Saturday, October 25, 2008

Interference Cancellation: II A Conventional Receiver Design Perspective

[ Interference Cancellation. I. A Short Overview of Multiuser Detection ]
[ Interference Cancellation: III. A Signal Subspace Perspective ]
[ Interference Cancellation: IV. A Blind Receiver Design Perspective ]


Interference cancellation provides a promising alternative to the conventional or optimum detectors in multiuser detection. Interference cancellation methods typically require less implementation complexity while practically o ering similar performance. The idea behind interference cancellation is to estimate the multiple access and/or multipath induced interference and then to subtract the interference estimate from the received signal. Hence, compared to other multiuser detection schemes, interference cancellation pays more attention on the estimation of the multiple access interference (MAI). Different schemes for the MAI estimation lead to different interference cancellation schemes. Actually, interference cancellation detector will cancel the interfering signal exactly provided that the decision was correct and channel information is known. Otherwise it will double the contribution of the interferers. The main alternatives for implementation of interference cancellation are parallel hard interference cancellation (PIC) and serial/successive hard interference cancellation (SIC), while many other variants on these basic principles have also been developed. With conventional PIC, all user are simultaneously demodulated and detected in a parallel behave. With conventional SIC, a decision for the symbol of the stronger user is made rst, the interference from this user is subsequently removed in the the next stronger user's receiver before the next user's receiver make its decision and so on.

On this blog, we consider a synchronous DS/CDMA system and review the principles of interference cancellation. several soft interference cancellation schemes, including direct interference cancellation detector, MAME interference cancellation detector and MMSE interference detector, are introduced with di fferent MAI estimation schemes. I show that, besides MAME interefence cancellation, the proposed direct interference cancellation detector has the same performance of the classic decorrelating detector while the MMSE multiuser detection and the MMSE interference cancellation actually are the same detectors.

System Model

Figure 1. Multiuser Detection System Model
We consider a single-cell synchronous DS/CDMA model and assume that there are K active users in the cell, the data { bk[n]: k = 1, 2, ..., K } of these K users are individually spread using the corresponding spreading sequences { ck = [c1k c2k ... cLck]T : k = 1, 2, ..., K; } with the spreading gain Lc and synchronously received from these users through multipath channel and corrupted additive white Gaussian noise (AWGN) with the variance ¾2 n [3]. The channel is a multipath channel with up to P resolvable paths and corrupted by AWGN. The baseband representation of the received signal due to user k is given by

rk(t) =  Σp=1PαpkAk[n]bk[n]ck(t-nT-τp) + nk(t)

where αpk is the gain of the pth path of user k’s signal and bk[n] is the nth bit sent by user k. We assume that the { bk[n] : k = 1, 2, . . . , K } are independent and identically distributed random variables with E{bk[i]} = 0 and E|bk[i]|2 = 1. The parameters {ck(t) : k = 1, 2, . . . , K} denote the normalized spreading signal waveform of K users during the interval [0, T] and {Ak[n] : k = 1, 2, . . . , K} are the signal amplitudes at time t = nT. Without loss of generality, the P propagation delays from the base station to user k are ordered such that 0 ≤ τ1 ≤ τ2 ≤ . . . ≤ τP

At the receiver side, the received signal passes through chip-matched filter (CMF) φ (t) and then RAKE combiner. The combined output r (t) is

r (t) = A1b1c1(t − nT − τ1) ⊗ φ (t − τ1) + mISI (t) + mMAI (t) + n (t)

Figure 2. A typical matrix representation of conventional multiuser detection system model

Interference Cancellation

Figure 3. The block structure of a basic interference cancellation detector.

As in Figure 3, it shows that there are usually two basic stages in interference cancellation realization. At the fi rst stage, the MAI from other users are reconstructed. At the second stage, the MAI is removed from the received signal and the nal decision is made from the rest signal through a matched lter. Thus, the key part in interference cancellation is how to estimate MAI as effciently as possible.

