IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST

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1 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST A Novel Modulation Diversity Assisted Ultrawideband Communication System Jin Tang, Member, IEEE, and Zhengyuan Xu, Senior Member, IEEE Abstract In this paper, a novel modulation diversity assisted (MDA) ultrawideband (UWB) communication system is proposed. Pulse position modulation and pulse amplitude modulation are applied to successive transmitted pulses alternately. The resulting modulation diversity helps to overcome channel estimation difficulties in typical UWB channels and permits low complexity receiver design. If every two consecutive pulses are grouped together, some connections with a transmitted reference (TR) system are demonstrated. But significant advantages of the proposed system are observed in smooth spectrum and increased data rate. Utilizing statistical properties of the modulated signals and inherent diversity, different receivers are designed for such a system. A conceptual receiver performs symbol detection using neighboring received signal to construct the template, while an advanced receiver uses a block of received signals to obtain a better template. The advanced receiver may continue to improve the template as ongoing detected symbols are available. A maximum likelihood estimator is also derived as a performance benchmark. The conceptual receiver shows slightly better performance than a conventional TR receiver while the advanced receiver shows comparable performance of the receiver using a maximum likelihood template estimator. Performance of the advanced receiver is studied both analytically and numerically. In a case of severe multipath channel distortion that results in interference between received signals from consecutive transmitted pulses, a corresponding template estimator and different receivers are also presented with detection performance numerically studied. Index Terms Intersymbol interference, low complexity, modulation diversity, optimum template estimation, transmitted reference (TR), ultrawideband (UWB). I. INTRODUCTION ALTHOUGH ULTRAWIDEBAND (UWB) technology was developed more than four decades ago [1], there emerges a renewed interest recently in the industry and academia after the first regulation for UWB was issued in 2002 [2]. UWB impulse radio transmits subnanosecond pulses using pulse posi- Manuscript received February 2, 2006; revised August 3, 2006 and September 21, 2006; accepted November 10, This work was supported by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD This paper was presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, March 2005, and at the IEEE International Conference on Ultra-Wideband, Waltham, MA, September The associate editor coordinating the review of this paper and approving it for publication was Dr. M. Buehrer. J. Tang was with the Department of Electrical Engineering, University of California, Riverside, CA USA. He is now with Neology Inc., San Diego, CA USA ( jin.tang@ieee.org). Z. Xu is with the Department of Electrical Engineering, University of California, Riverside, CA USA ( dxu@ee.ucr.edu). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TSP tion modulation [3]. It spreads the spectrum over a wide bandwidth. The large bandwidth has a great potential to support high data rate services. For example, UWB is being considered by the UWB Forum and WiMedia Alliance for wireless personal area network at bit rate up to 480 Mbps. Additionally, UWB communication systems are resilient to multipath distortion and can provide high multipath diversity [4]. On the other hand, the same features impose great challenges in implementation. Conventional UWB receivers, referred as RAKE receivers, correlate received signals with locally generated template signals and use a maximum ratio combining technique to capture multipath energy [4]. But in dense multipath channels, such as indoor environments, multipath components are very rich. It is practically difficult to estimate the channel accurately because there are too many unknowns [5]. Moreover, a low complexity RAKE receiver cannot afford too many fingers in multipath environments. To deal with those challenges, a transmitted reference (TR) scheme, which was originally introduced in [6] and [7], was proposed for UWB communications [8], [9]. Such a system transmits a pulse pair for each data symbol. A pulse without data modulation is transmitted before each data-modulated pulse. Because the two pulses undergo the same multipath channel, the first pulse in the doublet can be used as a reference to detect the information carried on the second pulse. Such a simple TR transceiver avoids explicit estimation of a possibly long UWB channel while still being capable of capturing full multipath energy. However, a conventional TR system suffers from severe performance degradation [9]. It is caused by the noisy template used in correlation receivers and 3 db energy loss from transmitting the reference pulse. Various improvements are investigated in [10] [14], by retrieving optimal template estimation, choosing appropriate integration interval, or accurately modeling propagation channel effects. Another widely recognized drawback of a TR system is its bandwidth inefficiency and power inefficiency by transmitting information-free reference pulses. Aiming at this issue, the inter-pulse interference is intentionally introduced by reducing pulse offset [15], [16]. A pilot waveform assisted modulation scheme is proposed to reduce the number of reference pulses and optimally allocate power [17]. In [18], a pulse interval amplitude modulation (PIAM) scheme is presented, which manages to increase bandwidth efficiency by transmitting two data bits in the second pulse. In addition, various TR variants such as differential modulation [19], [20], decision directed detection [21], and quadrature phase shift keying (QPSK) schemes [22] are also considered to reduce reference overhead and improve system throughput X/$ IEEE

