0018-9545 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2015.2503003, IEEE Transactions on Vehicular Technology 1 Noise-Loop Multiple Access Lorenzo Mucchi ∗ , Luca Ronga † , Giovanni Chisci ‡ ∗ Dept. of Information Engineering, University of Florence, Italy, lorenzo.mucchi@unifi.it † CNIT, University of Florence Unit, luca.ronga@cnit.it ‡ Dept. of Engineering, University of Ferrara, Italy, giovanni.chisci@unife.it Abstract—A fundamental problem for signal processing in wireless communications is the separation of multiple sig- nals/users from their mixture. The problem would be simpler if they are non-overlapping in either time domain or frequency domain. Two signals may be overlapping in both time and frequency, but they still can be easily separated if they are uncorrelated (orthogonal), like in Code Division Multiple Access system (CDMA). It may be interesting to know that two signals may be overlapping in both the frequency and time domain and also not orthogonal to each other, but they can still be separated if each autocorrelation function at the receiver is separable in the time-lag domain. In this paper, we will show how the Noise-Loop (NL) modulation, originally thought to produce security at the physical layer, can be used to effectively separate uncoordinated/non-orthogonal users sharing the same time and frequency interval. In order to show the potential of noise- loop multiple access (NLMA) scheme, the theoretical analysis is carried out and compared with simulations. In particular, together with the error probability, a new figure of merit is derived: the multiuser efficiency index. It can be shown that the NLMA is able to distinguish the bit stream of the users regardless of the their number. In addition, the capacity region of the NLMA is derived and compared to conventional CDMA scheme. All the above features together with the intrinsic security make the NL an interesting scheme for wireless technology. I. I NTRODUCTION In a multiple access wireless system, many users share the same communication channel and hence they interfere with each other. However, these interferences can be mitigated by using the orthogonal structure of the multiple access systems. The interferences that are difficult to deal with are the ones that are not coordinated with the multiple access system they are using. The uncoordinated interference in unlicensed spectrum is the major road block for wireless communications. Typically, multiple access schemes separate users by forcing them to use a different time slot, different frequency band or forcing them to be uncorrelated. Low cross-correlation prop- erty can be provided by applying a code to each transmitting signal, as in CDMA systems [1]. Unfortunately, low cross- correlation of codes cannot be always assumed at the receiver, resulting in complex scheme to recover the orthogonality and synchronicity. A key performance index for a multiple access system is the bit error rate (BER). It is known that the BER is very sensitive to total interference power at the access point (AP) demodulator. In interference-limited systems, huge improve- ment in performance can be achieved by reducing the total interference at the receiver, when deciding on the symbol of each user separately. Interference reduction techniques include, among others, spatial sectorization, smart antennas, interference averaging, multiuser detection, and interference pre-cancellation [1]. The sectorization and the interference averaging methods have the objective of reduction but not elimination of the interference. The pre-cancellation method requires channel state information (CSI) at the transmitter. The multiuser detection (MUD) method requires high computational effort as well as information about the distribution of the co-channel interferences which is usually not available. The technique is introduced in [2], while in [3] the error probability analysis is carried out for he optimum multiuser detector in asynchronous additive white Gaussian noise (AWGN) channels; in [4] the performance analysis is revisited by means of the Multiuser Efficiency (ME); in [5] is presented an hybrid detection technique, different from the optimal multiuser detection but considering the other active users; in [6] is shown that optimum multiuser detection, that achieves important performance gains over conventional single-user detection at the expense of an exponential computational complexity in the number of users, achieves those performance gains with a linear complexity in the number of users while considering the synchronous case. Currently MUD techniques has moved in the sense of low-complexity schemes, robust against the near-far effect [7]; some interesting results are given in [8]-[13]. A general classification of multiuser detection distinguishes between linear and nonlinear detectors. The former class includes the decorrelation receiver and the minimum mean square error (MMSE) receiver; the latter includes maximum likelihood sequence estimation (MLSE), interference cancellation, decision feedback receivers, and turbo receivers [14]. In [15], [16] the autocorrelation function was introduced as a domain for dividing the information streams of different users, or, equivalently, to reduce the co-channels interference. This method required pre-filtering/pre-coding or its equivalence and antenna arrays at the receivers in order to properly divide the users’ data. In addition, channel state information (CSI) is needed to perform the pre-filtering. In this paper we present a new multiple access scheme, called Noise-Loop Multiple Access (NLMA), which is able to separate the bit streams of uncoordinated users sharing the same time and frequency interval, without relying on pre- filtering, pre-coding, multiple antenna or CSI. The noise-loop modulation was originally designed to produce security at physical layer on a peer-to-peer communication link [17]-[19]. We will show here how the NL modulation can be used as