Mathematical Problems in Engineering

Volume 2016, Article ID 1930541, 9 pages

http://dx.doi.org/10.1155/2016/1930541

## Efficient DS-UWB MUD Algorithm Using Code Mapping and RVM

^{1}China Academy of Space Technology, Xi’an Branch, Xi’an 710100, China^{2}School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China^{3}Institute of Telecommunication Satellite, China Academy of Space Technology, Beijing 100000, China

Received 3 March 2015; Revised 14 December 2015; Accepted 21 December 2015

Academic Editor: Marzio Pennisi

Copyright © 2016 Pingyan Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A hybrid multiuser detection (MUD) using code mapping and a wrong code recognition based on relevance vector machine (RVM) for direct sequence ultra wide band (DS-UWB) system is developed to cope with the multiple access interference (MAI) and the computational efficiency. A new MAI suppression mechanism is studied in the following steps: firstly, code mapping, an optimal decision function, is constructed and the output candidate code of the matched filter is mapped to a feature space by the function. In the feature space, simulation results show that the error codes caused by MAI and the single user mapped codes can be classified by a threshold which is related to SNR of the receiver. Then, on the base of code mapping, use RVM to distinguish the wrong codes from the right ones and finally correct them. Compared with the traditional MUD approaches, the proposed method can considerably improve the bit error ratio (BER) performance due to its special MAI suppression mechanism. Simulation results also show that the proposed method can approximately achieve the BER performance of optimal multiuser detection (OMD) and the computational complexity approximately equals the matched filter. Moreover, the proposed method is less sensitive to the number of users.

#### 1. Introduction

Ultra wide band (UWB) is an attractive wireless communication technology for its characteristics of high data transmission rate, low power density, high interference resistance, strong multipath resolution, and so on [1–3]. The application range of UWB has been broadened to Wireless Local Area Networks (WLAN), Wireless Sensor Networks (WSN), radar detection, and high-speed communications of indoor and outdoor applications [4–6].

There are mainly two standard schemes of UWB formulated by IEEE 802.15.3a, that is, the multiband-based orthogonal frequency division multiplexing (MB-OFDM) and impulse-radio-based direct sequence UWB (DS-UWB) [7]. Compared with MB-OFDM scheme, DS-UWB has many attractive advantages such as low peak-to-average power ratio, significant ability of information hidden, and less sensitivity to multipath fading [8, 9]. In a sense, the multiple access scheme of DS-UWB is similar to code division multiple access (CDMA) systems; both of them use pseudo-random (PN) codes to distinguish different users. However, as in conventional CDMA systems, DS-UWB systems also suffer from the multiple access interference (MAI). The optimal multiuser detector (OMD) proposed by Verdu [10] could achieve the single user’s BER performance, but it had a very high computational complexity and was too expensive to handle [11]. Therefore, suboptimal detectors which may approximate OMD’s BER performance with an acceptable computational complexity have become a focus of research. In recent years, artificial swarm algorithms are widely used in multiuser detection (MUD). Literature [12] investigates an efficient multiuser detector by selection of initial states based on code mapping for the artificial bee colony algorithm. A complexity-performance-balanced MUD method based on artificial fish swarm algorithm for DS-UWB is introduced in [13]; the BER performance of these methods can approximate the performance of OMD while these artificial swarm algorithms need iterated operation. A multiuser frequency-domain turbo detector was employed which combines FD turbo equalization schemes with soft interference cancellation [14]. A code-aided interference suppression method was introduced for narrow band interference restriction in DS-UWB systems [15]. Adaptive MUD methods using the recursive least square (RLS) principles were studied in [16, 17]. In [18], a low-complexity approximate SISO MUD using soft interference cancellation and linear minimum mean square error (MMSE) filtering for coded CDMA system was introduced. However, few studies were reported that can approximate OMD’s BER performance with a computational complexity approximates to linear MUD.

In this paper, a novel MUD algorithm which combines a code mapping method and a wrong code recognition based on RVM is proposed to achieve a BER performance approximate to OMD method with a very low complexity which almost equals the complexity of matched filter.

The remainder of this paper is organized as follows. In Section 2, the DS-UWB system models are introduced. And in Section 3, the principles of the proposed algorithm are described, respectively. In Section 4, simulation results that compare the performance of the proposed algorithm and other approaches are illustrated and discussed, followed by conclusions given in Section 5.

#### 2. System Models

Consider a -user asynchronous DS-UWB system in additive white Gaussian noise (AWGN) channel, and assume that each user employs the binary phase-shift key (BPSK) modulation. In this paper, Scholtz’s monocycle is used as the UWB pulse waveform, which is approximated to the second derivation of Gaussian pulse. And the expression of Scholtz’s monocycle is [19]where and are the pulse center and the pulse shape parameter, respectively. At the transmitter (), BPSK symbols are spread with the specific PN codes , which are the binary bit stream valued only by −1 or 1, and is the length of bits per packet. The symbol duration is denoted by . We consider that each BPSK symbol can be divided into chips each with duration , where equals . In each chip, a monocycle is transmitted with the duration of to represent the sign of the chip. Practically, the duration of a chip is much longer than the duration of a UWB pulse; that is, . The th user’s transmission signal can be written aswhere represents the random delay of the th transmitter’s monocycle, .

Assume that each transmitter uses a time-invariant multipath channel in the same band. Let represent the impulse response of the transmission channel. Furthermore, suppose that UWB signals reach the receiving antenna by different paths. The channel impulse response can be written as [20]

The received signal that is transmitted from the th user is given by where denotes convolution operator.

The total received signal can be written aswhere is zero-mean additive white Gaussian noise (AWGN) with the unilateral power spectral density of .

In the receiver, the traditional receiver of a DS-UWB system consists of a pulse demodulator and a set of matched filters corresponding to each user. Regard signal as the input of the group of matched filters. Furthermore, the inter symbol interference (ISI) can be ignored when the base-band signal transmission rate is much lower than the UWB pulse rate.

Let vector represent the output of the matched filter group, and let vector represent the output of sign detectors, so the output of the matched filters can be represented as follows:where the vector denotes the correct bits of each user and the vector denotes the output of the AWGN from each user’s corresponding matched filter, while the random variable is normally distributed and and , denotes the cross-correlation matrix, where (what is more, ) and , in which the diagonal element (, ) represents the signal amplitude of the th user.

#### 3. The Proposed Hybrid Multiuser Detection

The main purpose of the proposed method is to pick out the error codes among the received signals and correct them. Firstly, the received codes are mapped into a feature space to make the error codes and the right ones different in some properties which can be easily distinguished. Secondly, identify and pick out the wrong codes by using some approaches in the feature space. Figure 1 shows the diagram of the algorithm. The first stage is corresponding to the code mapping, the second stage is corresponding to features extraction for RVM, and the third stage is corresponding to classification of the codes based on RVM and correcting the wrong codes.