Power control for successive interference cancellation with imperfect cancellation

This paper proposes and analyzes an iterative power control scheme for use with successive interference cancellation (SIC) in the presence of cancellation errors. In [1], SIC is shown to increase the capacity of cellular CDMA systems significantly, even if the signal cancellation is imperfect due to estimation errors. However, an important complication of SIC relative to conventional CDMA receivers is that a specific non-uniform distribution of powers must be assigned to the users in order for the system to function robustly [1], [2]. This paper proposes a simple up/down distributed iterative power control scheme for DS-CDMA systems employing SIC. We analyze its feasibility region and prove that it converges to close to the optimum solution even in the presence of estimation errors. The total received power is shown to be a reliable metric for admission control. This analysis considers both multi-rate CDMA where each user has a different target Signalto-Interference-and-Noise ratio (SINR), and asynchronous power control where user power updates occur asynchronously. I. INTRODUCTION Conventional Direct Sequence CDMA receivers treat all the other users as uncorrelated noise and use a rake receiver (also referred to as a matched-filter receiver) to suppress their interference. Analysis of multi-user detection [3] has shown that receivers employing multi-user detection techniques can provide significantly higher capacity compared to conventional implementations. However, receivers employing multi-user detection have received little support in industry primarily because multi-user receiver designs have not been able to match the low complexity and high robustness of conventional matched filter receivers. Successive interference cancellation (SIC) shows promise as a practical approach towards multi-user detection. Its complexity is linear in the number of users, it does not require dimensional separation of users using short signature sequences and can work equally well in any asynchronous environment. However, SIC has its own set of challenges that need to be overcome. Most importantly, the received power allocation between different users needs to be set properly. For a conventional matched-filter receiver, an equal SINR requirement for all the users corresponds to the familiar requirement that all users be received with the same power. For SIC, the situation is a bit more complicated, as users are decoded successively and have a large portion of their interference subtracted from the composite signal prior to the decoding of the next user. It is thus necessary for earlier users to have higher received powers, and later users to have lower received powers, in order to satisfy the equal SINR requirement. In [2], Warrier and Madhow This work is supported in part by National Semiconductors and Samsung proposed a power allocation scheme for successive interference cancellation on the assumption of perfect interference cancellation. In [1], Andrews and Meng extended the work of Warrier and Madhow and proposed a power allocation scheme for SIC in the presence of estimation error. Although [2] and [1] developed power control schemes that addressed the power inequality required for SIC, in an ideal and imperfect cancellation environment, respectively, there are still several important unresolved issues. Both assumed a static channel in which the receiver measured all the received signals and instantaneously adjusted the transmit powers of all the transmitters. A wireless channel is quite dynamic and changes fairly rapidly as users enter, move within and leave the system. It is impractical for the base station to update all the user powers constantly as the optimal power allocation varies. This paper proposes a simple distributed iterative power control scheme for a receiver employing SIC in the presence of estimation errors. Practical implementation issues suggest consideration of low feedback rates similar to those proposed in commercial CDMA systems (IS95, CDMA2000 and WCDMA). Section III determines its feasibility region for multi-rate CDMA (where each user has a different target SINR) and under certain assumptions calculates the system capacity and optimal power allocation as a function of target SINR and estimation error. Section IV proves that if the number of users is less than the system capacity, the iterative algorithm converges monotonically to a point within Æ of the optimal solution where Æ is the power control stepsize. The convergence proof is valid for both synchronous and asynchronous power control. Finally, in order to ensure the stability of the iterative power control scheme, Section V proposes the use of the total received power as a reliable metric for admission control. II. THE SYSTEM MODEL The system considered in this paper is a fully asynchronous system in which after despreading with the desired signature sequence, other users’ signals are modeled as pseudorandom Bernoulli f-1,+1g sequences. Only user powers are considered in the analysis, and actual transmitted bits and other subtleties affecting power control are ignored. Most of the necessary analysis and intuition is gained from the simplified power model. With this model, the received interference and noise power vector is expressed as: i(p(n)) = Fp(n) + n0 (1) 356 0-7803-7400-2/02/$17.00 © 2002 IEEE where p(n) 2 R is the received power vector for theK users in the system at the n time instant. i(p(n)) 2 R is the corresponding received interference and noise power vector and n0 2 R K is the vector of receiver noise and other cell interference power. F is a non-negative matrix that accounts for interference from other users in the same cell. Each vector is K dimensional whereK is the number of active users in the system. Notationally, vectors are represented as lower-case boldfaced characters, such as p, and matrices are represented as uppercase boldface characters, such as F. The objective of the power control algorithm is to minimize transmit power for each user under the constraint that each user’s SINR ( ̂k) is larger than the target SINR ( k). The SINR for the k user is calculated as ̂k = pk(n) ik(p(n)) ; (2) where pk(n) is the received power for the k th user at the n time instant and ik(p(n)) is the corresponding interference and noise power for the k user at the n time instant. III. FEASIBLE SOLUTION The received power vector, p, is considered feasible if ̂k k for received powers as specified through p. i.e.