2 4228 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 In this paper, we design a modulation diversity assisted (MDA) transmission scheme to solve some aforementioned problems in TR-UWB systems by utilizing modulation diversity [23], [24]. Pulse position modulation (PPM) and pulse amplitude modulation (PAM) are employed on a pulse train in an alternating way. As a result, two neighboring pulses have different modulation formats. Because information is modulated differently on pulses, diversity is created. At the receiver end, diversity can be exploited for direct demodulation of both information bits. Or it can facilitate template estimation and symbol detection in a sophisticated receiver. In PPM modulation, the pulse position is used to carry information, for example in a form of is a pulse, is a binary information bit taking zero or one with equal probability, is a modulation parameter. It can be found that this signal has mean which is nonzero [25]. Therefore, a first-order template estimator can be easily constructed for coarse estimation based on PPM signals. Subsequently, both PAM and PPM signals are used to improve estimation of the template. Finally, low complexity correlation receivers are employed to demodulate the two unknown bits. The proposed MDA-UWB systems overcome some drawbacks in TR-UWB systems, for example, improving bandwidth efficiency and spectral characteristics, while maintaining most of their merits. Although the PIAM scheme [18] can achieve the same information rate as our MDA system, it is shown to have worse power spectral density and detection performance. When severe multipath channel distortion causes interference of signals from consecutive data modulated pulses, a signal model is also developed to address intersymbol interference (ISI). Accordingly, a template estimator, matched filter (MF), and minimum mean-square-error (MMSE) receivers are suggested. This paper is organized as follows. In Section II, the signal model of our proposed MDA system without ISI is introduced. Then its spectral characteristic is analyzed and compared with some existing systems in Section III. Two receivers of different complexities are designed in Section IV and comparison with the optimum maximum likelihood (ML) receiver is made. Theoretical performance is analyzed for the advanced receiver in Section V. Section VI then particularly develops a model with ISI and presents corresponding receivers. Simulation results are finally presented in Section VII, followed by conclusions. II. MDA-UWB MODELING WITHOUT ISI In an MDA-UWB system, any two neighboring pulses are modulated by different modulation methods, PPM and PAM. The transmitted signal is given by Here, is a monocycle, is the frame duration and is the symbol duration. Each frame contains one doublet. Two information bits are transmitted during the th symbol interval. The first bit modulates the first pulse (1) using PPM and is the modulation delay. The second pulse delayed by is modulated by PAM. Each bit is transmitted repeatedly in frames. In order not to be distracted from the main idea, we only consider the special case that in this paper. That means each information-carried pulse is only transmitted once and the symbol duration is the same as the frame duration. But discussions can be readily extended to repetitive transmissions. The transmitted signal is distorted by the transmitter antenna, a multipath channel, the receiver antenna and additive white Gaussian noise (AWGN). To better capture signal energy, we use a filter matched to the transmitted pulse at the front end of the receiver. Assume the receiver is synchronized to the transmitter. If we define a new waveform, with denoting convolution and capturing effects of transmitter, channel, and receiver antenna, then we can obtain the following received signal model: is approximately AWGN with double-sided power spectral density. After sampling every seconds, we obtain discrete-time samples as follows:,, are integers satisfying,, and, is the sampled noise. Suppose the duration of is and is the length of the discretized waveform. and are chosen to be greater than and, respectively, to avoid ISI. We will address the ISI issue in a separate section later, by following some treatments proposed in [20] and [26]. Collect first samples within the first half frame into vector and similarly put first samples within the second half frame into vector, is the Kronecker delta function, and is a square matrix after shifting down all elements of an identity matrix by one row and.,, are corresponding vectors with length. In (4), the two separate signal vectors corresponding to two bits are modulated by different modulation schemes. Because the two pulses are transmitted through the same channel, they can be used as references for each other in order to detect information symbols. This will become clear when we discuss MDA-UWB receiver design. In addition, the inherent modulation diversity can be exploited to obtain accurate reference signals and thus improve detection performance. As we shall see shortly, the nonzero mean property of PPM signals will be utilized first to construct a preliminary low complexity template estimator. Then the estimator is improved (2) (3) (4)

3 TANG AND XU: MDA UWB COMMUNICATION SYSTEM 4229 based on preliminary bit estimates, received PPM and PAM signals in order to achieve better detection performance. Clearly, our proposed MDA approach is different from the TR approach [8]. But some connections can be built for these two schemes. First, both schemes transmit two pulses within one frame. Both pulses are modulated by data and no training pulse needs to be transmitted in an MDA system, while only the second pulse is modulated in TR and the first pulse is the information-free reference pulse. Information rate of an MDA system is thus doubled and it is more energy efficient than a TR system. Second, explicit channel estimation may not be required for data detection in both systems. To achieve this, a TR system only uses the first pulse of each doublet as a reference while both pulses are used as a reference to each other in an MDA system in order to detect two successive bits. Finally, an MDA system has better power spectrum density (PSD) than a TR system, which will be analyzed in detail in Section III. III. SPECTRAL CHARACTERISTICS In this section, we evaluate the PSD of transmitted MDA- UWB signal and compare it with two other UWB modulation schemes, namely conventional TR [8] and TR pulse interval amplitude modulation (TR-PIAM) [18]. For the three systems being considered, the transmitted signal can be expressed as the convolution of monocycle pulse and a series of Dirac delta functions at different delays denoted by as [27], [28]. For different systems, will have different forms. Then the PSD of transmitted signal can be calculated as, and represent the PSD of and the Fourier transform of, respectively. As is common for different systems deploying