and some fundamental tradeoffs between these secrecy metrics are also addressed. A comparison of the proposed scheme with the direct sequence spread spectrum (DSSS) technique is carried out, which demonstrates that proper combination of UWB and space-time coding can provide substantial enhancement to wireless secure communications over other concurrent systems.

## 1. Introduction

The rapid expansion and proliferation of the wireless applications, especially in military and commercial use, have been prompting a corresponding increasing demand for transmission security. Currently, chief among the methods of information security is cryptography. Working at the network or higher layers mostly, cryptography aims to deny the unintended attempt on the information content by making various transformations of the original message. Protection against unintended disclosure of the information, however, can also be enhanced at the physical layer. Three features are generally desired for transmission secrecy—low probability of detection (LPD), low probability of intercept (LPI), and anti-jamming protection [1]. LPD, LPI, and anti-jamming properties may be viewed as the counterparts of the three important objectives in cryptography: secrecy, integrity, and availability.

It is well known that code division multiple access (CDMA) systems can provide an inherent physical layer security solution to wireless communications. However, if an eavesdropper can intercept a 2 -bit sequence segment generated from an -stage linear feedback shift register, the characteristic polynomial and the entire spreading code can be reconstructed through certain algorithms [2]. This motivates researchers to study enhancing the physical layer built-in security of CDMA systems through secure scrambling [2] or random spreading codes [3]. In 1990s, chaos, a very universal phenomenon in many nonlinear systems, has also been found valuable in secure communication systems due to its extreme sensitivity to initial conditions and parameters [4]. As a hybrid approach, it was shown that CDMA systems employing time-varying pseudo-chaotic spreading sequences can provide improvements with respect to their conventional CDMA counterparts (employing binary-valued pseudo-noise spreading sequences) [5]. Techniques have also been proposed to use the characteristics of the radio channel itself to provide secure key distribution in a mobile radio environment, where the information bearing signal is modified to precompensate for the phase effects of the channel [6].

A recent breakthrough in wireless communications, multiple-input multiple-output (MIMO) technique, vastly expands the capacity and range of communications. An information-theoretic framework for investigating communication security in wireless MIMO links is proposed in [7]. One of the principal conclusions there is that proper exploitation of space-time diversity at the transmitter can enhance information security and information-hiding capabilities. Particularly, if a source with constant spatial inner products (see Section 3.1) is transmitted over an uninformed link, the cutoff rate of the channel will be equal to zero and the minimum probability of decoding error will be forced to one. There are many known signal constellations satisfying this perfect-secrecy property, like double unitary codes, square unitary codes, or space-time QPSK.

Reference [8] is an exemplary work of this principle, where the authors proposed a secure transmission scheme based on random space-time coding. The basic idea is multiplying a random coefficient to the symbol sequence to make the eavesdropper completely blind with the transmitted signal. However, this random space-time transmission scheme has some drawbacks as well. One is that since the weight should be randomly selected, it has to trade transmission power for secrecy. The other is that before the data transmission, a secure initialization method has to be adopted to set up the feedback channel.

Research interests in ultra-wideband (UWB) wireless communications have also proliferated in both industry and academia recently [9]. Besides many other advantages, UWB also offers salient features, like ultrashort pulse and noise-like power density, for secure communications [10, 11]. Intent to jointly exploit the advantages of MIMO and UWB has also been initiated. In particular, UWB-MIMO systems which employ space-time block coding have been proposed in [12–14]. More recently, cooperative schemes have also been considered for such systems [15]. These works show performance improvement over the conventional single-input single-output (SISO) UWB systems for commonly adopted modulation and multiple-access techniques, in both single-user and multiuser scenarios. But to the best of our knowledge, there is no formal discussion on security issues when multiple antennas are introduced to UWB systems.

This motivates us to investigate a unitary space-time coding scheme for UWB systems, coined as USTC-UWB, which can simultaneously exploit the information security and information-hiding capabilities of space-time coding and UWB. Compared with general approaches in [7], USTC-UWB employs real space-time codes suitable for UWB signals and can work at any transmission rate. Based on the performance analysis in a multipath fading channel, we demonstrate that USTC-UWB can achieve superior LPD, LPI, and anti-jamming performances, making it an outstanding candidate for wireless secure communications. In the analysis, some fundamental trade-offs between the secrecy metrics are also explicitly addressed. A comparison of USTC-UWB with the direct sequence spread spectrum (DSSS) technique is also carried out, which further demonstrates its advantages.

