Complexity adaptive iterative receiver performing TBICM-ID-SSD

Flexible and iterative baseband receivers with advanced channel codes like turbo codes are widely adopted nowadays, ensuring promising error rate performances. Extension of this principle with an additional iterative feedback loop to the demapping function has proven to provide substantial error performance gain at the cost of increased complexity. However, this complexity overhead constitutes commonly an obstacle for its consideration in real implementations. This article illustrates the opposite of what is commonly assumed and proposes a complexity adaptive iterative receiver performing iterative demapping with turbo decoding (TBICM-ID-SSD). Targeting identical error rate, the article shows that for certain system configurations TBICM-ID-SSD presents lower complexity than TBICM-SSD (without iterative demapping). This original result is obtained when considering the equivalent number of iterations through detailed analysis of the corresponding computational and memory access complexity. The analysis is conducted for different parameters in terms of modulation orders and code rates and independently from the architecture for a fair comparison. Considering the proposed adaptive receiver which is able to perform both TBICM-ID-SSD and TBICM-SSD modes, results demonstrate a reduced complexity with TBICM-SSD for high modulation orders. However, for low modulation orders as for QPSK, results show a reduction in arithmetic operations and read access memory up to 45.9% and 47%, respectively for using the TBICM-ID-SSD mode rather than TBICM-SSD performing six turbo decoding iterations over Rayleigh fading channel with erasures. Introduction Advanced wireless communication standards impose the use of modern techniques to improve spectral efficiency and reliability. Among these techniques, bit-interleaved coded modulation (BICM) [1] with different modulation orders and Turbo Codes with various code rates are frequently adopted. The BICM principle currently represents the state-ofthe-art in coded modulations over fading channels. The BICM with iterative demapping (BICM-ID) scheme proposed in [2] is based on BICM with additional soft feedback from the soft-input soft-output (SISO) convolutional decoder to the constellation demapper. In [3], the convolutional code classically used in BICM-ID schemes was replaced by a turbo code. Only a small gain of 0.1 dB was observed. This result makes BICM-ID with turbo-like coding solutions (TBICM-ID) unsatisfactory with respect to the added decoding complexity. *Correspondence: [email protected] 1Institut Mines-Telecom; Telecom Bretagne; UMR CNRS 3192 Lab-STICC Electronics Department, Technopôle Brest Iroise CS 83818, 29238 Brest, France On the other hand, signal space diversity (SSD) technique, which consists of a rotation of the constellation followed by a signal space component interleaving, has been recently proposed [4,5]. It increases the diversity order of a communication system without using extra bandwidth. Combining SSD technique with TBICM-ID at the receiver side has shown excellent error rate performance results particularly in severe channel conditions (erasure, multi-path, real fading models) [6,7]. These results were behind the adoption of this system in DVB-T2 standard (using LDPC channel code). These results will also lead for further adoption discussions in the upcoming standards using turbo codes [6]. The TBICM and TBICM-ID modes applying the SSD technique are denoted by TBICM-SSD and TBICM-ID-SSD. In fact, almost all related works using these techniques have focused only on error rate performance without considering the implementation perspective. This is due mainly to the commonly assumed impact in terms of complexity overhead. In this article, we demonstrate the © 2012 Haddad et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Haddad et al. EURASIP Journal on Advances in Signal Processing 2012, 2012:131 Page 2 of 12 http://asp.eurasipjournals.com/content/2012/1/131 effectiveness of the iterative demapping even in terms of complexity for certain system configurations (modulation orders and code rates). In this context, a novel complexity adaptive iterative receiver, performing either in TBICM-ID-SSD mode or in TBICM-SSD mode, is proposed. This original proposal is based on a thorough analysis of the corresponding computational and memory access complexity. It is worth to note that the article does not provide a comparison in terms of area, as one iterative receiver is considered