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Ultra-wideband impulse radio (UWB-IR) sensors should comply entirely with the regulatory spectral limits for elegant coexistence. Under this premise, it is desirable for UWB pulses to improve frequency utilization to guarantee the transmission reliability. Meanwhile, orthogonal waveform division multiple-access (WDMA) is significant to mitigate mutual interferences in UWB sensor networks. Motivated by the considerations, we suggest in this paper a low complexity pulse forming technique, and its efficient implementation on DSP is investigated. The UWB pulse is derived preliminarily with the objective of minimizing the mean square error (MSE) between designed power spectrum density (PSD) and the emission mask. Subsequently, this pulse is iteratively modified until its PSD completely conforms to spectral constraints. The orthogonal restriction is then analyzed and different algorithms have been presented. Simulation demonstrates that our technique can produce UWB waveforms with frequency utilization far surpassing the other existing signals under arbitrary spectral mask conditions. Compared to other orthogonality design schemes, the designed pulses can maintain mutual orthogonality without any penalty on frequency utilization, and hence, are much superior in a WDMA network, especially with synchronization deviations.

Ultra-wideband impulse radio (UWB-IR) is a promising technique in short-range high-data-rate communication scenarios, such as wireless personal area networks (WPANs) [

For thorough spectral compatibility between those systems sharing the same band, the released UWB emission limits are very strict; for example, the FCC allowable equivalent isotropically radiated power (EIRP) for UWB transmitted signals is below −41.3 dBm/MHz. Hence, with respect to this EIRP mask, only when the transmitted pulses make full use of the regulated spectral energy, can a sufficiently high signal to noise ratio (SNR) be obtained in UWB receivers, which in turn enhances transmission reliability. Although the traditional Gaussian monocycle has been widely used in the early stages because of its simple realization, its frequency utilization is quite limited [

In addition, modern communication design has gradually paid attention to resolving the spectrum scarcity, so that the orthogonal waveform multiplexing have been widely adopted to further improve the frequency efficiency, which can also eliminate mutual interference or provide considerable waveforms diversity gain in UWB sensor networks [

In this paper, we propose a novel pulse forming technique for UWB-IR sensors. The frequency domain representation of the emission pulse is firstly derived from the product of a weight vector and the cyclic shift matrix (CSM) constructed from the basis waveforms. As a result, the spectral shaping problem is transformed to an optimization of the corresponding weight vector. With the permission that the designed PSD can temporarily outstrip UWB spectral masks, the design process can be simplified greatly. Later, this preliminary waveform would be further modified iteratively to lower the excess PSD until UWB pulses totally conform to emission constraints. Numerical evaluations indicate that our pulse can match the arbitrary spectral constraint much more completely than the other existing schemes. The proposed structure can also be viewed as a versatile pulse generator which can be efficiently implemented for digital signal processing (DSP). Hence, it can be directly applied to arbitrary UWB masks. We also design UWB waveforms with spectrum notch attenuated nearly 50 dB in specific bands, which is of great significance for cognitive radios (CRs) considering spectral avoidance to primary users.

Based on this already proposed algorithm, the constraint on orthogonal waveforms has also been derived. In order to obtain orthogonal pulses, schemes both from time domain and frequency domain have been addressed. We demonstrate that our designed orthogonal waveforms can use spectral mask as entirely as a single pulse. It is shown through analysis and simulation evaluations that the designed orthogonal pulses outperform other UWB waveforms in a WDMA network if mutual interference from nearby sensors is taken into account, especially when the synchronization deviation exists.

The rest of this paper is organized as follows: Section 2 elaborates on the design algorithm in detail. The orthogonal UWB pulses with efficient frequency utilization will be analyzed in Section 3. In Section 4, we discuss and evaluate the performance of UWB pulses in WDMA network with different degree of timing accuracy. At last, we conclude the paper in Section 5.

In order to eliminate potential interference from UWB sensors to the other vulnerable wireless systems sharing the same frequency band, the emission power of transmitted UWB pulses has been rigorously limited in different frequencies [

Thus, UWB sensors in preparation for data transmissions should make sure that their power spectrum density (PSD) remains below _{FCC}^{2} [^{2} ≤ _{FCC}^{2} ≤

To improve SNR in receivers, on the other hand, the transmitted UWB pulse is also supposed to use the regulatory spectral power as fully as possible. The spectral utilization efficiency of UWB signals is always measured in terms of the normalized effective signal power (NESP) [

Where _{B}^{2}

To begin this goal-directed design algorithm, we may select specific waveform meeting the following two restrictions as the basis waveform in frequency domain:

The basis waveform should be symmetric. Actually, the symmetry waveform is much suitable in the sense that the UWB spectrum mask remains constant in most frequency range. Besides, it is easy to generate an even symmetry waveform from the classical FIR filter [

