On the polar code for the 60-GHz millimeter-wave systems

Wei et al. EURASIP Journal on Wireless Communications and Networking On the polar code for the 60-GHz millimeter-wave systems Zhuangkun Wei 0 Bin Li 0 Chenglin Zhao 0 0 School of Information and Communication Engineering (SICE), Beijing University of Posts and Telecommunications (BUPT) , Beijing 100876 , China Given the high operating frequency band and high emission power, 60-GHz millimeter radars or communications will suffer seriously from realistic hardware impairments. Among this, a nonlinear power amplifier (PA) will significantly degrade its transmission performance. In this investigation, a polar code scheme originally developed by Arikan is suggested to enhance the transmission performance of 60-GHz millimeter communications. Considering the realistic difficulties remained in calculating the Bhattacharyya parameters and likelihood ratios, unfortunately, the classical polar coding scheme only limited to a 2 2 matrix 11 10 ; which may lose its effect when flexibly applying other l l matrix instead. To deal with this major challenge in flexibly applying polar code, polarization feature, a method to seek out a matrix on which can be based, to construct polar code schemes, will be demonstrated mathematically. That is, any specified not upper triangular matrix can be used to generate a generalized polar code scheme. Secondly, two efficient recursive algorithms, i.e., recursive Z algorithm and recursive likelihood ratio algorithm, are innovatively proposed, in order to design such a generalized polar code scheme after an l l matrix with polarization feature is specified. Then, the process of constructing a new polar code scheme, based on a 3 3 matrix, is presented to test the effectiveness of the recursive Z algorithm and the recursive likelihood ratio algorithm. Experimental simulations that show a significant promotion on bit error ratio (BER) of that new polar code scheme, and illustrate a similar performance of BER with Arikan's original scheme, verify a successful process of flexibly constructing a generalized polar code scheme, on which a more sophisticated scheme based on other l l matrix can be rested. It is further demonstrated that polar coding schemes can surpass the popular low-density parity-check (LDPC) code, especially when dealing with nonlinear distortions in 60-GHz communication system, which hence provides a greater promise for practical use. 60-GHz millimeter communication; Nonlinearity; Polar code; LDPC 1 Introduction Compared with the traditional radars, a 60-GHz millimeter-wave (mm-Wave) radar is promising to more adverse environmental conditions, e.g., fog, rain, and snow, which may recognize the target more accurately [1,2]. The earlier research of 60-GHz systems is mainly focused on some military applications, e.g., the frequency-modulated continuous wave (FM-CW) radars and crash-avoidance radars [3]. With the potential of providing high data rate of Gbps, 60-GHz mm-Wave communications have also drawn the world-wide attentions, which have also been considered as not only a promising candidate for the emerging fifth-generation (5G) communications but also an innovative idea for radar and sonar systems [3]. A major advantage of 60-GHz communications over other techniques is the enormous vacant bandwidth available at this mm-Wave band. For instance, the USA has assigned 57- to 64- [4] GHz for 60-GHz communications. Further adopting a large effective isotropic radiated power (EIRP), the achieved transmission rate may easily surpass IEEE 802.11n or UWB [5]. In the current wireless personal area networks standard, e.g., IEEE 802.11ad and 802.15.3c, the single-carrier modulations have also been recommended as a physical layer (PHY) solution due to its flexibility and implementation simplicity. As a double-edge sword, both the 60-GHz radars and commercial communications, however, also encounters some challenges from practical hardware impairments. Due to its high operating frequencies and high emission power, 60-GHz millimeter communications may suffer seriously from nonlinear power amplifier (PA) [5,6], which will significantly degrade its transmission performance. It is well known that the coding approach may reduce the bit error ratio (BER) even in the presence of nonlinear distortions, which can be suggested as a feasible approach to combat the performance degradation aroused by nonlinear PA. Since the 60-GHz communications are mainly oriented toward high-speed transmissions, the date rate is very huge and the frame length is therefore extremely long. This may, in practice, facilitate the designing of coding schemes, by concentrating on improving the transmission performance. For example, in the IEEE 802.11ad standard draft, lowdensity parity-check (LDPC) with a length of 672 bits can be specified in the encoding method [6]. Unfortunately, with the nonlinear PA, it is shown that even such a long LDPC code has been applied, the BER performance seems still to be less attractive to practical use (especially for the high-order modulations). In this paper, we suggest a promising coding scheme to further promote the BER performance of 60-GHz communication with nonlinear PA. Firstly, an original construction scheme for polar code is applied to a 60GHz system, which however has been constrained only to the 2 2 matrix: F = 11 10 . Secondly, after mathematically analyzing the polarization feature of any l l matrix, two algorithms are proposed to calculate the Bhattacharyya parameters and likelihood ratios, respectively, the former of which are the most vital components for constructing a generalized polar code scheme after an l l matrix with polarization feature is specified, while the latter of which are the necessary preparation for a mature decoding method. Therefore, generalized polar code schemes can be created after given a specified l l matrix with polarization feature. In order to testify the validity of two algorithms, as well as to testify the effectiveness of polar code schemes when combatting with nonlinear distortion in a 60-GHz system, a new polar code scheme based on an example 3 3 matrix is proposed. Experimental simulations verify firstly the two algorithms for constructing generalized polar code schemes and decoding schemes, secondly the effectiveness of our new polar code scheme, which will significantly promote the transmission performance of 60-GHz communications, especially in the presence of nonlinear distortions aroused by the radio frequency PA. It is also demonstrated that, compared with the popular LDPC code, the two polar code schemes can acquire more competitive BER performance, which hence provides a greater promise to practical use. The rest of this investigation is listed as follows. Section 2 described the system model and successive cancellation (SC) modulation schemes on 60-GHz millimeter-wave communications. Then, in Section 3, the basic idea of polar code is introduced, based on which, polarization (...truncated)