to perform both modes (TBICM-ID-SSD and TBICM-SSD). The rest of the article is organized as follows. Section Systemmodel and algorithms presents the system model with the associated parameters and gives a brief description of the underlined algorithms for iterative demapping and turbo decoding. Section Complexity evaluation and normalization presents an evaluation of the receiver complexity in terms of number and type of arithmetic operations and memory access. Section Number of iterations analysis for identical complexity analyzes the number of TBCIM-SSD and TBCIM-ID-SSD iterations for identical complexity. Section Complexity analysis for identical performance shows a complexity analysis for identical TBCIM-SSD and TBCIM-ID-SSD error rate performances. Finally, Section Conclusion concludes the article. Systemmodel and algorithms This section describes the system model and the considered parameters of the transmitter, channel, and receiver of Figure 1. In addition, it gives a brief presentation of the underlined algorithms for the iterative demapping and decoding. Systemmodel On the transmitter side, information bits U which are called systematic bits are regrouped into symbols ui consisting of q bits, and encoded with an q-binary turbo encoder. It consists of a parallel concatenation of two identical convolutional codes (PCCC). The output codeword C is then punctured to reach a desired coding rate Rc. We consider in this work the 8-state double binary (q = 2) [8] turbo code adopted in the WiMax standard. In order to gain resilience against error bursts, the resulting sequence is interleaved using an S-random interleaver 2 with S = √N/4. Punctured and interleaved bits denoted by vi are then gray mapped to complex channel symbols sq chosen from a 2M-ary constellation X, where M is the number of bits per modulated symbol. Applying the SSD consists first of the rotation of the mapped symbols sq. The resulting rotated symbols are denoted as sr,q. The performance gain obtained when using a rotated constellation Xr depends on the choice of the rotation angle. The optimum rotation angle depends Figure 1 The systemmodel of the transmitter, channel, and TBICM-ID-SSD receiver. Haddad et al. EURASIP Journal on Advances in Signal Processing 2012, 2012:131 Page 3 of 12 http://asp.eurasipjournals.com/content/2012/1/131 on the chosen modulation and channel type. In this regard, a thorough analysis has been done for the 2ndgeneration terrestrial transmission system developed by the DVB Project (DVB-T2) which adopted the rotated constellation technique. A single rotation angle [7] has been chosen for each constellation size independently of the channel type. These angle values are presented in Table 1 and are adopted in this work. The second step when applying SSD at the transmitter consists of signal space component interleaving. A simple delay is introduced between the transmission of I and Q components. Mapped and shifted symbols s′r,q are then transmitted over a noisy and Rayleigh fast fading channel with or without erasure. The erasure channel model has been used in the case of the DVB-T2 standard to model the destructive interferences caused by the existence of a single-frequency network (SFN). Each received symbol x′r,q is affected by a different fading coefficient, an erasure coefficient, and an additive Gaussian noise. The channel model considered is a frequency nonselective memoryless channel with erasure probability. The received discrete time baseband complex signal can be written as: x′r,q = hq.ρq.s′r,q + nq = h′q.s′r,q + nq (1) where hq is the Rayleigh fast fading coefficient, ρq is the erasure coefficient probability taking value 0 with a probability Pρ and value 1 with a probability of 1 − Pρ . nq is a complex white Gaussian noise with spectral density N0/2 in each component axes, and h′q is the channel attenuation. Max-log-map demapping algorithm At the receiver side, the complex received symbols x′r,q have their Q-components re-shifted resulting in xr,q. An extrinsic log-likelihood ratio Lext,Dem(ck,q/xr,q) is calculated for each bit ck,q corresponding to the kth bit of the received rotated and modulated symbol xr,q. After deinterleaving, de-puncturing and turbo decoding, extrinsic information from the turbo decoder Lext,Dec(ck,q) is passed through the interleaver, punctured and fed back as a priori information Lapr,Dem(ck,q) to the demapper in a turbo demapping scheme. The extrinsic information Table 1 Rotation angle values in DVB-T2, adopted in this work Modulation Rotation angle (degrees)