the same pulse shape filter, we focus our attention only on for comparison purposes. For MDA-UWB signal (1), we know Because is a cyclostationary process, its autocorrelation function (ACF) is periodic in variable with period. The time-averaged ACF over one period is derived in Appendix A and has the following form: (5) (6) The first two terms represent the continuous part of the signal spectrum as the last term represents discrete spectral lines. Note both of them are related to parameter. Similarly, we can find and That means the PSDs of TR signal and PIAM signal are identical. Now let us examine the signal power included in the continuous spectrum within the frequency band from to by integrating the corresponding part in this frequency range. The following can be easily found (8) (9) (10) As for any, it can be observed that the continuous spectrum is larger than for any with. Because the total powers of the three signals are the same, we can thus conclude the spectrum of the MDA signal is smoother than that of the TR signal or PIAM signal if spectral lines are taken into account. IV. MDA-UWB RECEIVER STRUCTURE A. Conceptual Receiver Because the channel responses to the two pulses within each frame are the same, any of the two pulses can be used as a reference to demodulate the other pulse thanks to the modulation diversity. To illustrate how we can accomplish symbol detection without explicitly estimating the channel, we introduce a simple receiver first, termed as conceptual receiver for convenience. To detect a PAM modulated bit, we use its neighboring PPM signal as a reference. To align the reference signal with signal, it is desirable to choose as a reference if and if, the superscript in denotes transpose for notational convenience. However, it is not known a priori whether or. Noticing the autocorrelation function of at zero offset is significantly larger in magnitude than any other at a nonzero offset, we construct a correlation template as to ensure that one desired reference signal and one offset reference signal are always included for each of the two possible cases. The resulting superimposed reference signal provides a large enough positive correlation with which may correctly reflect the polarity of. Consequently, the decision rule can be expressed by The PSD is the Fourier transform of (11) denotes transpose and function is defined as (7)

4 4230 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 With the help of demodulated, the signal waveform is recovered as, and a template is constructed to detect PPM bits (12). The template is similar to the one used in a conventional PPM-UWB correlation receiver [3]. We call the above receiver a conceptual receiver because our purpose for introducing it is only to highlight the main idea how diversity can assist symbol detection in its simplest form. Despite the simple structure, this receiver may show poor detection performance at low to moderate signal-to-noise ratios (SNRs) due to noisy reference signals, similar to the TR receiver [8]. This motivates us to seek an advanced receiver for performance improvement, as practiced in [15] and [16]. B. Advanced Receiver Now, we develop a more elegant receiver for a better performance-complexity tradeoff. It can achieve a significant performance gain over the conceptual receiver by fully utilizing the diversity embedded in PPM and PAM modulated signals. Yet it still has a simple structure and reasonable complexity. In the MDA signal model (4), the information about the pulse shape and multipath channel response is included in the vector. We shall use it as a reference waveform to detect information bits. As briefly explained earlier and in [25], PPM signals have a nonzero mean. Thus, a first-order blind estimator is constructed to obtain an estimate of the reference waveform. With (4), the mean of vector is (13). Use data vectors to estimate the mean by sample average and minimize the estimation error. This yields our initial estimator (14) Although this estimator has a simple structure, it may have poor performance as analyzed later. Fortunately, we can improve it greatly as a result of the diversity design in MDA-UWB systems. With the initial template, correlation-based detectors are used to demodulate those PAM bits and PPM bits in the same interval (15) Here, the template for PPM detection resembles the template in conventional PPM-UWB systems [3]. Once both bits are estimated, their waveforms can be recovered from PPM signal and PAM signal, and used to improve our template estimate. From PAM signal, is extracted as. To extract from PPM signal, denote the vector with first samples of the th frame and the vector with samples from to. We can see. Since can be either zero or one, correspondingly yielding waveform or according to (4), can be recovered from by. Therefore, a cleaner reference signal is obtained through a simple average operation (16) As we will show later, this is a much better estimate than.it is then used to construct correlation templates for symbol detection. The detection process is similar to (15), but with being replaced by the improved waveform (17) In order to further improve system performance, we may continue to update the estimate of in an adaptive way after as more data are received (18) and perform symbol detection using this updated waveform each time. In this paper, we present a discrete-time model and digital receivers for MDA-UWB systems. Further study on the quantization effect using low resolution high rate analog-to-digital converters can be carried out but beyond the scope of this work. Interesting readers are referred to detailed discussion for TR-UWB systems in [29], [30]. As shall be shown in Section VII, an advanced receiver improves the performance of a conceptual receiver greatly. The price paid for this performance gain is increased buffer size since the first PPM symbols and PAM symbols need to be stored in the initial stage for better reference estimation. However, the moderate complexity increase in the advanced receiver still makes it an appealing choice in achieving a complexity and performance tradeoff. C. Comparison With the Maximum Likelihood Estimator Performance of correlation receivers highly depends on how well the template is estimated. In this subsection, we first develop an ML template estimator for the MDA signal model and then compare it with our estimator used in the advanced receiver. Consider a time interval of. In the th symbol interval, samples are collected into a vector. The received long data vector is denoted as. Corresponding noise-free signal conditioned on the -bit data vector is. Assuming equal a priori probabilities of the data vectors, the likelihood function after ignoring irrelevant constants with respect to is given by [10] and [11] (19)