Figure 4. The structure of a direct interference cancellation, an equivalent to multiuser decorrelation detector 
Figure 5. The structure of a linear MAME interference cancellation, an equivalent to multiuser MAME detector 
Figure 7. The structure of a linear MMSE interference cancellation, an equivalent to multiuser MMSE detector 

Wednesday, October 8, 2008

Interference Cancellation: I. A Short Overview Multiuser Detection

[ Interference Cancellation: II. A Conventional Receiver Design Perspective ]
[ Interference Cancellation: III. A Signal Subspace Perspective ]
[ Interference Cancellation: IV. A Blind Receiver Design Perspective ]
[Toward Forward Link Interference Cancellation, CDMA Development Group (CDG) Technology Forum 2006]

CDMA cellular network capacity is known to be interference-limited since the same spectrum is shared by many users and there exists a near-far problem due to multiple access interference (MAI). Multiuser receiver is highly regarded as one of the promising interference management techniques improving spectrum efficiency and achieving high-data rates for wireless multimedia communication. It has been intensively investigated over the last two decades and received much attention for next-generation radio access network [Andrews 05, Wang 05]. Optimum multiuser receivers and conventional multiuser receivers are known to be able to solve the near-far problem at the knowledge of the signature information of all users [Verdu 98]. However this assumption isn’t always consistent with practical situations where the receiver may know only the signatures of the expected signals not interfering signals. Recent research work is mostly devoted to semiblind or blind multiuser receiver design and also signal signature estimation [Verdu 98, Madhow 98, Andrews 05]. It is known that most blind implementation of conventional multiuser receivers achieve the same performance as conventional multiuser receivers providing enough pilots or training signals available [Honig 95, Torlak 97, Wang 98, Zhang 02]. For example, with sufficiently training on receiver, blind minimum mean squared error (MMSE) receiver is known to achieve the performance of conventional MMSE detector [Verdu 98]. If enough signals are available for signal subspace separation or signal signature estimation, subspace-based blind multiuser receivers can achieve the performance of various conventional multiuser detectors too [Wang 98]. As long as interfering signal structure is pretty stable during the signal detection procedure, these blind multiuser receivers can work well with constant performance. They may not function well when the multiuser channel or system load experiences dynamic changes. However, this happens very frequently in reality, especially when the channel coherence time is not large enough. Therefore it is important to design multiuser receiver that requires a limited number of previous signals with better channel tracking capability and possible low implementation complexity. And it is also interesting to understand how the number of employed previous signals affect the performance of blind multiuser receivers and what are the tradeoffs between complexity and performance of blind multiuser receiver design in this case and in general too.

Figure 1. A List of Conventional Multiuser Detection Design Approaches

In the development of advanced multiuser receivers, it is known that a proper received signal model can give a lot of help with multiuser receiver design in addition to the understanding of received signals. There are two most popular multiuser signal models which have extensively been discussed and employed for receiver design and performance analysis. They are the conventional multiuser signal model and the subspace-based multiuser signal model [Verdu 98, Wang 98]. In the conventional signal model, each received symbol is expressed as a linear combination of actual signal signatures with their amplitude and timing [Verdu 98, Honig 95, Zhang 02]. The theory of optimal multiuser receivers and the conventional receivers are well developed with this model [Verdu 98]. Most related blind multiuser receivers are also developed either by explicitly estimating the signal signature [Torlak 97] or by removing interfering signal components using adaptive filtering techniques, e.g., blind receiver design with Wiener [Honig 95] and Kalman filter [Zhang 02] techniques. Though the conventional signal model provides a natural view of received signals, the involved signature waveforms information are unknown in reality and it requires considerable processing to obtain them before detection. To compensate for the weakness of the conventional signal model, the subspace signal model was developed with the statistic signal spectral analysis techniques termed subspace-based signal processing [Wang 98]. Subspace-based signal processing techniques are previously developed for array signal processing since 1970s [Schmidt 86, Hero 98]. In the multiuser subspace signal model, each received signal is taken as a linear combination of signal subspace bases, which are obtained by subspace analysis on the correlation matrices of the received signals. The subspace signal model can also be considered as the result of parametric signal modelling, which provides an in-depth description of the received signals. Though the subspace-based approach does not require explicit estimation of each user’s signature waveform and the adaptivity speed can be improved with some subspace tracking techniques [Yang 95], the signal subspace formation procedure itself is not trivial.