The basis waveform is also supposed to attenuate fast. This is mainly because the regulatory UWB spectral masks always contain

In general, the energy concentration of the basis/windowing waveforms can be used to essentially reflect their attenuation characteristic, which can be usually defined as _{f}_{1}^{2}_{fw}|w^{2}

However, it should be noted that although the rectangular waveform has an ideal energy concentration, the corresponding infinite waveform in time domain may prevents it from being applied. In our following analysis, we adopt the Gaussian monocycle as the basis waveform because of its simple realization on hardware. So, we have:
_{s}

We denote the first column of _{0}:

After the cyclic shift of _{0}, we have:

Here, the notation _{0}((_{N}_{0} [

From (8), it is clear that each column of the cyclic shifted matrix

As a result, we obtain the frequency domain representation of UWB pulse conveniently, from the product of the optimized weight vector

In order to maximize NESP, from (10), optimization should be performed on the weight vector ^{2}_{FCC}

It is obvious that the objective function in (11) is a _{opt},^{2}_{FCC}_{opt}_{k}_{↓} can be rewritten as:
_{↓} is now a non-square matrix. Accordingly, the inverse matrix in (12) can be replaced by the _{↓} [_{opt}

At the expense of the complexity reduction, slight fluctuations will appear in the flat part of spectral mask and the smooth transitions will replace the sharp discontinuous edges in the designed PSD, which may reduce the obtained NESP. In most cases, however, this compromise between the complexity and the NESP is worthwhile, especially when the downside influence on NESP is insignificant.

Although the output pulse based on (12) can meet the spectral constraint in most frequency bands, it is also noteworthy that the designed PSD has exceeded the emission limit during the narrow range near the sharp discontinuous edges. From the numerical simulation shown in _{ECC}

It is noteworthy that the slope mask is in ^{2} ≤ _{FCC}_{opt}_{mod} which corresponds to the mismatched band [_{dowm}_{up}

The subscript in (15) is determined by:

So, the subset _{mod}_{n}^{th}_{opt}^{2}(_{n}_{FCC}_{n}_{mod}

Now, we investigate the convergence property of this iterative updating process. In fact, much similar to the Gibbs phenomenon encountered in most

It is also noted that, from (11), the optimization formulation is essentially a convex problem. Hence, the adopted LMS algorithm can definitely find the minimum MSE solution. Alternatively, the first stage can be also directly realized by resorting to numerical computation based on (13). Consequently, given that the convergence of both the two phases can be guaranteed, this whole proposed algorithm can also converge to the optimal solution after the finite iterations.

To sum up the points which we have just indicated, our proposed designing algorithm contains the following two phases:

_{opt}^{2}(

_{mod}

After the spectrum pruning process, the UWB pulse can be immediately derived by the inverse discreet Fourier transform (IDFT) on _{even}

Also, the phase response should be specified to be a linearly odd function of

The descriptive structure of the proposed UWB pulse is illustrated in _{i_down}_{i_up}^{th}_{s}_{ub_i}

The expression of subband UWB signal _{sub_i}_{s}_{ub_i}_{sub_i}_{sub_i}_{i}_{max}

It is observed that, from _{i}_{↓}) is

In our simulation, the maximum working frequency of UWB pulse is set to 12.5 GHz; the basis waveform length _{1} = [0.96,1.12], _{2} = [1.43,1.6], _{3} = [2.95,3.1], _{4} = [10.6–10.76]. However, the modified PSD |^{2}

Meanwhile, it is noted from

Clearly, this UWB pulse can also entirely utilize the frequency band below 1GHz. Although slight mismatches appear near the spectral sharp discontinuous edges in original MSE-based algorithm, the obtained NESP of modified pulses is quite encouraging. For UWB waveform that totally keeps below FCC spectral mask, the NESP can even reach 98.71% when the dimension of _{↓} is 32 × 128.

Although the FCC spectral limit _{FCC}_{FCC}

If the center and shape of each basis waveform _{i}

As is indicated by recent investigations, the regulatory constraint on spectral limit is not safe enough for certain specific legal systems in many cases, such as the fixed wireless access (FWA) [

Without loss of generality, assume that there is only one vulnerable service located in [5 5.5] GHz. With little effort, the corresponding sub weight vector, denoted by _{avoid}_{down}_{up}_{avoid}

From this two-phase design algorithm presented above, high NESP can be easily achieved under any emission constraint. Nevertheless, the designed waveforms are not mutually orthogonal, which has ruled out its significant applications in the multidimensional modulations and WDMA to further improve frequency efficiency. However, orthogonal pulses can be conveniently derived based on the proposed algorithm.