The rest of the paper is organized as follows. Section 2 describes the system model and assumptions. The proposed USTC-UWB scheme is presented in Section 3, together with its BER performance analysis. Security metrics for USTC-UWB, including LPD, LPI, and anti-jamming properties, are analyzed in Section 4. The trade-off between anti-jamming and LPD performance is also addressed. In Section 5 the simulation results are presented. And finally, some concluding remarks are given in Section 6.

## 2. System Model

*M*transmit antennas and receive antennas. The transmitted waveform at the

*i*th transmit antenna during time frames can be described as

where represents the pulse repetition time (frame) interval corresponding to one symbol transmission. is the transmitted monocycle with the pulse duration , which is modulated by the (real) space-time code . Typically, the duration is between 0.2–2 nanoseconds, resulting in a transmitted signal of ultra-wideband, while is hundred or thousand times longer than [9, 13]. The factor ensures that the total transmitted power is . For simplicity, the random time-hopping (TH) codes for multiple access are omitted ([13]).

A class of unitary space-time signals is proposed in [16] for flat-fading channels where neither the transmitter nor the receiver necessarily knows the fading coefficients. Suppose that signals are transmitted in blocks of
time samples, over which interval the fading coefficients are approximately constant. Then, this space-time coding design admits a constellation of
(
is the data rate in bits per channel use) signals
,
, with the property that
are
complex-valued matrices obeying
(We use superscripts *T* and *H* in this paper to respectively denote the transpose and conjugate transpose operations.).

Extending this discussion to UWB systems, and assuming (without loss of generality), the transmit signal matrix can be formed as

where is a unitary matrix to be designed.

*i*th transmit antenna to the

*j*th receive antenna can be described as

*l*th path, respectively. At the receiver, we employ an -finger Rake receiver to exploit the multipath diversity inherent in UWB systems, each adopting the delayed versions of the received monocycle as the reference waveform. It can be shown that if , , and the autocorrelation function of the pulse for , all

*L*correlators' outputs at the

*j*th receive antenna can be collected into a (equivalently ) matrix

## 3. Unitary Space-Time Coding for UWB Systems

Conveying information with ultrashort pulses, UWB signals can resolve many paths and thus are rich in multipath diversity. This has motivated research toward using Rake receivers to collect the available diversity and thus enhance the performance of UWB communication systems. On the other hand, multi-antenna-based space-time systems offer an effective means of enabling space diversity, which has the potential to improve not only error performance but also capacity. In this section, we consider the construction of space-time codes for UWB systems. A novel unitary space-time code is designed, which can exploit the full spatial diversity and fulfill the purpose of secure communications. In Section 3.1, we first elaborate the design of this space-time code, and then its performance is characterized by a union bound on the block error probability in Section 3.2.

### 3.1. Construction of Unitary Space-Time Codes for UWB

Rank and determinant criteria are proposed in [18] for space-time code design. That is, in order to achieve the maximum diversity, the matrix has to be full rank for any different codewords and . It is shown in [19] that all optimal (full-rank) space-time group codes are unitary, which coincide with the secure space-time code structure found in [7].

*m*an integer, a Hadamard matrix is generated by a simple recursion

The code design for general odd constitutes our future work. In the following, we give some performance analysis of this code for cases.

### 3.2. Performance of USTC-UWB System

where
is the *l* th column of
(cf., (5)).

## 4. Security Performance Analysis

There are a variety of metrics used to describe the security properties in a wireless communications system from different aspects. The most important of them is LPD, LPI, and anti-jamming capability. LPD is concerned with preventing adversaries from detecting a radio transmission. Low probability of being detected also means low probability of being jammed by hostile transmitters, which is especially preferable for military communications. Even after being detected, a good secure communication system is still expected to have a strong ability to prevent being intercepted and jammed; therefore these properties should be considered equally important. In this section, we analyze the LPD, LPI, and anti-jamming performance of the proposed USTC-UWB scheme.

### 4.1. Low Probability of Detection (LPD)

When the channel is unknown, a common detecting approach for the eavesdropper is to use radiometer [10, 11], which measures the energy in a bandwidth over a time interval . The received signal is fed to a bandpass filter with bandwidth , followed by the squaring device and the -second integrator. The output of the integrator is sent to a comparator with a fixed threshold level. If the integrator output is higher than the threshold, the presence of a signal is declared.

where the mean and the variance are given by , , , and denotes the SNR.

This nice and simple relationship coincides with the intuition that a system with larger time-bandwidth product owns better secure properties.

