Channel Order Estimation for Multiuser Detectors

Most wireless networks use direct sequence code division multiple access (DS-CDMA) scheme. A DS-CDMA signal is formed by multiplying each data bit by the signature waveform of the modulating sequence. In an ideal case, the signature waveforms form an orthogonal set. Therefore, the data bit is estimated by multiplying the received signal by the corresponding signature waveform. However, in practice, the signature waveforms are rarely orthogonal. For instance, in cellular networks, the received signal is the superposition of the actual signal and inter-cell and intra-cell interference.
The interference is generated by the transmitters that use a signature waveform that is not orthogonal to the signature waveform of the desired signal.
Nonetheless, if the signature waveforms are selected at transmitters as orthogonal signals, channel impairments such as random delay and multipath transmission may shift the signals so that they become non-orthogonal at the receiver. Another example arises in WLANs. In practice, it is possible to operate several WLANs in the same environment. In that case, the signal of each WLAN will act as an interference for other WLANs.
Since wireless terminals operate on different WLANs, the signal received by a receiver is the combination of the signals transmitted by terminals communicating on different WLANs, and since the DS-CDMA signals are generated on different WLANs, they may not be orthogonal.

In both examples above, the channel is interference-limited. In such systems, the performance of the conventional receivers---in terms of bit-error-rate (BER)---is very poor. To combat the degradation of performance of conventional detectors, multiuser detectors are usually used. A multiuser detector can significantly reduce the BER. Multiuser detectors need to know the true number of signals and their corresponding signature waveforms.
If only the signature waveform of the signal of interest is known to the receiver, a blind multiuser detector should be used. An example of this case is the reception of downlink signals at a mobile terminal. A blind multiuser detector uses the {\it signal subspace} methods to detect the transmitted data.
These methods should know the true number of transmitted signals (including interference).

In various occasions, the true number of signals is not known and should be estimated prior to the application of multiuser detectors. Here, we present two such examples. In wireless cellular networks, the true number of signals is not known at mobile terminals. Therefore, if blind multiuser detectors are to be used, the true number of signals should be estimated. In WLANs, since each WLAN is an autonomous system, it is very difficult to determine the number of users and communicate it to all wireless terminals. Therefore, effective techniques should be developed to detect the number of signals by observing the waveform of the received signal. In this research, we introduce a novel technique to enumerate DS-CDMA signals that are used in both cellular networks and WLANs.

We develop an algorithm based on the predictive description length (PDL). The PDL criterion is the cumulative log-likelihood function of the observation vectors such that at each time instant, the maximum likelihood (ML) estimate of the parameter based on the past data is used in the probability distribution function. It has been shown that the PDL achieves the shortest codelength for data relative to the generating model class. The PDL technique has a structure that is suitable for on-line tracking of time-varying systems.
 

Further Reading:

[1] S. Valaee, “An Information Theoretic Transmitter Enumerator for DS-CDMA Wireless Networks”, in the proceedings of IEEE Globecom 2004 - Wireless Communications, Networks, and Systems, Dec 2004. [pdf]