Zhonghua Liang ＊, Junshan Zang 2, Xiaojun Yang Xiaodai Dong 3, Huansheng Song

1 School of Information Engineering, Chang’an University, Xi’an 710064, China

2 Jushri Technologies Inc, Shanghai, China

3 Department of Electrical and Computer Engineering, University of Victoria, BC 8W 3P6, Canada

* The corresponding author, email: lzhxjd@hotmail.com

I. INTRODUCTION

Noncoherent ultra-wideband (UWB) communication systems have received considerable attention from both academic and industry due to their low-complexity and low-power consumption [1-8]. Among them, transmitted reference (TR) signaling in conjunction with autocorrelation receiver (AcR) has become one of the two popular noncoherent ultra-wideband (UWB) systems (the other popular scheme is the noncoherent UWB system with energy detector) [1]. TR-UWB systems do not need channel estimation and accurate synchronization [9-10]. However, in order to avoid inter-pulse interference (IPI), a large delay line between reference pulses and data pulses is required in TR signaling [11].Such an impractical stringent requirement for the long wideband delay line is a major challenge for the implementation of TR-UWB systems [12-13]. Therefore, transmitted reference pulse cluster (TRPC) was proposed as an improved TR signaling to avoid the long delay line [14]. TRPC signaling has a more compact and uniform spacing between reference pulses and data pulses that repeat everyseconds.Although this structure will introduce the IPI,results reported in [14] show that two benefits in terms of signal energy efficiency and noise reduction can be achieved using TRPC structure and they significantly exceed the penalty caused by the IPI. Therefore, TRPC-UWB systems have been further investigated in various interesting issues in recent years [15-23].

Based on the TRPC signaling, an improved TRPC scheme, referred to as iTRPC, was recently proposed in [20] to obtain better bit error rate (BER) performance. In iTRPC signaling, a number of “zero”pulses are inserted at the end of each reference pulse clusters (RPC)and each data pulse clusters (DPC). According to this improvement, the IPI can be effectively reduced and more multi-path components can be exploited for data detection. However, the zero-padding space still does not exceed the maximum multi-path delay. Therefore, the IPI still exists in iTRPC.

In this paper, iTRPC with integration interval determination and decision threshold optimization (iTRPC-IAD) is investigated as the modified iTRPC. Firstly, considering the dispersive energy distribution of multi-path components, the integration interval is determined at the autocorrelation receiver using the methods proposed in [21], in which more energy can be captured than iTRPC. Moreover, since iTRPC cannot completely remove the IPI, zero decision threshold (ZDT) is not the optimal decision threshold and hence the decision threshold is optimized by employing adaptive decision threshold (ADT) [22]. Based on the two modifications mentioned above,iTRPC-IAD can achieve better BER performance compared with iTRPC.

The reminder of this paper is organized as follows. Section II describes the signal and channel models. Integration interval determination and decision threshold optimization are presented for iTRPC in section III and IV, respectively. Section V gives the simulation results to demonstrate the superiority of iTRPC-IAD. Finally, section VI provides the conclusions.

II. SIGNAL AND CHANNEL MODELS

In this section, we introduce the signal and the channel models for iTRPC-UWB systems.

2.1 Original TRPC signaling

Before discussing the iTRPC, it is necessary to introduce the original TRPC signaling. In TRPC signaling, the information packet is first modulated as a BPSK symbol sequencewhich is then converted into UWB signals and transmitted. We suppose that a dual pulse pair composed of a reference pulse and a data pulse with very short delay, is repeated uniformly everyseconds. The corresponding signal generated at the transmitter can be written as [14]

2.2 iTRPC signaling

The iTRPC signal is composed of RPC’s and DPC’s, where a RPC consists ofreference pulses with pulse widthand“zero”pulses with pulse widthDPC and RPC are alternately conjugated and repeated everyseconds in one iTPRC symbol. The transmitted iTRPC signal can be represented by [20]

where

2.3 IEEE 802.15.4a Channel Model

The UWB channel impulse response (in complex baseband form) described in the IEEE 802.15.4a standard can be written as [24]

III. INTEGRATION INTERVAL DETERMINATION

In this section, integration interval determination is presented for iTRPC-IAD (modified iTRPC) systems.

The decision variable ofi-th symbol is given by [20]

where (for simplicity, the index “i” is omitted in the following expressions)

where

Accordingly, the parameters given by (9)-(12) can be improved using the modified integration interval, in which the integration parametersandcan be determined using the algorithms presented in [21].

IV. DECISION THRESHOLD OPTIMIZATION

4.1 Decision threshold in iTRPC

The decision threshold used in iTRPC system[20] is ZDT, that is, the estimated symbolis obtained with zero threshold, and therefore the symbol decision can be made by

The probability of error for the iTRPC system conditioned on the channel realization is given by [20]

Although the iTRPC structure can mitigate the IPI with the zero-padding space at the end of DPC and RPC, the IPI cannot be eliminated completely since the zero-padding space is still not sufficient to cover the maximum delay of multi-path components. Therefore, zero is not the optimal decision threshold.

4.2 Improved decision threshold for iTRPC

In order to improve the performance for symbol detection, ADT [22] is used to optimize the decision threshold.

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According to the Gaussian approximation(GA) analysis in [25], forthe two conditional distributions of the decision variablecan be approximated as two Gaussian RV’s withandrespectively. Without loss of generality, we assumeTherefore, there must exist an optimal decision thresholdthat corresponds to the minimum probability of error.