5 TANG AND XU: MDA UWB COMMUNICATION SYSTEM 4231 Fig. 1. Illustration of different decision functions. V. PERFORMANCE ANALYSIS We provide performance analysis of the advanced receiver in this section. For correlation receivers, detection performances are dependent on the accuracy of the estimated template. Now we first derive the general expression of bit error rate (BER) when a correlation receiver and template are used. Then we will evaluate template estimation performance in the measure of mean-square-error (MSE). Define the template error as. Its mean and correlation matrix are and, respectively. The decision statistic of PPM demodulation in (15) and (17) is Our objective is to maximize this likelihood function. Then the parameter is the ML estimator of. Following [10], [11], it is shown in Appendix B that the ML estimator satisfies the following:. After expansion, it becomes (21) (20) (22) Strictly speaking, is not Gaussian distributed due to the last noise-by-noise term in (22). However, it converges to Gaussian with large product of bandwidth and integration length [26], [31]. Thus, in order to easily obtain an analytical BER expression, it is reasonable to assume is a Gaussian random variable. The simulation results presented later can verify this assumption. The mean of conditioned on is (23) and is the hyperbolic tangent function. Comparing (20) with (16), we can see and play similar roles as and, given by (17). Corresponding decision functions are,,, and, respectively. We can observe some similarities from their plots in Fig. 1. However, and are piecewise functions while and are continuous functions. Thus, and can be interpreted as soft decisions of and. If they are replaced by hard decisions and, we end up with our proposed estimator (16). It can be expected that the optimal ML estimator has better performance than the estimator. But it shows much higher complexity to solve (20) for because and are still highly nonlinear functions of. It has to be solved iteratively. Meanwhile, the convergence relies on initialization. If the initial guess is far away from the true vector, the iteration may never converge to the optimum and performance will be very poor. As we will see from simulations, performance degradation of is marginal compared with. The good tradeoff between performance and complexity motivates our adoption of estimator instead of. This suboptimal estimator can even converge to the ML estimator at high SNRs. To avoid iteration in solving, one can derive an approximate ML estimator by approximating both nonlinear functions and with piecewise linear functions as in [10]. This topic is not the focus of our current work, and thus will not be further discussed. The variance conditioned on is (24) is the covariance matrix of template estimation error. Similarly, the mean and variance conditioned on are and (25) (26) respectively. Then the averaged BER for PPM modulated bits is. (27)

6 4232 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 From (15), the decision statistic of PAM demodulation is (28) Its mean and variance conditioned on are found to be (29) Without loss of generality, we assume all errors appear in the leading positions of any given data block of size bits. The average number of errors among the bits for PPM is and that for PAM is. Because wrong detections imply becomes and becomes, the template estimation error can be calculated using (16) as (30) It is easy to verify the error probability conditioned on is the same as that given. Because the two values are equally probable in data sequence, the average BER of detecting PAM bits is (31) (37) It is clear from (27) and (31) that detection performance is related to the template estimate through and. Next, we will derive these quantities for both proposed estimators and. For the estimator (14), we obtain (32) Invoking we obtain has zero mean and correlation matrix equals covariance (33). Under our assumption of absence of ISI, and are independent for. Then (33) can be simplified to (34) (38) Invoking (4) and (13), Substituting (35) into (34), we obtain can be evaluated as (35) (36) represents a vector with only nonzero noise samples appearing at the tail. The mean and covariance matrix of can be computed (39) The MSE of the estimate is calculated as the trace of the above matrix. Let us denote the error probabilities of and in (15) as and, respectively. Subscript 0 refers to, represents PPM and PAM. Then BERs and are calculated by (27) and (31) after considering and (36). The analysis of the estimator (16) and corresponding BERs are more complicated because it depends on the detection performance of and, and in turn on performance of. (40) is a matrix of all zero entries but with only ones appearing on the trailing main diagonal. The correlation matrix becomes. Substituting, (39) and (40) into (23) (26), and the corresponding results into (27), we can obtain the BER for PPM bits, denoted as. Similarly, using

7 TANG AND XU: MDA UWB COMMUNICATION SYSTEM 4233, (39), (40), and (29) (31), we obtain the BER for PAM bits, denoted as. With above analytical results, we can gain more insight into performance of estimators, and corresponding receivers. Obviously, the mean of by (39) is nonzero in general. Therefore, is a biased estimator. But with increasing SNR, both and decrease and the bias reduces. Despite the bias, the MSE of is usually much smaller than that of. To see this point, we notice both and are below for medium to high SNRs. Consequently, it is reasonable to approximate the MSE of, which is the trace of, with On the other hand, the trace of the second term of (36) is (41). The trans- the time hopping code to be periodic with period mitted signal (1) is modified as (43) At the receiver, the signal over symbol intervals is sampled every seconds and stacked into a single vector of length, in contrast to two separate vectors by (4). In choosing, it is preferable to ensure is not smaller than the channel span for sufficient signal energy capture. Then for simplicity of receiver design, the period of the time hopping sequence is chosen same as. Accordingly denote successive hopping codes by. Due to ISI, past symbols also contribute to the received signal. Following (4) and references [5], [25], the received data vector can be written as (42) and we have used the fact that As a consequence, even if we ignore the first positive term in (36). For low SNRs, the above reasoning still holds if is not too large because the last three terms of dominate in. Thus, we conclude the estimator improves the performance of substantially, and much lower probability of error can be achieved if is used to construct a correlator template. VI. MDA-UWB MODELING WITH ISI AND SIGNAL DETECTION All above discussions are based on the assumption that there does not exist ISI. In some applications, such as high rate data communications in the presence of large channel delay spread, ISI is unavoidable. If ISI is not severe, the proposed transmission scheme together with receiving algorithms still show some robustness to ISI, demonstrated in later simulations. This advantage is a direct result of the modulation diversity design because alternating transmissions with two different modulation schemes incur a silent period from time to time for each of modulated signals with different characteristics. However, if ISI is severe, the corresponding signal model and receiver structure should be modified for receivers to better tackle ISI. For example, interference issues together with corresponding solutions are particularly discussed in [14], [20], and [26] for their proposed different systems. In this section, we consider an MDA system with ISI, i.e.,. A signal model is first developed and then signal detection is discussed. In order to identify the received waveform affected by interferences, each frame is divided into chips, each with duration with as a positive integer, and time hopping code is used to control the signal transmission chip [25]. In addition, we choose (44) is a selection matrix constructed by shifting rows of the matrix down by rows or up by rows, is a Toeplitz matrix whose th element is if and if. Matrix consists of only zeros and ones with sparse nonzero subdiagonals and possibly main diagonals whose elements equal to one. Positions of those nonzero diagonals depend on hopping codes. Equation (44) can be further expressed in a compact form as (45) Here,,, and consists of column vectors corresponding to elements of as shown in (44). Similarly as in deriving the advanced receiver, the mean of is obtained from (44) as. Therefore, an esti- mate of the waveform can be obtained as (46) (47) The receiver uses as an estimate to replace in the above equation. Subtract the mean from the received signal to obtain a zero mean data vector. Subsequent data demodulation will be based on this vector [5]. With (46), is given by (48) has zero mean. Consider detection of PPM bit

8 4234 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 and PAM bit. Two linear receivers and can be applied to for estimation of these bits as follows [5], [26] (49) The negative sign above is due to the relation between and defined before, and the subscripts and indicate PPM and PAM, respectively. Receivers can take different forms [5], [26]. The MF receivers have low complexity, given by (50) and are two column vectors of corresponding to and, given by The MMSE receivers have favorable capability to suppress interference. They are given by (51) Fig. 2. Continuous spectra of different transmitted signals. and factor 1/4 stems from the correlation of. Both estimation and detection performance for the above algorithms in systems with ISI can be analyzed but is omitted. Interested readers are referred to [5] and [25] for relevant discussions. VII. SIMULATIONS We present some numerical results from Monte Carlo simulations in this section. Without otherwise specified, we use the following simulation setup. The transmitted monocycle waveform is chosen as normalized second derivative of Gaussian pulse with duration of 0.7 ns. A discrete-time IEEE multipath channel model CM1 [32] with sampling period 0.1 ns is adopted, which describes line-of-sight (LOS) channels between 0 and 4 meters. The tail of channel is truncated so that the maximum delay spread is 40 ns. 50 randomly generated channels are used for simulations and we assume they are static. The receiver is synchronized with the transmitter. Sampling interval is. Other system parameters are chosen as,, leading to a raw data rate of about 24 Mbps. Reducing these parameters can increase the data rate while incurring possible ISI that may degrade detection performance. The PPM modulation delay. SNR is set at and the length of data bits employed for template estimation is small with only. According to (7) and (8), we plot the continuous spectrum of three UWB signals: MDA, TR, and PIAM in Fig. 2. They are normalized by the peak of the MDA signal spectrum. The shape of MDA signal spectrum varies with different while that of TR or PIAM signal is independent of. Nonetheless, the continuous spectrum of MDA signal is always higher than that of the TR or PIAM signal at any values of. This implies the MDA signal has lower discrete spectral lines and smoother spectrum. Thus it will cause less interference to other coexisting radio systems. From the simulation results, will maximally smooth the signal spectrum in MDA systems. Averaged MSEs of the two template estimators ( and ) with respect to data length are plotted in Fig. 3. The circle Fig. 3. MSE of two template estimators under E =N =15dB. symbol represents the simulated performance of the initial estimator while the star symbol represents that of the final estimator. We can see MSEs decrease inverse proportionally to for both estimators. The plot confirms our previous conclusion that estimator has a significant smaller error than. The improvement is almost two orders. For the verification purpose, we plot the analytical results in the same figure. Analytical curves for both estimators match with corresponding simulations quite well. MSE with respect to SNR is presented in Fig. 4. We can still observe linear decreasing of MSE with increase of SNR in this figure. But from analytical expressions (36) and (40), we know there is an error floor above a certain SNR with finite. Since this critical SNR is very high, the error floor does not appear within our observation window. ML estimation results are also presented in this figure. It is initialized using our estimator and obtained after five iterations. We notice the difference between the estimator and the ML estimator is marginal. The MSE curve of converges to that of the ML estimator at high SNR. This implies that is asymptotically optimal.

