MIMO Self-Encoded Spread Spectrum with Iterative Detection Over Rayleigh Fading Channels Shichuan Ma

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln CSE Journal Articles Computer Science and Engineering, Department of 2010 MIMO Self-Encoded Spread Spectrum with Iterative Detection over Rayleigh Fading Channels Shichuan Ma Lim Nguyen Won Mee Jang Yaoqing Yang Follow this and additional works at: https://digitalcommons.unl.edu/csearticles This Article is brought to you for free and open access by the Computer Science and Engineering, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in CSE Journal Articles by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Hindawi Publishing Corporation Journal of Electrical and Computer Engineering Volume 2010, Article ID 492079, 9 pages doi:10.1155/2010/492079 Research Article MIMO Self-Encoded Spread Spectrum with Iterative Detection over Rayleigh Fading Channels Shichuan Ma, Lim Nguyen, Won Mee Jang, and Yaoqing (Lamar) Yang Department of Computer and Electronics Engineering, University of Nebraska-Lincoln, Omaha, NE 68182, USA Correspondence should be addressed to Shichuan Ma, [email protected] Received 15 February 2010; Revised 15 July 2010; Accepted 16 August 2010 Academic Editor: Christian Schlegel Copyright © 2010 Shichuan Ma 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. Self-encoded spread spectrum (SESS) is a novel communication technique that derives its spreading code from the randomness of the source stream rather than using conventional pseudorandom noise (PN) code. In this paper, we propose to incorporate SESS in multiple-input multiple-output (MIMO) systems as a means to combat against fading effects in wireless channels. Orthogonal space-time block-coded MIMO technique is employed to achieve spatial diversity, and the inherent temporal diversity in SESS modulation is exploited with iterative detection. Simulation results demonstrate that MIMO-SESS can effectively mitigate the channel fading effect such that the system can achieve a bit error rate of 10−4 with very low signal-to-noise ratio, from 3.3 dB for a 2 × 2 antenna configuration to just less than 0 dB for a 4 × 2 configuration under Rayleigh fading. The performance improvement for the 2 × 2 case is as much as 6.7 dB when compared to an MIMO PN-coded spread spectrum system. 1. Introduction components by matching the Rake fingers with the delayed PN codes to achieve multi-path diversity. By deploying Self-encoded spread spectrum (SESS) and multiple access multiple antennas at both transmitter and receiver, MIMO communications have been proposed and shown to have a architectures are capable of mitigating channel fading by number of unique features [1, 2]. By deriving its spreading taking advantage of the spatial diversity and enhancing sequences from the randomness of the source stream, SESS system capacity by employing spatial multiplexing [9–11]. provides a feasible implementation of random-coded spread In this paper, we propose a novel approach to combat spectrum and potentially enhances the transmission security. against fading in wireless channels by incorporating SESS in Since the use of PN code generators is obviated, SESS can MIMO system. Our motivation is based on the observation simplify multirate transmissions with variable processing that SESS not only can achieve multi-path diversity like PN- gains in multimedia applications [3]. In previous works, coded spread spectrum, but it can also provide both inherent we have shown that the modulation memory in SESS can temporal diversity and signal gain. Our work combines yield signal gain in AWGN channels [4]. We have also orthogonal space-time block-coded MIMO technique and demonstrated that the inherent temporal diversity in SESS iterative detection to obtain spatial and temporal diversi- modulation can be exploited with iterative detection to ties, respectively. We determine the bit error rate (BER) significantly improve the system performance over time- performance of MIMO-SESS system over Rayleigh fading varying fading channels [5]. channels and show that the fading effects can be completely It is also well known that PN-coded spread spectrum mitigated by exploiting diversities in both space and time can be incorporated with multiple-input multiple-output domains. The proposed scheme in this paper employs only (MIMO) techniques to achieve multipath and spatial diver- one spreading sequence which we refer to as the single-code sities [6–8]. In delay-spread or frequency-selective fading, scheme. Recently, we have reported a multicode Alamouti the system performance can be improved with a Rake scheme that can enhance the system throughput [12]with receiver that can resolve and combine the multi-path signal multiple spreading