For a better design of multiuser receivers, the evaluation and understanding of multiuser receiver are traditionally based on the link-level parameters like asymptotic multiuser efficiency (AME) and near-far resistance (NFR) in addition to signal-to-interference/noise ratio (SINR) and bit-error rate (BER) [Verdu 98]. These parameters show the capability of a multiuser receiver to reject various interference. Among them, One of the most important measurements is SINR and most other parameters can be derived from it. For example, the AME of a multiuser receiver is the ratio between the actual multiuser receiver output SINR and the corresponding single-user output signal-to-noise (SNR) in high SNR region. The AME shows how steep the slope of a multiuser is when its BER goes to zero in logarithmic scale. The best achievable AME value is 1, which means the receiver works exactly the same way as if there is no interference at all. The worst value is close to 0 when the outputs of a multiuser receiver are completely determined by interference. The NFR of a multiuser receiver is defined by the minimum AME over the received energies of all other users. It shows the receiver’s ability to reject the worst-case interference. However, link level evaluation usually depends on the actual employed receiver structure and the signature waveforms. Recently several large-system measurements are developed to evaluate multiuser receiver’s behaviors in a system with large processing gain and lots of users [Tse 99]. In a large-scale system, one concept termed effective interference describes how the total received interference can actually be taken as a sum of other individual user’s effective interference. Effective interference itself is independent to the particular realization of random signal signatures. Extended from the concept of effective interference, effective bandwidth and user capacity are the terms describing how the system resource, in terms of power and degree of freedom, are assigned to users for achieving their target SINRs. I will show that these parameters can also be derived from asymptotic SINR too. One interesting thing here is these large-system evaluations only depend on the power distribution, system load, target SINR and receiver design, not the actual employed signal signatures for each user. This make it easy for giving some insights of multiuser receiver behaviors in an actual wireless communication environment.

While the conventional signal model provides a foundation for both optimal and conventional multiuser receiver design and the subspace signal model aids understanding of the underlying signal structure, neither is simple enough for developing blind multiuser receivers for high-speed CDMA systems [Andrews 05]. In order to address the near-far problem with minimum prior knowledge and computational complexity, a blind multiuser signal model and blind multiuser receiver design framework are firstly presented here. With this framework, the blind receiver only requires several previously received symbols in addition to its own signal signature(s), amplitude(s) and timing(s). Different to the conventional multiuser model and subspace signal model [Verdu 98, Wang 98], there is no signal signature or signal subspace basis of interfering signals necessary and no signal signature estimation or signal subspace separation procedure required in the proposed detection framework. Based on this model and detection framework, several optimal blind linear multiuser detectors are individually developed and analyzed with maximum likelihood (ML), MMSE and least squares (LS) criteria. In order to further reduce the complexity, some implementation considerations are outlined. In addition, I compared the proposed multiuser receivers with existing ones from several practical implementation prospects. For each of these blind linear multiuser receiver, I not only evaluate its link-level performance but also discuss how it behaves in a large-scale system. It shows that there is an additional noise enhancement in the proposed detection framework due to the limited number of previous knowledge but its computation complexity and detection delay is lower than most existing multiuser receivers. In a large-scale system with large spreading gain and high SINR, the asymptotic performance of the proposed blind multiuser receivers are close to the conventional ones. Due to the limited space, many detailed proofs of my conclusions are omitted in this blog.

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