Similar to the analysis in [22], the error probability with the optimal decision threshold is obtained as

where

Based on the analysis above, we see that in the presence of IPI, zero is no longer the optimal decision threshold for iTRPC systems.Therefore, the decision threshold optimization can improve the BER performance. The optimal decision thresholdcan be approximated with the ADT [22]. In practice,can be estimated by employing a simple training sequence with lengthLin which containsconsecutive symbols “+1” which are used to estimateandconsecutive symbols “-1”which are used to estimateThen,can be estimated by averagingand

Table I Signaling parameters for TRPC, iTRPC, and iTRPC-IAD

Table II Abbreviations for TRPC, iTRPC, and iTRPC-IAD systems

Table III Performance gain of iTRPC-IAD over iTRPCzdt with different L values in CM1 channels (BER =1×10-6)

V. SIMULATION RESULTS

Fig. 1 BER performance of TRPC, iTRPC, and iTRPC-IAD systems in CM1 channels

Fig. 2 BER performance of TRPC, iTRPC, and iTRPC-IAD systems in CM2 channels

In this section, we present the simulation results on the BER performance of the original TRPC, iTRPC and iTRPC-IAD systems in CM1, CM2 and CM8, respectively. CM1 and CM2 model residential line-of-sight (LOS)and non-light-of-sight (NLOS) channels,respectively, and CM8 represents NLOS industrial channels with an extremely large delay spread [24]. The signaling parameters and some abbreviations of TRPC, iTRPC and iTRPC-IAD are described in Tables I and II,respectively. It is noted that the parameters provided in Table I are selected empirically by performance evaluation reported in [14] and[20] (particularly, more details can be found in[20] to determineand

For simplicity, only the threshold-crossing algorithm [21] was used in this paper to determine the integration parametersandfor IID operation. However, the BER minimizaperformance gap betweenL=32 and the ideal decision thresholdis as small as 0.1 dB.Therefore,L=32 is used as a practical parameter setting for iTRPC-IAD, and only the performance withL=32 is given in subsequent figures (L=32 is also employed for TRPCadt[22]).

From Fig. 1, we see that in the residential LOS channels, the benefit of integration interval determination is not significant. For example, iTRPC-IID outperforms iTRPCzdt by only 0.5 dB at BER=1×10-6. However,according to Fig. 2, it is noted that due to the tion and the hybrid methods proposed in [21]can also be considered according to the system requirements. All simulation results provided in this paper were obtained by averaging the output BER for 100 random channel realizations of a given channel model.

In order to determine a practical training length for iTRPC-IAD, the BER performances with differentLvalues were evaluated and similar results were obtained in CM1, CM2 and CM8 channels. Hence, as an example,Table III presents the performance gain of iTRPC-IAD over iTRPCzdt, with different training lengthLfor BER=1×10-6in CM1 channels. From Table III we see that, increasingLfrom 32 to 1024 improves the performance gain by only 0.05 dB. Moreover, the integration interval determination, the performance gain becomes significant in NLOS channels. For example, the performance gain reaches about 2 dB at BER=1×10-6. Moreover,significant improvement can be obtained with ADT in both LOS and NLOS channels. For example, iTRPC-IAD outperforms iTRPC-IID by about 1.5 dB and 1.8 dB in CM1 and CM2,respectively.

In Fig. 3 we see that in industrial NLOS channels with extremely large delay spread,the performance of iTRPC is even worse than that of original TRPC. It is just because the integration interval in iTRPC cannot collect sufficient multi-path components in CM8.However, with the employing of IID, iTRPCIID has significant performance improvement over iTRPCzdt. Furthermore, an additional gain of 0.5 dB can be obtained via IAD.

Based on the discussion above, we see that iTRPC cannot get significant performance gain in multi-path channels, and it even becomes worse than the original TRPC in NLOS channels with extremely large delay spread.However, iTRPC-IID can provide significant improvement because more multi-path energy can be captured. Meanwhile, since the presence of IPI, ZDT cannot be used as the optimal decision threshold. Therefore, iTRPCIAD can get further improvement than iTRPCIID.

VI. CONCLUSIONS

In this paper, the integration interval determination and decision threshold optimization issues were investigated for iTRPC-UWB systems. Accordingly, the iTRPC-IID and the iTRPC-IAD were presented as two modified iTRPC systems. Compared with iTRPC,iTRPC-IAD has significant performance improvement in both LOS and NLOS channels.Moreover, iTRPC-IAD possesses superior performance over iTRPC-IID due to the introduction of ADT at a cost of feasible training overhead. Although the performance gain of iTRPC-IID is limited in LOS channels, it still yields significant benefit in NLOS channels. In practice, there can be a trade-off between the BER performance and transmission efficiency.Therefore, both iTRPC-IID and iTRPC-IAD can be considered as two promising candidate schemes for noncoherent UWB communications.

Fig. 3 BER performance of TRPC, iTRPC, and iTRPC-IAD systems in CM8 channels

ACKNOWLEDGEMENTS

This work was supported in part by the National Natural Science Foundation of China under Grant 61271262, 61473047 and 61572083, in part by Shaanxi Provincial Natural Science Foundation under Grant 2015JM6310, and in part by the Special Fund for Basic Scientific Research of Central Colleges, Chang’an University 310824152010 and 0009-2014G1241043.

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