Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 6971083, 7 pages

http://dx.doi.org/10.1155/2016/6971083

## Coherent RAKE Receiver for CPM-Based Direct Sequence Spread Spectrum

^{1}Department of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China^{2}Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China

Received 6 March 2016; Revised 20 May 2016; Accepted 29 May 2016

Academic Editor: Leonid Shaikhet

Copyright © 2016 Ke Zhou 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

Direct sequence spread spectrum (DSSS) using continuous phase modulation (CPM) inherits the techniques’ benefits, constant envelope, anti-interference, and spectral efficiency. To get diversity gains over a Rayleigh-fading multipath channel as in conventional direct sequence spread-spectrum binary phase shift keying (DSSS-BPSK) system, a new class of coherent RAKE receivers is proposed in this work. By introducing chip branch metric to the receiver scheme, despreading and data detection can be done meanwhile based on Maximum Likelihood Sequence Detection (MLSD). Compared to the conventional RAKE receiver which sums decision metrics symbol-by-symbol, the proposed DSSS-CPM RAKE receiver accumulates symbol branch metric increments over every phase state of multiple paths after chip phase synchronization. Numerical results show that DSSS-CPM using the synchronous despreading and demodulation algorithm has no performance loss compared to CPM system that employs MLSD algorithm under the same test conditions. Moreover, the proposed RAKE receiver outperforms conventional RAKE receiver and achieves a remarkable diversity gain of bit error rate (BER) under the Rayleigh-fading multipath channel.

#### 1. Introduction

The state-of-the-art continuous phase modulation (CPM), known for its efficient spectral properties, has the merits of continuous phase and constant envelop [1], while Direct Sequence Spread Spectrum (DSSS) is a mature technique and benefits from narrowband interference suppression, low probability of intercept, and multiple-access communication [2]. The so-called DSSS-CPM signals inherit both of the technical merits specifically. Firstly, the constant envelope allows the usage of the nonlinear amplifiers which are more power-efficient and cheaper. Moreover, the narrow power spectral density (PSD) will increase the processing gain in band-limit conditions and the spread-spectrum techniques will make the signal format to have a low probability of intercept (LPI) [3]. Finally, based on the correlation properties of pseudorandom spreading sequences, a remarkable diversity gain effect can be obtained using RAKE receiver under a multipath channel and a code division multiple-access (CDMA) system is available for multiuser scenarios [4].

Historically, several types of DSSS-CPM scheme have been proposed, but most of the studies focused on modulation schemes, signal format design, multiaccess interference (MAI), and CDMA under the AWGN channel. Lok and Lehnert presented a DSSS-CPM format with continuous phase in symbol transitions as well as chip intervals [5], which is the basic scheme discussed in this paper. Because spreading sequences and data symbols are not separable, the conventional receiver structure of DSSS is not available in this DSSS-CPM system. To solve this problem, Hsu and Lehnert proposed a CDMA system. In this work, the transmitter firstly generates CPM signal of pseudorandom spreading sequence using a continuous phase modulator, and then the CPM signal is multiplied by data signal [6]. Obviously, this kind of signal is not efficient in PSD due to discontinuities at symbol intervals. Thus, McDowell proposed a dual-phase DSSS-CPM signal format [7, 8], which is unique from the aspect of spreading sequences and data symbols effecting the carrier phase separately. Even though this signal format is phase-continuous and despreading and dada detection are separable, the data signal is limited in a minimum-shift keying (MSK) format and the scheme is a compromise between performance and complexity. There are also some other researches that concentrate on spreading sequences design to eliminate the multiaccess interference (MAI) and achieve multiuser communication [9–13]. However, all of these studies did not consider RAKE receiver for DSSS-CPM system.

Diversity combining techniques were proposed because the received multipath signal will cause errors in a multipath fading channel [14]. Specifically, if the same messages over different paths are collected and recombined after phase chip synchronization, the receiver will overcome this problem and get diversity gain in performance. Conventional DSSS-PSK RAKE receiver takes advantage of pseudorandom spreading sequences to despread multipath signals and recombines the decision metrics symbol-by-symbol. This kind of RAKE receiver cannot be used in DSSS-CPM system since CPM signal is nonlinear and sequence detection is required due to the phase memory feature.

In this paper, we propose and analyze a coherent RAKE receiver for DSSS-CPM system under a Rayleigh-fading multipath channel. By introducing chip branch metric to the receiver scheme, synchronous despreading and data detection can be done based on Maximum Likelihood Sequence Detection (MLSD). The proposed RAKE receiver accumulates the symbol branch metric increments over every phase state of multiple paths after chip phase synchronization. Consequently, large diversity gains as well as desirable spectral properties can be achieved.

This paper is organized as follows. In Section 2, we describe the transmitter, the signal format, and the Rayleigh-fading multipath channel model. Section 3 presents the coherent RAKE receiver techniques. Some evaluations and comparisons illustrate the result in Section 4.

#### 2. System Model

We describe the DSSS-CPM communication system in this section. The transmitter for this DSSS-CPM signal is presented in Section 2.1. The signal format and state trellis structure are defined in Section 2.2. Finally, in Section 2.3, we provide a model for the Rayleigh-fading multipath channel.

##### 2.1. Transmitter

The conceptual transmitter structure of the DSSS-CPM signal is shown in Figure 1. Each information symbol is multiplied by a finite-length pseudorandom spreading sequence to form baseband spreading signals, which are then used as input to the CPM modulator. Since the signal phase is continuous throughout the symbol and chip transmissions, it inherits the desirable properties of typical CPM signals.