Asymptotic and Finite User PER Analysis of Successive Interference Cancellation for DS-CDMA

Abstract

Abstract-An expression is derived for the average Packet Error Rate (PER) of a Successive Interference Canceller (SIC) for DS-CDMA when the number of users asymptotically tends to infinity. The asymptotic probability density function of the interference power is governed by a Fokker-Planck differential equation with drift and (asymptotically vanishing) diffusion depending on the PER function of the adopted forward errorcorrecting code (FEC). In addition to the asymptotic solution for the PER, a particle-based algorithm is also developed for computing efficiently the PER in the finite user case.Index Terms-Successive interference cancellation, FokkerPlanck equation, packet error rate, CDMA, particle.

Asymptotically Optimum Energy Profile for Successive Interference Cancellation in DS-CDMA under a Power Unbalance Constraint

“…Although the results in [2] are valid for an arbitrary s ( ), we will understand that s ( ) is non-increasing in (ordered users), as is usually assumed when optimizing SIC performance. Then, the power unbalance and average symbol energy parameters mentioned in section I may be defined as ℎ = s (0)/ s (1) and s = ∫ 1 0 s ( )d , respectively.…”

“…In this section, we summarize the basic definitions and results in [2] used for the computation of the asymptotic PER. New results will be presented in section III onwards.…”

“…Then, the power unbalance and average symbol energy parameters mentioned in section I may be defined as ℎ = s (0)/ s (1) and s = ∫ 1 0 s ( )d , respectively. It was shown in [2] that the average PER, ( ), is given by the following expression, where = lim →∞ / is the load factor (ratio of users to spreading factor ) in the long spreading code model [3] and is a generic decorrelation factor accounting for inter-user timing misalignment and/or carrier phase differences,…”

“…The usual error propagation model considers that at each stage, a fraction ( ) of the current user's energy affects users in subsequent stages with ( ) = (imperfect cancellation under successful decoding) or ( ) = 1 (no cancellation under unsuccessful decoding). Thus, it was shown in [2] thatˇ( ) becomes deterministic and constitutes a solution to the following Ordinary Differential Equation (ODE), with boundary constraintˇ(0) = 0,…”

“…With this setting, an exponential energy profile, which leads to a uniform per-user Signal to Noise plus Interference Power Ratio (SNIR) profile, is shown to optimize the average capacity [1]. In constrast, in this work we consider real (implementable) noncapacity-achieving channel encoders characterized by their Packet Error Rate (PER) function versus the per-user symbol energy s to noise plus interference power spectral density ratio t : s / t (SNIR), with t = 0 + i , and we seek to maximize the average spectral efficiency over all users, , using the expression previously derived in [2] for SIC and summarized in section II. Although the average received symbol energy per user s is the usual constraint when optimizing the average capacity over the per-user symbol energy distribution at the SIC input, it does not reflect possible and practical limitations in terms of the dynamic range of users, as upper/lower bounds on the received symbol energy profile (i.e.…”