1544 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 61, NO. 4, APRIL 2013 NLOS UV Communications Using M -ary Spectral-Amplitude-Coding Mohammad Noshad, Student Member, IEEE, Ma¨ ıt´ e Brandt-Pearce, Senior Member, IEEE, and Stephen G. Wilson, Senior Member, IEEE Abstract—We present an M-ary spectral amplitude code (SAC) modulation technique to improve the performance of free-space optical (FSO) communication systems. Although this approach can be used in any dispersive FSO system, in this paper we focus on non-line of sight (NLOS) ultraviolet (UV) systems relying on atmospheric scattering. Spectral amplitude encoding is applied on a broadband UV source using the same code families for the M-ary alphabet as used previously in SAC optical code division multiple access (OCDMA) systems. A differential struc- ture using two photomultiplier tubes is utilized in conjunction with various demodulation algorithms to decode the received signal. Intersymbol interference (ISI), received beam divergence and shot noise are considered as the main factors limiting the system performance. An upper bound on the bit error probability is presented and compared with simulation results for various geometries and for different code parameters. The maximum bit rate for a fixed bit error probability is calculated in terms of the link length, and results for different alphabet sizes are shown. By sacrificing spectral efficiency without becoming more susceptible to ISI, the proposed system can support higher rates and longer distances for the same performance compared with on-off keying systems. Index Terms—M-ary communication, ultraviolet communi- cations, non-line of sight communication, spectral amplitude coding. I. I NTRODUCTION T HE application of free space optics (FSO) for non-line of sight (NLOS) communications has attracted increasing interest because of its relative insensitivity to pointing errors and robustness against shadowing [1]. Atmospheric scattering in the UV band is higher than in other optical bands, and, consequently, in NLOS systems the receiver can receive more power from the transmitter than if it used another portion of the optical spectrum [2], making the UV band an interesting choice for NLOS communications [1]. Furthermore, back- ground irradiance severely limits the performance of NLOS infrared and visible light optical communications, while the ultraviolet (UV) band (200-280 nm) has low background light because of sunlight filtering by the upper atmosphere [1]. Yet the strong scattering in the NLOS UV channel imposes a temporal dispersion on the transmitted optical pulses. Thus, both intersymbol interference (ISI) and low received power can be factors limiting the data rate in NLOS UV links [3]. Manuscript received May 30, 2012; revised October 12, 2012. The associate editor coordinating the review of this paper and approving it for publication was W. Kwong. The authors are with the Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia Charlottesville, VA 22904 (e- mail: {mn2ne, mb-p, sgw}@virginia.edu). Digital Object Identifier 10.1109/TCOMM.2013.020813.120371 In this paper we propose single-user M -ary modulation and demodulation techniques to combat the channel degradation and increase the distance-rate product of NLOS UV systems. The distance-rate product is an important measure for evalu- ating the performance of optical communication systems. It is defined as the product of the transmitter-receiver distance of the optical channel and its maximum achievable data rate for a predefined maximum acceptable bit error probability. This product is usually limited by either intersymbol interference (ISI) or low signal to noise ratio (SNR). Error correcting codes, equalization and M -ary transmission are the most common techniques for increasing the distance-rate product in both radio frequency (RF) and optical communications. The maximum data rate versus the distance between the transmitter and receiver has been presented in previous work on NLOS UV communications for on-off keying (OOK) and different system geometries [3], [4]. In [5] we propose a novel structure using spectral amplitude coding (SAC) for improving the performance of the single- user NLOS UV communication system. We utilize fixed cross- correlation codewords, shown to have optimal properties in [6], as modulation symbols in order to increase the bit rate of the NLOS UV communication system. In [5], an avalanche photodiode (APD) array is used for extracting the received signal in each wavelength. However, because of the low gain of the APD arrays in the UV range and the small aperture size of each element of the array, the system is not able to transmit data for distances longer than 100 m. Photomultiplier tubes (PMT) are a better choice for detecting weak signals. Due to the high gain of the PMTs, shot noise dominates and other noise sources, such as thermal noise, can be neglected. An experimental demonstration of a NLOS UV communication system using OOK and PMTs is reported in [7], but communications is still limited to 500 Kb/s and 200 m range. In this paper we consider a different transmitter/receiver structure than in [5]. A broadband optical source is required for SAC, thus, since high-power broadband UV sources are scarce, widely-available broadband spectrum visible lasers are proposed as transmitter light sources. The encoding is done in the visible/infrared (IR) region, and then the encoded signal is frequency-doubled (or tripled) to the UV range. We use symmetric balanced incomplete block designs (BIBD) [8] to construct spectrally encoded symbols. At the receiver side, one or two PMTs can be used for decoding the received signal. The symbol time period, T s , is divided into smaller 0090-6778/13$31.00 c  2013 IEEE