A Low-Complexity SISO Multiuser Detector for Iterative Decoding of Asynchronous CDMA Systems With Convolutional Codes
Abstract”
The optimal decoding scheme for asynchronous codedivision multiple-access (CDMA) systems that employ convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. A direct implementation of the optimal SISO multiuser detector, however, has exponential computational complexity in terms of the number of users which is still prohibitive for channels with a medium to large number of users. This paper presents a low-complexity SISO multiuser detector using the decision-feedback scheme, of which tentative hard decisions are made and fed back to the SISO multiuser from the previous decoding output. In the proposed scheme, the log-likelihood ratios (LLR) as well as the tentative hard decisions of code bits are fed back from the SISO decoders. The hard decisions are used to constrain the trellis of the SISO multiuser detector and the LLRs are used to provide a priori information on the code bits. The detector provides good performance/complexity tradeoffs. The computational complexity of the detector can be set to be as low as linear in the number of users. Simulations show that the performance of the low-complexity SISO multiuser detector approaches that of the single-user system for moderate to high signal-to-noise ratios even for a large number of users.

---

Presented By
Mao-Ching Chiu, Associate Member, IEEE

---

I. INTRODUCTION
CONVENTIONAL design of multiuser detector focuses on the uncoded receiver structure [1], i.e., on the demodulation of multiuser signals. In practice, most code-division multiple- access (CDMA) systems employ error control coding and interleaving. When conventional multiuser detectors are employed in coded CDMA systems, the multiuser interference is first resolved using the conventional uncoded receiver, and the channel decoders are then applied independently. In this case, soft decisions or hard decisions on the coded bits of each user are made prior to decoding. This separated receiver design has low complexity, but the performance is poor. The optimal decoding scheme joins the operations of multiuser detection and decoding in a maximum likelihood (ML) sense. The computational complexity of the optimal decoding scheme for convolutional coded CDMA systems was shown to be 2 [2], where is the number of users and is the code constraint length. Owing to the high computational complexity, it is not practical to decode the CDMA channel code using the full-complexity decoding technique. This motivates the study of a number of low-complexity suboptimal decoders [3]“[12]. A synchronous (respectively, asynchronous) CDMA channel could be viewed as a block code [10] (respectively, convolutional code [5]). Therefore, an iterative decoding scheme that exchanges soft information between the multiuser detector and the channel decoders can be employed. This technique has been successfully applied to many detection/decoding problems such as the parallel concatenated code (turbo code), serial concatenated code, equalization, and coded modulation. The results [3]“[7] show that, with the iterative decoding scheme, the performance of the coded multiuser system approaches that of the single-user system for moderate to high signal-to-noise ratio (SNR). The computational complexity of these methods, however, is 2 2 per bit per iteration, which is still prohibitive for channels with a medium to large number of users. Iterative decoding schemes for convolutional or turbo coded CDMA systems were proposed in [3]“[12]. The main difference in the structure of those schemes is the type of single-input single-output (SISO) multiuser detector used. In [3] and [4], a full-complexity SISO multiuser detector was proposed for convolutional coded synchronous CDMA systems, resulting in a computational complexity of for the multiuser detector. The work was then extended to coded asynchronous CDMA systems [5]“[7], where forward and backward recursions, similar to those of the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm [13], were proposed for the SISO multiuser detector. In [9], a step-wise difference calculation was presented to determine all the 2 possible likelihood values for synchronous CDMA systems. In addition, a reduced-complexity multiuser detector was proposed to keep a variable number of likelihood values at each step as determined by comparing likelihood values with a threshold. The max-log-map algorithm [14] is then used to obtain the log-likelihood ratio (LLR) of each coded bit. Another type of iterative decoding involves the soft interference cancellation [10]“[12]. In these schemes, soft estimates of code bits from SISO decoders are cancelled from the received signal. The signal after cancellation is then used to calculate the LLR of the desired code bit. The LLRs of code bits are then fed to the SISO channel decoders for the next iteration of decoding.