In order to achieve waveform orthogonality and differentiate multiple users, a ^{th}_{i}_{i,p}^{th}^{th}^{th}

Consequently, the time sequence _{i}_{i}

By substituting the expression of _{i}

Combing the previous target of maximizing the NESP with the orthogonality constraint together, the general objective of the orthogonal waveform design is given by:

From (27), the design process can be viewed as an optimal problem subject to a specific constraint. An intuitive solution is to design the code set _{i}

_{i,q}|=1_{i}_{0}(_{1}(

With increasing prospective orthogonal users, the solution to (28) would become much more complicated. If the constraint is further weakened where the expectation of _{i}_{k}_{k}^{2} represents the bearable degradation on the already maximized NESP. If the code set _{i}_{k}_{k}

From above analysis, the orthogonal waveforms design schemes directly in time domain are either complicated or suboptimal in NESP. Before reaching a more effective solution to _{i}_{i}_{i}_{i}_{12}(0) is 0, when these two arbitrary pulses _{1}(_{2}(

Furthermore, if we let _{i}_{i}_{i}_{12}(0) can be simplify to ^{2} _{f}_{1}(_{2}(_{1}(_{2}(

To reduce the complexity of (33), we may further specify the phase response θ_{i}

Then, _{f}c_{1}(_{2}(_{i}^{⌊log2} ^{N}^{⌋} is when the length of

By now, we can come back to the general solution to the spectrally efficient orthogonal waveform design in ^{(}^{k}^{)}(^{(}^{k}^{)}(^{(}^{k}^{)}(_{i}^{(}^{k}^{)}(^{(}^{k}^{)} represents the length of the ^{th}^{(}^{k}^{)}(^{⌊log2} ^{N}^{⌋} – 2^{⌈log2 (12.5/0.38)⌉}, which exactly corresponds to the narrow band occupying 1.61–1.99 GHz. The maximum orthogonal waveform set is only eight when

To enlarge this orthogonal set, it is necessary to modify FCC mask with the slightest discrepancy from _{FCC}

The designed _{FCC}_{1} has been shown in ^{(2)}(_{2} has also been illustrated in _{FCC}_{FCC}

In ^{(}^{k}^{)}(

Correspondingly, the ^{(3)}(

With the aid of the proposed shaping filter in _{even}

Practically, the cross correlation is not zero because the designed amplitude response can hardly remain constant during each spectral line. If we denote the error between the ideal spectrum and the actual output spectrum by

Considering that the high-order error part ^{2}(

Without loss of generality, we assume that there are three users transmitting signals simultaneously in UWB sensor networks. The autocorrelation and correlation of these three orthogonal waveforms have been illustrated in ^{−3}, even with perfect synchronization. The mainly reason lies in that the actual designed PSD in

It is also noteworthy that, attributed to the combination concept of several narrow-band signals that have no mutual phase constraints, the orthogonal signal generated from

In this part, we evaluate the performance of our proposed scheme in a waveform division multiple access (WDMA) network.

The achieved SNR is proportional to the emission power when the template-matched demodulation has been employed in receiver [_{n}_{a}_{n}

In our following simulation, the parameters are set as the same in Section 2.

When it comes to multiple orthogonal UWB pulses, we should employ the average NESP to judge the transmission performance. From

For example, the NESP of the first obtained pulse is 76.51%, and that of the second designed pulse is only 51.31%. As a result, the average NESP is only 59.26% for three UWB users. Based on this sequential solving scheme, the design algorithm is also much more complicated than our algorithm. The average NESP of another SOCP based orthogonal pulse design algorithm in [

As far as the waveform division multiple access networks are concerned, in practice, the synchronization deviation caused by the devices movement or clock drift may dramatically worsen receiving performance. Supposed the maximum timing deviation is δ, the BER performance with _{c}(

It should also be emphasized that, in addition to the distinguished transmission performance in WDMA, this proposed algorithm has some other mentionable merits. The implementation of our UWB pulse is much more competitive. The baseband processing frequency is only about 7 GHz when the total occupying band is 12.5 GHz, which is substantially smaller than the desired baseband sampling rate of 28 GHz in the SOCP method. The design orders are also far less than that of the SOCP scheme given an expected NESP. Based on cyclic shift and FFT, our proposed structure also has the virtues of simple implementations compared to pulse generator which employs dozens of carrier synthesizers.

