2420 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 61, NO. 6, JUNE 2013 Fourth-Order Statistics for Blind Classification of Spatial Multiplexing and Alamouti Space-Time Block Code Signals Yahia A. Eldemerdash, Student Member, IEEE, Mohamed Marey, Member, IEEE, Octavia A. Dobre, Senior Member, IEEE, George K. Karagiannidis, Senior Member, IEEE, and Robert Inkol, Senior Member, IEEE Abstract—Blind signal classification, a major task of intelligent receivers, has important civilian and military applications. This problem becomes more challenging in multi-antenna scenarios due to the diverse transmission schemes that can be employed, e.g., spatial multiplexing (SM) and space-time block codes (STBCs). This paper presents a class of novel algorithms for blind classification of SM and Alamouti STBC (AL-STBC) transmis- sions. Unlike the prior art, we show that signal classification can be performed using a single receive antenna by taking advantage of the space-time redundancy. The first proposed algorithm relies on the fourth-order moment as a discriminating feature and employs the likelihood ratio test for achieving maximum average probability of correct classification. This requires knowledge of the channel coefficients, modulation type, and noise power. To avoid this drawback, three algorithms have been further developed. Their common idea is that the discrete Fourier trans- form of the fourth-order lag product exhibits peaks at certain frequencies for the AL-STBC signals, but not for the SM signals, and thus, provides the basis of a useful discriminating feature for signal classification. The effectiveness of these algorithms has been demonstrated in extensive simulation experiments, where a Nakagami-m fading channel and the presence of timing and frequency offsets are assumed. Index Terms—Signal classification, spatial multiplexing, Alam- outi space-time block code, fourth-order statistics. I. INTRODUCTION B LIND signal classification, an important task of intel- ligent receivers, finds applications in both military and commercial communications, such as electronic warfare, radio surveillance, civilian spectrum monitoring, and cognitive radio systems [1]–[7]. For example, the strategies employed by cog- nitive radio systems to opportunistically exploit the available Manuscript received August 27, 2012; revised January 14 and March 5, 2013. The editor coordinating the review of this paper and approving it for publication was C. da Silva. This paper was presented in part at the IEEE International Conference on Communications, 2012 and 2013. This work was supported in part by the Defence Research and Development Canada (DRDC). Y. A. Eldemerdash and O. A. Dobre are with the Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, Canada (e-mail: {yahia.eldemerdash, odobre}@mun.ca). M. Marey is with the Faculty of Electronic Engineering, Menoufyia University, Menouf, 32952, Egypt (e-mail:mfmmarey@mun.ca). G. K. Karagiannidis is with the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece (e-mail: geokarag@auth.gr). R. Inkol is with Defence Research and Development, Canada (e-mail: robert.inkol@drdc-rddc.gc.ca). Digital Object Identifier 10.1109/TCOMM.2013.042313.120629 spectrum require knowledge of signals in the environment to evaluate the likelihood of interfering with them [4]–[7]. Most previous work on blind signal classification has fo- cused on single-input single-output scenarios [8]–[16]. How- ever, the advent and rapid adoption of multiple-input multiple- output techniques adds a further level of complexity. These multiple antenna systems introduce new and challenging signal classification problems, such as estimation of the number of transmit antennas and the space-time code. Signal clas- sification in the context of multiple antenna systems has been addressed by a relatively small number of papers [17]– [26]. The problems considered by these papers included the estimation of the number of transmit antennas [17], [18], modulation classification [19], [20], and the classification of linear space-time block codes (STBCs) [21]–[26]. Regarding STBC classification algorithms, they can be divided in two general categories: likelihood-based [21] and feature-based [22]–[26]. Likelihood-based algorithms calcu- late the likelihood function of the received signal, and employ the maximum likelihood criterion to make a decision [21]. These algorithms require channel estimation, time, block, and frequency synchronization, and knowledge of the modulation format, while they suffer from high computational complexity. In [22], [23], the space-time second-order correlation function is used as a discriminating signal feature, with the decision being made by comparing the feature with a threshold [22] or based on the minimum distance between the theoretical and estimated features [23]. Signal cyclostationarity-based features are used in [24]–[26], with the decision made based on a cyclostationarity test. Most of the previous research [22]– [25] require multiple receive antennas. However, in many practical applications, size, power, and cost constraints on the receivers may favor single receive antenna solutions for STBC classification. In this work, the goal is to investigate the classification capability of a radio equipped with a single receive antenna. Given the assumption that either spatial multiplexing (SM) or Alamouti (AL) STBC is used by the received signal, it is shown that the fourth-order moment (FOM) and the discrete Fourier transform (DFT) of a fourth-order lag product (FOLP) can be efficiently used to blindly classify these signals 1 . Based 1 Note that the second-order signal statistics can be employed as dis- criminating features with multiple receive antennas [22]–[25]. Hence, the direct extension of a fourth-order statistic-based algorithm to multiple receive antennas makes little sense. 0090-6778/13$31.00 c  2013 IEEE