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An Iterative Multiuser Detector for Overloaded LDPC Coded CDMA Systems

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Abstract

Maximum number of users in a Code Division Multiple Access (CDMA) system, disregarding the type of used signature sequences, is equal to the processing gain; but in overloaded CDMA systems, it is tried to use some special methods of applying signature sequences so that the number of users exceeds the processing gain of the system. This growth in capacity is gain at the cost of decrease in performance of the conventional systems; and usually it is tried to use channel coding methods or multi-user detectors to compensate this decrease. Because of advantages of using coding methods joined with multiuser detectors in achieving better performance and also because of some benefits of using (Low Density Parity Check) LDPC method in comparison with similar capacity achieving coding methods, in this article, an iterative multi-user detector for an overloaded LDPC Coded CDMA system is proposed. This receiver consists of a combination of matched filters in the first stage and a linear (Minimum Mean Square Error) MMSE detector and an Interference Cancellation (IC) scheme in the successive stages. In the suggested method, a bank of LDPC decoders gives the soft information to the IC blocks, which help for the better interference cancellation. Comparing the performance of the proposed system with that of Turbo coded system shows that the proposed system, in addition to advantages of using LDPC codes instead of Turbo codes, has better bit error rate performance.

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Abbreviations

PG:

Processing gain

N :

Number of users

G :

Generator matrix

H :

Parity check matrix

x :

Information matrix

c :

Code vector

r(t):

Received signal

T b :

Bit Period

A k :

Received amplitude of kth user

C k (i):

Transmitted bit by kth user in ith bit period

p(t):

Rectangular pulse with power 1 and period T b

S k (t):

Spreading sequence with unit power for the kth user

n(t):

Additive white Gaussian noise

σ 2 :

Double sided spectrum density of white Gaussian noise

Y k :

Output of the kth matched filter

ρ jk :

Normalized correlation factor between the ith and jth users’ signature sequences

n k :

Gaussian zero mean random variable with variance of σ 2

L ap :

A-priori log-likelihood ratio

\({\tilde {Y}_k (i)}\) :

Soft output of IC module

\({\hat{{c}}_j^{(m)}}\) :

Estimation of c j in the mth iteration

\({{\bf L}_{{\rm ex}}^{(m-1)}}\) :

Extrinsic information

\({z_k^{(m)}}\) :

kth signal after the mth iteration of IC

\({\tilde {{\bf n}}_k }\) :

Gaussian zero mean random variable

A :

Diagonal matrix of received amplitudes

R :

Cross correlation matrix

T :

Equals to the product M*R

\({\hat{{\bf b}}}\) :

Output of detector

M :

MMSE filter

SNR:

Signal to noise ratio

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Authors and Affiliations

  1. Electrical and Computer Engineering Department, Tarbiat Modares University, Tehran, Iran

    Paeiz Azmi & Tahereh Shojaee Zand

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  1. Paeiz Azmi
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  2. Tahereh Shojaee Zand
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Correspondence to Paeiz Azmi.

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Azmi, P., Shojaee Zand, T. An Iterative Multiuser Detector for Overloaded LDPC Coded CDMA Systems. Wireless Pers Commun 66, 41–56 (2012). https://doi.org/10.1007/s11277-011-0324-5

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