Besides, this goal-directed algorithm provides great reconfigurability to any specific pulse design, which makes our scheme a general signal generator given an arbitrary spectral shape. As a useful application, we have designed UWB pulse with satisfactory frequency utilization under some regulatory spectral constraints. This method also paves the way for the

Throughout the above discussions the ideal UWB antenna is assumed, which exhibits a flat amplitude frequency (AF) response in a large range which covers from the DC frequency to 12.5 GHz. Nevertheless, in practice, the realistic front-end amplifier or UWB antenna acts as the band-pass filters that can only utilize a part of authorized spectrum, generally focused on the FCC regulated 3.1–10.6 GHz band. Thus, the well-designed UWB waveform will be further filtered by these non-ideal devices. As a result, the effort put into waveform design that occupies the FCC approved spectrum below 960 MHz may have little actual impact on the increase of receiver SNR. Specifically, the achieved NESP in the whole FCC band will be decreased to 87.6%, for the single user, which is slightly superior to the SOCP based UWB waveform with a NESP of 82.08% in [

If the AF response of realistic UWB antennas remains flat in this partial frequencies range, then the number of the orthogonal UWB users may not be determined by the narrow spectral lines any more. Similarly, if we represent ^{⌊log2 N⌋}, since the used basis waveforms in this case are mainly located in occupied band of 3.1–10.6 GHz, so it can provide much more UWB users to simultaneously access to the spectrum, accompanying the simplified processing. On the other hand, if the non-flat AF response of the realistic front-end is taken into consideration, the validity of the presented orthogonality derivation for multiple UWB waveforms under the ideal RF device assumption may be lost. As a result, except for the performance degradation in UWB receivers, even the mutual orthogonality of multiple users could be destroyed.

As a simply potential solution to still keep the orthogonality of designed waveforms and also enhance receiving SNR even in the presence of non-plat UWB antennas, the

Although UWB-IR techniques show many attractive features in short-range high-data-rates communication as well as in other important applications, electromagnetic compatibility (EMC) between UWB sensors and the other vulnerable wireless systems sharing the same band should be carefully investigated. It is encouraging to see that many countries have already regulated UWB emission limits according to their own practical situations, which lays the foundation for widespread applications of UWB. Since the UWB emission limit always remains below −41.3 dBm/MHz, the UWB transmitted pulses should fully make use of authorized spectral energy to enhance the SNR in receiver. At the same time, in order to provide the orthogonal waveform diversity and mitigating the mutual interference between UWB sensors, orthogonality is also worthy to be included in the waveforms designing.

In this paper, we have presented a versatile UWB waveform from the transform domain. Although FCC spectral mask is taken as an example to design the UWB signal, our algorithm can actually be used for any spectral mask. Compared with the other existing UWB spectrum forming techniques, such as the FIR shaper and the pulse optimization, our proposed optimal algorithm is considerably simpler in realization and superior in NESP. Based on this suggested algorithm, the obtained UWB waveform with specific spectrum notches also has an important application in CR networks. What’s more, orthogonal pulses can be easily derived from the presented scheme without any degradation on NESP, which can be suitably applied in UWB systems to improve the frequency efficiency. The generated mutually orthogonal waveforms are also much more competitive than other schemes in a multiuser scene, especially when the WDMA sensor networks can not acquire accurate synchronization.

This work was supported by NSFC (60772021, 60972079, 60902046), the National High-tech Research and Development Program (863 Program) (2009AA01Z262), Important National Science & Technology Specific Projects (2009ZX03006-006/-009) and the BUPT Excellent Ph.D. Students Foundation (CX201013). This work was also received supports from the Ministry of Knowledge Economy, Korea, under the ITRC support program supervised by the Institute for Information Technology Advancement (IITA-2009-C1090-0902-0019).

Basis waveforms meeting the requirements.

Structure of proposed UWB pulse generator. Note that the _{even}_{sub_}_{1}⊗_{sub_1}^{1×}^{N}

_{↓} is 32 × 128. Notice that the modified UWB pulses can now totally comply with emission limits. _{↓} is 48 × 128. _{↓} is 48 × 128. _{↓} is also 48 × 128.

Modified UWB emission limit. Note that PSD_{1} represents designed PSD from (37), whereas PSD_{2} extends its second piece spectral line ^{(2)}(_{1}.

Correlation of orthogonal UWB waveforms based on (37). The corresponding autocorrelation is normalized, whereas the cross correlation is about 1.97 × 10^{−3}.

Time domain waveforms for orthogonal UWB pulses.

BER performance by taking consideration of realistic UWB antennas.

NESP of the existing UWB signals under FCC mask Note that the filter orders of both the proposed method and SOCP scheme are 32. The average NESP is evaluated under the modified FCC mask. Assume that the total orthogonal users are 4; however, the average NESP in [

Seventh derivative Gaussian pulse [ |
46% | - |

Hermite Gaussian Functions [ |
65% | 65% |

PM algorithm [ |
72.41% | - |

SOCP based FIR filter [ |
79% | 77.5% |

SOCP based FIR filter [ |
92.16% | 59.26% |

Proposed UWB pulse | 98.7% | 98.7% |