sequences, but at the expense of a BER 2 Journal of Electrical and Computer Engineering Tx Rx Self-encoding e(k, n) Correlation detection b(k) c(k, n) y(k, n) b(k) Acc Sgn b(k) d(k, n) d(k, n) Tb Tb b(k − 1) b(k − 1) T T b b(k − 2) b(k − 2) b N N . Tb Tb . b(k − N +1) b(k − N +1) Tb Tb b(k − N) b(k − N) (a) Transmitter (b) Receiver Figure 1: Block diagram of SESS system. degradation. The orthogonal space-time block codes and Thus, with a random input data stream, the sequence is multiple iterations in this paper thus could be incorporated also random and time varying from one bit to another. into the multi-code scheme in order to improve the BER We assume that the delay registers have been seeded by a performance. randomly selected sequence (which has also been acquired The rest of this paper is organized as follows. In at the receiver to initialize the despreading process). Section 2, we briefly describe the original SESS system. The The spread spectrum chips are then transmitted as proposed MIMO-SESS with iterative detection is described = in Section 3. Section 4 presents the simulation results and c(k) b(k)d(k). (2) compares the proposed system to an MIMO PN-coded Clearly, SESS signal has a modulation memory depth equal spread spectrum (MIMO-PNSS) system. Finally, Section 5 to N: concludes this paper. c(k, n) = b(k)d(k, n) = b(k)b(k − n). (3) Notations. The superscripts ∗ and T represent the conjugate and the transpose operations, respectively. |·|, E{·},and 2.2. Receiver. We assume that the chips are transmitted over diag(·) denote the absolute value of a scalar, the expectation a wireless channel and each bit experiences independent operation, and the diagonal vector of a matrix, respectively. Rayleigh fading that is constant over the bit duration. The Matrix (vector) is represented by capital (small) bold letter, channel coefficient for the kth bit interval is represented by with a(k, n) representing the nth element of vector a(k). α(k). The received signal y(k, n) can be expressed as y(k, n) = α(k)c(k, n) + e(k, n), (4) 2. Background where the additive Gaussian noise e(k, n) has zero mean and In this section, we briefly review the concept of self-encoding variance NN0/2. Note that the noise is sampled at the chip spread spectrum. The readers are referred to the original rate and is broadband; its variance is thus the narrow-band description in [1] for more details. noise variance N0/2 multiplied by the spreading factor N. The soft correlation estimate of the kth bit is computed 2.1. Transmitter. A block diagram of SESS system is shown from in Figure 1, where each rounded corner block represents one 1 N delay register, N denotes the length of spreading sequence, b(k) = y(k, n)d(k, n) and Tb is the bit duration. N n=1 The source information b is assumed to be bipolar values (5) of ±1. The bits are first spread by the self-encoded spreading 1 N = α(k)c(k, n)d(k, n) + u(k), sequence d(k)oflengthN at a chip rate of N/Tb. This N n=1 sequence is constructed from the source information stored in the delay registers that are updated every Tb.Forexample, where the spreading sequence for the kth bit, b(k), is given as 1 N u(k) = e(k, n)d(k, n) (6) = − − ··· − T d(k) [b(k 1)b(k 2) b(k N)] . (1) N n=1 Journal of Electrical and Computer Engineering 3 is the narrow-band Gaussian noise component of the self-encoding as can be seen from Figure 2. The decoupling correlation output and d(k, n) is the nth chip of the de- nature of this approach simplifies decoding at the receiver spreading sequence d(k) generated by the delay registers. We and lets us employ, in principle, any MIMO techniques assume that the receiver delay registers have been initialized for signal transmission, such as beamforming for spatial by the same seed sequence at the transmitter. The content filtering [14] and for signal quality improvement [15–17], space-time block coding for spatial diversity [18–20], and of the delay registers, d(k), are then updated by the hard layered space-time architecture for spatial multiplexing [21– decision of the correlation estimate, b(k) = sgn[b(k)]. Since 23]. In this paper, we adopt OSTBC which provides full the hard decision may be erroneous, the reconstructed de- diversity gain and allows linear maximum-likelihood (ML) ff spreading sequence could be di erent from the self-encoded decoding [24]. spreading sequence at the transmitter. A bit error therefore Numerous OSTBCs have been reported in the literature. will propagate through the delay registers for the next N bits In this work, we employ the full-rate code G2 for the two- and cause self-interference that attenuates the strength of the G transmit-antenna case, the half-rate code 3 for the three- despread signal b(k).

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