9 TANG AND XU: MDA UWB COMMUNICATION SYSTEM 4235 Fig. 4. Effect of SNR on estimation performance with N =100. Fig. 6. Performance comparison of MDA conceptual receivers and other systems. Fig. 5. Performance comparison of different MDA receivers. Solid lines: simulation results; dash-dotted lines: analytical results for the advanced receiver. Next, we examine the detection performance of different proposed receivers in an MDA system in Fig. 5. Because the PPM modulation and PAM modulation have distinct performances, we plot their BERs separately. The conceptual receiver is susceptible to noise. It performs well at high SNR region. The advanced receiver improves performance of the conceptual receiver considerably: about 7 db for PPM bits and 9 db for PAM bits at BER of. Such an improvement is gained with a cost of increased buffer size. However, since the advanced receiver still has very simple structure, the large performance gain well pays off the moderate complexity increase. Thus, we believe the advanced receiver is a good practical option. Compared with the ML-based receivers, the advanced receiver suffers from some performance loss. But the difference diminishes with increase of SNR. Also observed from this figure is a good agreement between analysis and simulations for the advanced receiver. In order to gain more insight into the system performances, we compare our proposed MDA receivers with closely related receivers in other systems: our conceptual receiver versus the conventional TR receiver [8] and a PIAM receiver [18] in Fig. 6; Fig. 7. Performance comparison between MDA advanced receivers and DDA receivers with different data (window) length N. Dash-dotted lines: DDA receivers; solid lines: MDA receivers; dashed lines: bound. our advanced receiver versus the sliding window-based decision directed autocorrelation (DDA) receiver [21] in Fig. 7. In contrast to two bits in an MDA system or a PIAM system, only one bit, either PPM or PAM, is transmitted over each symbol interval in the conventional TR system. As observed from Fig. 6, a conceptual MDA receiver has comparable performance as a PIAM receiver and both of them outperform a conventional TR receiver at high SNR. In all settings, detection performance of PAM bits is better than corresponding PPM bits. In Fig. 7, we adopt the same simulation environment as that in [21] (a short channel with only 35 paths) and compare detection performance for PAM bits only. The bound is obtained by using true channel. It is seen that the DDA receiver needs a relatively larger window size to approach the bound while our advanced receiver converges to the bound even with. The better performance of our receiver at low SNR region with small window size is observed. To further demonstrate performance of our advanced receivers, additional simulations are conducted. The effect of

10 4236 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 Fig. 8. Effect of data length on detection performance. Fig. 10. Performance of advanced receivers with moderate ISI in different channel models. Solid lines: PAM bits; dash-dotted lines: PPM bits. Fig. 9. Effect of time offset between pulses for CM1 channels. Fig. 11. Performance of advanced receivers with severe ISI in different channel models. Solid lines: PAM bits; dash-dotted lines: PPM bits. data length is tested by fixing the template that is estimated based on an observation window of size, no updating of template afterwards. Corresponding results are presented in Fig. 8. The BER curve assuming true template is treated as a bound and plotted with star symbols. With increase of, BER keeps decreasing and approaching the bound. This phenomenon is not surprising given the fact that MSE is inversely proportional to as shown in Fig. 3. This motivates the continuous update of template estimate with ongoing symbol detections in our algorithm. For example, in a system with data rate of 24 Mbps, template update within 0.05 ms (equivalent to data length of ) could lead to a performance very close to the bound. Although we adopt larger than the channel delay spread in all previous simulations, this time delay between two pulses can be reduced to improve system throughput. How it affects system performance is studied in Fig. 9 for CM1 channels. Three different values are tested. With, the two pulses after multipath channel are overlapped and interference is incurred. However, no severe performance degradation is introduced with our designed advanced receivers. Finally, we examine system performance when ISI exists. Fig. 10 illustrates a scenario ISI is not severe. Both and are chosen to ensure that each pulse only interferes with the next neighboring pulse in all channel models (CM1 CM4). For example, if the channel delay spread is 40 ns, and are set to be 20 and 40 ns, respectively. In such a benign environment, it is noticed that the receiver performance with large (1000 in this example) keeps unchanged compared with previous results without ISI. The good performance is partially attributed to the modulation diversity in the transmission scheme. However, this receiver experiences severe degradation in a harsh ISI environment, shown in Fig. 11. In this figure, and are fixed for all four channel models. These parameters are much smaller than before, leading to a much higher raw data rate (about 333 Mbps). The channel delay spreads for CM1 CM4 are set, respectively, as 7, 11, 27, and 46 ns in order to capture 85% channel

11 TANG AND XU: MDA UWB COMMUNICATION SYSTEM 4237 Fig. 12. Performance of MF and MMSE receivers with severe ISI in different channel models. energy within the chosen time window. Because very long CM3 and CM4 channels introduce severe ISI, system performances are the worst in these two channels. As explained earlier, one has to resort to the corresponding estimation algorithm in Section VI, and the MF or MMSE receivers proposed therein. Fig. 12 shows performance of these two receivers with infinite data length. Through accurate modeling of ISI in (44), the waveform can be estimated with a sufficiently small error. In all four channel models, both the MF and MMSE receivers show better performance than those advanced receivers in Fig. 11 without particular ISI treatment. Meanwhile, the MMSE receiver outperforms the MF receiver at a price of higher complexity. VIII. CONCLUSION We propose a novel modulation diversity assisted transmission scheme for UWB systems and design corresponding receivers in this paper. The new system structure is particularly suitable for UWB applications because of low cost and low complexity requirements in most UWB systems and special UWB channel conditions. Both estimation performance and detection performance are analyzed for the advanced receiver in detail. The conceptual receiver has comparable performances as an existing PIAM receiver and is slightly better than a conventional TR receiver. The proposed advanced receiver improves performance dramatically and attains the same estimation performance as maximum likelihood estimators at high SNR. System performance is found to be insensitive to the time delay between pulses and robust to ISI in a benign environment. When ISI is severe, corresponding data model, template estimator and receivers are presented to tackle ISI based on the unique signal structure. Simulation results demonstrate their effectiveness in detection of signals corrupted by such interference. APPENDIX A PROOF OF (6) AND (7) Without loss of generality, we calculate the time-averaged ACF over one period starting from (52)