In a secure communications system, the intended communicators (transmitter/receiver) should avoid signal detection/interception, which implies that the minimum transmit power should be used at the transmitter end and the highest sensitive receiver employed at the receiver end. But the communications should also prevent signal jamming, in this regard the transmitter should use the maximum transmit power and employ the least sensitive receiver (see Section 4.3). Therefore, certain trade-off exists between these objectives. Equation (25) also explicitly illuminates the trade-off between anti-jamming and LPD performance: while the performance of the desired user in the presence of jamming will certainly benefit from a larger transmit power, such an SNR increase inevitably leads to a higher probability of being detected by the eavesdropper.

### 4.2. Low Probability of Intercept (LPI)

where denotes the trace of matrix . When the channel is known to the receiver, the ML decision rule is given by (6). So if we can keep the desired user informed, but the eavesdropper uninformed, the later will be absolutely blind to the transmitted information (see (26)). Thus a perfect secrecy can be achieved.

To reach this objective, we can use a reverse-channel estimation method motivated by [6]. That is, let the desired receiver transmit pilot signals periodically, by which the transmitter can estimate the channel state information. Once the transmitter gets the CSI, it can precode the transmit signal to compensate for the effect of the forward channel and make the composite channel effectively constant. Thus, the desired user can be regarded as equivalently informed, while the eavesdropper is still kept uninformed, assuming the independence of the channels between the transmitter and the desired user, and the eavesdropper. This approach is valid when channel reciprocity holds. Otherwise, some secured feedback can be adopted for this purpose [8].

That is, the received signal of the eavesdropper does not contain any information of the transmitted signal .

where is the precoding weight matrix and represents the channel between the transmitter and the desired receiver, which is an block diagonal matrix with (see (5)) as the block diagonal elements. It is easy to see that the secrecy capacity is maximized by choosing under the constraints of and .

### 4.3. Anti-Jamming Performance

with
denoting the transmit signal from *i* th transmit antenna at *k* th time interval as defined in (2).

Direct-sequence spread spectrum signals are also widely used as a secure communications technique. With much larger bandwidth, UWB is expected to outperform DSSS for transmission secrecy [22]. An immediate conclusion from (25) is that UWB has a better asymptotic LPD performance than DSSS due to larger bandwidth and lower SNR, given the same observation interval . This conforms to earlier observations in [10, 11]. In the following, we further examine the anti-jamming performance.

where is the frequency response of and is the bandwidth of the DSSS signal.

Comparing (34) and (37), it is observed that the output jamming power for DSSS is larger than that for UWB as long as , which means that UWB provides a better anti-jamming protection than DSSS.

## 5. Numerical Results

with chosen such that the pulse has unit energy.

## 6. Conclusions

Motivated by some recent research progress on applying MIMO technique in UWB and secure communications, we propose a new unitary space-time coding scheme for impulse radio UWB systems. Its error rate and various transmission secrecy metrics are analyzed. The tradeoff between low probability of detection and anti-jamming is revealed, which indicates that any of these security features could not be solely enhanced without sacrificing another. Our work demonstrates that introducing properly designed space-time codes into UWB systems not only improves the performance of conventional single-antenna schemes but also offers prominent benefits on physical-layer transmission covertness, making it a strong candidate for wireless secure communications, especially for short-distance applications.

## Declarations

### Acknowledgment

This work was supported in part by the US National Science Foundation under Grant CCF-0515164, CNS-0721815 and CCF-0830462. Part of the results in this work appeared in [23].

