Iterative Detection and Decoding for Cell-Free Massive Multiuser MIMO with LDPC Codes Tonny Ssettumba Roberto B. Di Renna Lukas T. N. Landau and Rodrigo C. de Lamare

2025-05-03 0 0 467.73KB 8 页 10玖币

Iterative Detection and Decoding for Cell-Free

Massive Multiuser MIMO with LDPC Codes

Tonny Ssettumba, Roberto B. Di Renna, Lukas T. N. Landau and Rodrigo C. de Lamare

Abstract

This paper proposes an iterative detection and decoding (IDD) scheme for a cell free massive multiple input multiple output

(CF-mMIMO) system. Users send coded data to the access points (APs), which is jointly detected at central processing unit (CPU).

The symbols are exchanged iteratively in the form of log likelihood ratios (LLRs) between the detector and the low-density parity

check codes (LPDC) decoder, increasing the coded system’s performance. We propose a list-based multi-feedback diversity with

successive interference cancellation (MF-SIC) to improve the performance of the CF-mMIMO. Furthermore, the proposed detector

is compared with the parallel interference cancellation (PIC) and MF-PIC schemes. Finally, the bit error rate (BER) performance

of CF-mMIMO is compared with the co-located mMIMO (Col-mMIMO).

Keywords

Iterative detection and decoding, MMSE-SIC, MF-SIC, Cell-free Massive MIMO, co-located MIMO.

I. INTRODUCTION

Massive multiple-input multiple-output (mMIMO) is a multi-user communications solution that involves a large number of

antennas to provide service to multiple users in centralized [1], [2] and distributed [3] settings. The large antenna array yields

high throughput and also improves the propagation conditions because of the channel hardening property [4], [5], [7]. mMIMO

leverages on the assumption that users have a single-antenna whereby there are signiﬁcantly more antennas at the Base Station

(BS) than the number of served users [7]. The signals transmitted by the users to the receiver overlap, resulting in multi-user

interference at the receiver. These interfering signals cannot be easily demodulated at the receiver, which call for techniques

that can separate such signals [8]. The major aim is to reduce the Euclidean distance between the transmitted signal and the

estimate of the received signal [9]. Several works have studied optimal detection techniques to improve the performance of

mMIMO. However, the complexity of such schemes increases with the modulation order and the number of antennas [9].

Furthermore, sub-optimal detectors that use iterative detection and decoding (IDD) that utilise non-linear techniques such as

minimum mean square error with successive interference cancellation (MMSE-SIC) and parallel interference cancellation (PIC)

have been studied in different works [4], [6], [9], [10]. These schemes have been found to achieve close to optimal bit error

rate (BER) performance.

The key aspect in IDD based strategies is the exchange of soft information between the soft detector and the decoder in

terms of likelihood ratios (LLRs). After some iterations, the decoder sends the interleaved posterior probabilities (extrinsic)

information to the soft detector in form of feedback [10], [11]. The use of codes that use message passing such as low-density

parity check codes (LPDC) and turbo codes has been studied in several works [12].

Prior works on IDD that employ channel codes that use message passing such LDPC and turbo codes include the work

in [4], [6], [7], [8], [9], [10], [11]. Such code designs are less complex which simpliﬁes communication system. The use of

list-based detection approaches such as: Multiple-feedback (MF) with SIC (MF-SIC) and multiple-branch-MF processing with

SIC (MB-MF-SIC) detection schemes have been applied in MIMO architectures to lower the BER [9], [10]. Such schemes

achieve close to optimal performance and also reduce the brief error propagation that is prevalent when using SIC based

detection. In [11], the uplink of a CF-mMIMO network has been studied. The access points (APs) are assumed to locally

implement soft MIMO detection and then share the resulting bit LLRs on the front-haul link without exchanges between the

detector and the decoder. The CPU was used to decode the data while the non-linear processing at the APs consisted of the

approximate computation of the posterior density for each received data bit. Moreover, the detection was performed via Partial

Marginalization.

In this work, we present an IDD scheme for CF-mMIMO systems, which unlike the work in [11], employs message passing.

In particular, we propose list-based MF-SIC detectors based on soft interference cancellation for a centralized CF-mMIMO

network. To the best of the authors’ knowledge, no such detector has been presented in the previous works for the CF-mMIMO

architecture. Moreover, the use of message passing strategies can signiﬁcantly reduce the BER. Therefore, the main contributions

of this paper are summarized as follows. First, a list-based soft MF-SIC detector is proposed for the CF-mMIMO architecture.