12 4238 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 Notice must be equal to 0 in order that is nonzero within the integration interval. Then the above equation can be simplified after evaluating the integral. Take derivative with respect to, set it to zero, and omit some scalars (53) we have used the fact that and are independent for any and,(,1). Since each takes 1 with equal probability, we further evaluate expectation in the above equation and obtain (57) (54) which is (6). We intentionally add and then subtract the terms for in the above equation or for each pair of takes two possible values. We factorize the terms corresponding to and, then the left-hand side (LHS) of the equality becomes (55) Taking the Fourier transform of this equation and using the fact that Carrying out the factorization sequentially on all, one obtains we arrive at (7). APPENDIX B DERIVATION OF (20) The likelihood function (19) can be expressed in terms of and by ignoring some terms irrelevant to as Then, factorize with respect to (56)

13 TANG AND XU: MDA UWB COMMUNICATION SYSTEM Use the same techniques on the right-hand side (RHS) of the equality. Equation (57) can be simplified to Pull out (58). Then ML estimator is obtained from the first term inside the summation (59) (60) Simplify the above by dividing both the numerator and denominator of the second term by. Then we have (20). REFERENCES [1] R. Fontana, A. Ameti, E. Richley, L. Beard, and D. Guy, Recent advances in ultra wideband communications systems, in Proc Ultra Wideband Systems Technologies (UWBST), Baltimore, MD, May 2002, pp [2] Revision of Part 15 of the Commission s rules regarding ultra-wideband transmission systems, Federal Commun. Commission News Release, Washington DC, Tech. Rep. ET Docket , Feb [3] M. Z. Win and R. A. Scholtz, Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications, IEEE Trans. Commun., vol. 48, no. 4, pp , Apr [4] M. Z. Win and R. A. Scholtz, Characterization of ultra-wide bandwidth wireless indoor channels: A communication-theoretic view, IEEE J. Sel. Areas Commun., vol. 20, no. 9, pp , Dec [5] Z. Xu, P. Liu, and J. Tang, A subspace approach to blind multiuser detection in ultra-wideband channels, EURASIP J. Appl. Signal Process., vol. 2005, no. 3, pp , Mar [6] C. K. Rushforth, Transmitted-reference techniques for random or unknown channels, IEEE Trans. Inf. Theory, vol. 10, no. 1, pp , Jan [7] G. D. Hingorani and J. C. Hancock, A transmitted rference system for communication in random or unknown channels, IEEE Trans. Commun., vol. 13, no. 3, pp , Sept [8] R. T. Hoctor and H. W. Tomlinson, Delay-hopped transmitted reference RF communications, in Proc Ultra Wideband Systems Technologies (UWBST), Baltimore, MD, May 2002, pp [9] J. D. Choi and W. E. Stark, Performance of ultra-wideband communications with suboptimal receivers in multipath channels, IEEE J. Sel. Areas Commun., vol. 20, no. 9, pp , Dec [10] S. Franz and U. Mitra, On optimal data detection for UWB transmitted reference systems, in Proc. IEEE GLOBECOM, San Francisco, CA, Dec. 2003, vol. 2, pp [11] S. Franz and U. Mitra, Generalized UWB transmitted reference systems, IEEE J. Sel. Areas in Commun., vol. 24, no. 4, pp , Apr [12] Y. L. Chao and R. A. Scholtz, Optimal and suboptimal receivers for ultra-wideband transmitted reference systems, in Proc. IEEE GLOBECOM, San Francisco, CA, Dec. 2003, vol. 2, pp [13] S. Franz and U. Mitra, Integration interval optimization and performance analysis for UWB transmitted reference systems, presented at the IEEE Conf. Ultra Wideband Syst. Tech., Kyoto, Japan, May [14] Q. H. Dang, A. Trindade, A.-J. van der Veen, and G. Leus, Signal model and receiver algorithms for a transmit-reference ultra-wideband communication system, IEEE J. Sel. Areas Commun., vol. 24, no. 4, pp , Apr [15] Z. Xu, B. M. Sadler, and J. Tang, Data detection for UWB transmitted reference systems with inter-pulse interference, presented at the IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Philadelphia, PA, Mar [16] Z. Xu and B. M. Sadler, Multiuser transmitted reference ultra-wideband communication systems, IEEE J. Sel. Areas Commun., vol. 24, no. 4, pp , Apr [17] L. Yang and G. B. Giannakis, Optimal pilot waveform assisted modulation for ultra wideband communications, IEEE Trans. Wireless Commun., vol. 3, no. 4, pp , Jul [18] T. Zasowski, F. Althaus, and A. Wittneben, An energy efficient transmitted-reference scheme for ultra wideband communications, in Proc Ultra Wideband Systems Technologies (UWBST), Kyoto, Japan, May [19] M. Ho, V. S. Somayazulu, J. Foerster, and S. Roy, A differential detector for an ultra-wideband communications system, in Proc. EEE 55th Vehicular Technology Conf. (VTC), May 2002, vol. 4, pp [20] M. Pausini, G. J. M. Janssen, and K. Witrisal, Performance enhancement of differential UWB autocorrelation receivers under ISI, IEEE J. Sel. Areas Commun., vol. 24, no. 4, pp , Apr [21] S. Zhao, H. Liu, and Z. Tian, Decision directed autocorrelation receivers for pulsed ultra-wideband systems, IEEE Trans. Wireless Commun., vol. 5, no. 8, pp , Aug [22] J. Romme and K. Witrisal, Analysis of QPSK transmitted-reference systems, in Proc. IEEE Int. Conf. Ultra-Wideband, Sept. 2005, pp [23] J. Tang and Z. Xu, A novel modulation diversity assisted ultra wideband communication system, presented at the IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Philadelphia, PA, Mar [24] J. Tang and Z. Xu, Performance study of a near-optimum modulation diversity assisted ultra-wideband receiver, presented at the IEEE Int. Conf. Ultra-Wideband, Waltham, MA, Sep , 2006.