## Authors’ Affiliations

## References

- Tsay M-K, Liao C-H, Shyn C-S, Yang T-Y: Simultaneous AJ and LPD evaluations for secure communication.
*Proceedings of IEEE Military Communications Conference (MILCOM '07), October 2007, Orlando, Fla, USA*Google Scholar - Ling Q, Li T, Ren J: Physical layer built-in security enhancement of DS-CDMA systems using secure block interleaving.
*Proceedings of the 38th Asilomar Conference on Signals, Systems and Computers, March 2004, Pricenton, NJ, USA*Google Scholar - Nguyen L: Self-encoded spread spectrum communications.
*Proceedings of IEEE Military Communications Conference (MILCOM '99), October 1999, Atlantic City, NJ, USA*1: 182-186.View ArticleGoogle Scholar - Yang T, Chua LO: Secure communication via chaotic parameter modulation.
*IEEE Transactions on Circuits and Systems I*1996, 43(9):817-819. 10.1109/81.536758View ArticleGoogle Scholar - Hwang Y, Papadopoulos HC: Physical-layer secrecy in AWGN via a class of chaotic DS/SS systems: analysis and design.
*IEEE Transactions on Signal Processing*2004, 52(9):2637-2649. 10.1109/TSP.2004.832029View ArticleGoogle Scholar - Koorapaty H, Hassan AA, Chennakeshu S: Secure information transmission for mobile radio.
*IEEE Communications Letters*2000, 4(2):52-55. 10.1109/4234.824754View ArticleGoogle Scholar - Hero AO III: Secure space-time communication.
*IEEE Transactions on Information Theory*2003, 49(12):3235-3249. 10.1109/TIT.2003.820010MathSciNetView ArticleMATHGoogle Scholar - Li X, Chen M, Ratazzi EP: A randomized space-time transmission scheme for secret-key agreement.
*Proceedings of the 39th Annual Conference on Information Sciences and Systems (CISS '05), March 2005, Baltimore, Md, USA*Google Scholar - Yang L, Giannakis GB: Ultra-wideband communications: an idea whose time has come.
*IEEE Signal Processing Magazine*2004, 21(6):26-54. 10.1109/MSP.2004.1359140View ArticleGoogle Scholar - Bharadwaj A, Townsend JK: Evaluation of the covertness of time-hopping impulse radio using a multi-radiometer detection system.
*Proceedings of IEEE Military Communications Conference (MILCOM '01), November 2001, Washington, DC, USA*1: 128-134.Google Scholar - McKinstry DR, Buehrer RM: Issues in the performance and covertness of UWB communications systems.
*Proceedings of IEEE Midwest Symposium on Circuits and Systems, August 2002, Tulsa, Okla, USA*3: 601-604.Google Scholar - Yang L, Giannakis GB: Analog space-time coding for multi-antenna ultra-wideband transmissions.
*IEEE Transactions on Communications*2004, 52(3):507-517. 10.1109/TCOMM.2004.823644View ArticleGoogle Scholar - Siriwongpairat WP, Olfat M, Liu KJR: Performance analysis and comparison of time-hopping and direct-sequence UWB-MIMO systems.
*EURASIP Journal on Applied Signal Processing*2005, 2005(3):328-345. 10.1155/ASP.2005.328View ArticleMATHGoogle Scholar - Tyago A, Bose R: M-PAM space-time trellis codes for ultra-wideband multi-input multi-output communications.
*IET Communications*2008, 2(4):514-522. 10.1049/iet-com:20060405MathSciNetView ArticleMATHGoogle Scholar - Abou-Rjeily C, Daniele N, Belfiore J-C: On the amplify-and-forward cooperative diversity with time-hopping ultra-wideband communications.
*IEEE Transactions on Communications*2008, 56(4):630-641.View ArticleGoogle Scholar - Hochwald BM, Marzetta TL: Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading.
*IEEE Transactions on Information Theory*2000, 46(2):543-564. 10.1109/18.825818MathSciNetView ArticleMATHGoogle Scholar - Paulraj AJ, Nabar R, Gore D:
*Introduction to Space-Time Wireless Communications*. Cambridge University Press, Cambridge, UK; 2003.Google Scholar - Tarokh V, Seshadri N, Calderbank AR: Space-time codes for high data rate wireless communication: performance criterion and code construction.
*IEEE Transactions on Information Theory*1998, 44(2):744-765. 10.1109/18.661517MathSciNetView ArticleMATHGoogle Scholar - Hughes BL: Optimal space-time constellations from groups.
*IEEE Transactions on Information Theory*2003, 49(2):401-410.View ArticleMathSciNetMATHGoogle Scholar - Damen MO, Abed-Meraim K, Belfiore J-C: Diagonal algebraic space-time block codes.
*IEEE Transactions on Information Theory*2002, 48(3):628-636. 10.1109/18.985979MathSciNetView ArticleMATHGoogle Scholar - Csiszar I, Körner J: Broadcast channels with confidential messages.
*IEEE Transactions on Information Theory*1978, 24(3):339-348. 10.1109/TIT.1978.1055892View ArticleMathSciNetMATHGoogle Scholar - Sadler BM, Swami A: On the performance of episodic UWB and direct-sequence communication systems.
*IEEE Transactions on Wireless Communications*2004, 3(6):2246-2255. 10.1109/TWC.2004.837433View ArticleGoogle Scholar - Zhang Y, Dai H: A unitary space-time coding scheme for UWB systems and its application in wireless secure communications.
*Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '06), May 2006, Toulouse, France*4: 485-488.Google Scholar - Siwiak K, Petroff A: A path link model for ultra wide band pulse transmissions.
*Proceedings of the 53rd IEEE Vehicular Technology Conference (VTC '01), May 2001, Rhodes, Greece*2: 1173-1175.View ArticleGoogle Scholar

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