This proposed approach gives lower BER values at the same computation complexity as the traditional SIC scheme. Secondly,

the proposed detector is compared with other detectors such as the linear MMSE, SIC, PIC and MF-PIC. Thirdly, the impact

Tonny Ssettumba, Roberto B. Di Renna, Lukas T. N. Landau and Rodrigo C. de Lamare, Center for Telecommunications Studies (CETUC), Pontiﬁcal

Catholic University of Rio de Janeiro (PUC-Rio), E-mail: tssettumba@aluno.puc-rio.br, {roberto.brauer, lukas.landau, delamare}@cetuc.puc-rio.br

arXiv:2210.12906v1 [cs.IT] 24 Oct 2022

of increasing the IDD iterations is examined. Finally, the CF-mMIMO architecture is compared with the co-located mMIMO

(Col-mMIMO) system in terms of the BER performance. The CF-mMIMO signiﬁcantly achieves lower BER values than the

Col-mMIMO.

The rest of this paper is organized as follows: Section II presents the system model and the statistical analysis. The proposed

MF-SIC and MF-PIC detectors are presented in III. Section IV discusses the IDD scheme. Simulation results and discussions

are presented in V. Finally, concluding remarks are given in section VI.

Symbol notations: We use lower/upper bold case symbols to represent vectors/matrices, respectively. The Hermitian transpose

operator is denoted by (·)H.

II. PROPOSED SYSTEM MODEL

The proposed low complexity IDD scheme for CF-mMIMO systems is shown in Fig. 1. Particularly, an LDPC-coded CF-

mMIMO system comprising of LAPs, Ksingle antenna user equipments (UEs), a joint detector at the CPU and an LDPC

decoder is considered.

Mod

Enc

AP1

AP2

APL

Joint

Soft

Detector

LDPC

Decoder

CPU

Fig. 1

BLOCK DIAGRAM OF A COMMUNICATION SYSTEM WITH AN IDD SCHEME.

The data are ﬁrst encoded (Enc) by an LDPC encoder having a code rate R. This encoded sequence is then modulated

(Mod) to complex symbols with a complex constellation of 2Mcpossible signal points and average energy Es. The coded data

is then transmitted by KUEs through the channel Gto the APs.

We assume a centralized user-centric CF-mMIMO scenario, where the CPU does soft proceesing and joint detection on the

received signal vectors from the APs. Then the CPU sends these soft outputs LEin the form of LLRs to the LDPC decoder.

The decoder adopts an iterative strategy by sending extrinsic information LUto the CPU which improves the performance of

the entire network. Additionally, the performance of the proposed detector is examined for the case with no iterations and the

case with iterations. The channel coefﬁcients between the l-th AP and the k-th UE are given by [13]

gk,l =pβk,lhk,l,(1)

where βk,l is the large-scale (LS) fading coefﬁcients as a result of path loss (PL) and shadowing. The small scale fading

coefﬁcients are given by hk,l, that are independent and identically distributed (i.i.d.) Gaussian random variables with variance

E{h∗

k,lhk,l}= 1.

The LS fading coefﬁcient are assumed to be deterministic and can be obtained using the three-slope PL model [13]. More

precisely, the PL exponent is 3.5if the distance dkl between the k-th UE and l-th AP is greater than d1, equals 2if d1≥dkl > d0,

and equals 0if dkl ≤d0, for some d0and d1. For dkl > d1, the Hata-COST231 propagation model is applied. The PL P Lkl

in dBs between the k-th UE and l-th AP can be given such as

PLkl =









−Λ−35 log(dkl), dkl > d1

−Λ−15 log(d1)−20 log(dkl), d0<dkl ≤d1

−Λ−15 log(d1)−20 log(d0),if dkl ≤d0

.(2)

The parameter Λis given by

Λ,46.3 + 33.9 log10(f)−13.82 log10(hAP)(3)

−(1.1 log10(f)−0.7)hu+ (1.56 log10(f)−0.8),

where fis the carrier frequency (in MHz), huand hAP are the antenna heights of the UE and AP, respectively. The LS

coefﬁcient βkl models the PL and shadow fading that is given by

βlk =P Lkl ×10σsh ζlk .(4)

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IterativeDetectionandDecodingforCell-FreeMassiveMultiuserMIMOwithLDPCCodesTonnySsettumba,RobertoB.DiRenna,LukasT.N.LandauandRodrigoC.deLamareAbstractThispaperproposesaniterativedetectionanddecoding(IDD)schemeforacellfreemassivemultipleinputmultipleoutput(CF-mMIMO)system.Userssendcodeddatatotheaccess...

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Iterative Detection and Decoding for Cell-Free Massive Multiuser MIMO with LDPC Codes Tonny Ssettumba Roberto B. Di Renna Lukas T. N. Landau and Rodrigo C. de Lamare

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