14 4240 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 8, AUGUST 2007 [25] Z. Xu, J. Tang, and P. Liu, Multiuser channel estimation for ultrawideband systems using up to the second order statistics, EURASIP J. Appl. Signal Process., vol. 2005, no. 3, pp , Mar [26] J. Romme and K. Witrisal, Transmitted-reference UWB systems using weighted autocorrelation receivers, IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp , Apr [27] Y. Li and X. Huang, The spectral evaluation and comparison for ultra-wideband signals with different modulation schemes, in Proc. 4th World Multiconf. Systems, Cybernetics, Informatics (SCI) 2000, Orlando, FL, Jul. 2000, vol. VI, pp [28] M. Z. Win, A unified spectral analysis of generalized time-hopping spread-spectrum signals in the presence of timing jitter, IEEE J. Sel. Areas Commun., vol. 20, no. 9, pp , Dec [29] J. Tang, Z. Xu, and B. M. Sadler, Digital receiver for TR-UWB systems with inter-pulse interference, in IEEE Workshop Signal Processing Advances in Wireless Communications (SPAWC), New York, Jun. 2005, pp [30] J. Tang, Z. Xu, and B. M. Sadler, Performance analysis of b-bit digital receivers for TR-UWB systems with inter-pulse interference, IEEE Trans. Wireless Commun., vol. 6, no. 2, pp , Feb [31] T. Quek and M. Z. Win, Ultrawide bandwidth transmitted-reference signaling, in Proc. IEEE Int. Commun. Conf., Jun. 2004, vol. 27, pp [32] Channel Modeling Sub-Committee Rep. Final, IEEE P Working Group, IEEE P /490r1-SG3a, Feb Jin Tang (S 03 M 06) received the B.S. degree in electrical engineering and business administration from Beijing University of Aeronautics and Astronautics, Beijing, China, in 1995, the M.S. and Ph.D. degrees in electrical engineering from the University of California at Riverside, in 2003 and 2006, respectively. From 1997 to 1998, he was with GE Medical Systems, Beijing. Then, he joined PriceWaterhouse- Coopers Consulting in 1998 and worked as a consultant until Currently, he is employed as a R&D engineer by Neology Inc., San Diego, CA. His research interests include channel estimation, multiuser detection, and transceiver design for wireless communication systems, including ultrawideband and RFID systems. Zhengyuan Xu (S 97 M 99 SM 02) received the B.E. and M.E. degrees in electronic engineering from Tsinghua University, Beijing, China, in 1989 and 1991, respectively, and the Ph.D. degree in electrical engineering from Stevens Institute of Technology, Hoboken, NJ, in From 1991 to 1996, he was a System Engineer and Department Manager at the Tsinghua Unisplendour Group Corporation, Tsinghua University. Since 1999, he has been a faculty member with the Department of Electrical Engineering, University of California, Riverside, he is currently an Associate Professor with tenure. He has held visiting positions with Stanford University, Stanford, CA, and the University of Science and Technology of China. His research interests lie in wireless communications and related signal processing. They include multiuser spread spectrum, impulse radio, ultrawideband, wireless optics, hybrid radio frequency and optical communication systems, and sensor and ad hoc networks. Dr. Xu is an Associate Editor for the IEEE TRANSACTIONS ON SIGNAL PROCESSING and a Guest Editor of the Special Issue on Performance Limits of Ultra-Wideband Systems of the IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING. He also served as an Associate Editor for the IEEE COMMUNICATIONS LETTERS during , and the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY during He is an elected member of the IEEE Signal Processing Society s Technical Committee on Signal Processing for Communications. He has served as a Session Chair and Technical Program Committee member for many international conferences. He received the Outstanding Student Award and the Motorola Scholarship from Tsinghua University, and the Peskin Award from Stevens Institute of Technology. He also received the Academic Senate Research Award and the Regents Faculty Award from the University of California, Riverside.