612 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 4, APRIL 2004 Subspace-Based Active User Identification for a Collision-Free Slotted Ad Hoc Network Darryl Dexu Lin, Student Member, IEEE, and Teng Joon Lim, Senior Member, IEEE Abstract—We propose a novel spreading code scheme, trans- mitter–receiver-based code, for wireless ad hoc networks. The de- sign facilitates collision resolution using multiuser detection at each node, and is more bandwidth efficient than creating orthogonal channels in time or frequency. A subspace-based receiver struc- ture is introduced, which identifies users of interest, or “active” users, with minimal prior information on the spreading code en- semble. A subspace-based blind multiuser detector can then be im- plemented to suppress multiaccess interference. The performance of the proposed active user identifier is studied by investigating its false alarm rate and miss rate . Tradeoffs between and are discussed, and a graphical method to determine the threshold value of the decision statistic used in discriminating between active and inactive channels is introduced. Index Terms—Ad hoc networks, code-division multiple access (CDMA), collision resolution, multiuser detection, subspace iden- tification. I. INTRODUCTION I N PACKET-ORIENTED, random-access ad hoc networks, packet collision is an important problem to address. Conven- tionally, when a collision occurs, the collided packets are dis- carded and later retransmitted. However, retransmissions have the potential to create further collisions, and thus, severely pe- nalize the throughput performance, even at relatively light traffic loads. Effective collision resolution is, therefore, an important system design issue. Current collision-resolution research in random-access, slotted wireless systems [1] involves techniques at the protocol level, modulation level [2], and signal processing level [1], [3], [4]. Protocol-level collision resolution concentrates on avoiding collisions before they take place, and in scheduling retransmis- sions after a collision is detected. However, this implies that only one packet can access the channel in a time slot and results in low maximum throughput. Signal-processing-level collision resolution usually requires a large amount of overhead, such as embedding known symbols in the transmitted data packets. It also tends to be very computationally expensive when applied to an uncoordinated system. Modulation-level collision resolu- Paper approved by X. Wang, the Editor for Equalization of the IEEE Commu- nications Society. Manuscript received February 28, 2003; revised August 27, 2003. This work was supported in part by a grant from Bell Canada University Laboratories and in part by an Ontario Graduate Scholarship. This paper was presented in part at the IEEE International Symposium on Information Theory, Yokohama, Japan, July 2003. The authors are with the Department of Electrical and Computer Engi- neering, University of Toronto, Toronto, ON M5S 3G4, Canada (e-mail: linde@comm.utoronto.ca; limtj@comm.utoronto.ca). Digital Object Identifier 10.1109/TCOMM.2004.826415 tion, on the other hand, is much more versatile and attractive. It enables multipacket reception in a well-designed system, as we will demonstrate in this paper. Modulation-level collision resolution is achieved with the help of channelization. Channelization is traditionally achieved by transmitting signals in orthogonal channels. The most common channelization techniques include frequency-divi- sion multiple access (FDMA), time-division multiple access (TDMA), and code-division multiple access (CDMA). Given a central controller, such as a cellular base station assigning orthogonal channels to individual users, packet collision will not arise. However, applying the same concept to a fully connected wireless network with nodes requires orthogonal channels, one for each possible transmitter–receiver pair, in order to totally solve the packet-collision problem via channelization. This translates into a bandwidth expansion factor of , whether using TDMA, FDMA, or CDMA, and represents a great waste of bandwidth, because when the network carries bursty traffic, only a small percentage of these channels are occupied at any given time. However, with a carefully tailored spreading code design, such as the one to be presented in Section II, CDMA allows us to have a small bandwidth expansion factor which is designed for the average network traffic, instead of the max- imum number of possible connections. In the proposed design, the value of must not be smaller than , but can otherwise be chosen as spectrally efficient as desired under some quality of service (QoS) constraints, such as the probability of missing a transmitted packet or the probability of flagging an inac- tive channel as active . The coupling of this spectrally efficient CDMA modulation scheme and random access comes with a price, however, as packets are no longer transmitted using orthogonal channels. Fortunately, multiuser detection enables the reliable separation of nonorthogonal signal streams. In particular, certain multiuser detection schemes [5], [6] are “blind,” in the sense that they do not require knowledge of the interfering code channels at the receiver. Once the desired spreading code is known, in our case, through active user identification, multiaccess interference (MAI) can be suppressed using a blind multiuser detector. This setup consisting of a subspace-based active user identifier, fol- lowed by a subspace-based blind multiuser detector, is what we propose in our “collision-free” CDMA ad hoc network de- sign. Unlike the protocol-level collision resolution method, it allows for multipacket reception; unlike previous signal-pro- cessing-level techniques, it is not fully blind and is therefore less complex to implement. In fact, because both of the main modules in the receiver are based on subspace identification, a 0090-6778/04$20.00 © 2004 IEEE