BER PERFORMANCE OF JOINT POLAR CODED SIGNAL AND MIMO USING MILLIMETER WAVE

Abstract– There have been active researches worldwide for evolving the next-generation networks such as 5G. The 5G network is predicted to ensure considerable mobile data traffic having large number of wireless connections. This is combined with high energy-efficiency and Quality of Service (QoS). For these reasons, 5G should be exploited the prospect of new developments, including multiple-input multiple-output (MIMO) technology and using higher frequencies such as the millimeter-wave (mmWave) frequency band. Error correction techniques are commonly utilized to reduce transmission error and enhance QoS. In the present paper, polar codes with successive cancellation list (SCL) decoding is used in conjunction with mmWave and MIMO system in order to gain the advantages of these techniques together. The mentioned combined techniques are simulated to show their performances over different wireless channel models mainly: an Additive White Gaussian Noise (AWGN) channel, flat fading channel, and mmWave indoor fading channel models. The results of the simulation tests showed that combination of polar code with MIMO system improves the Bit Error Rate (BER) performance by at least 6 dB at high SNR compared to the case where no polar code being used


I. INTRODUCTION
Millimeter wave (mmWave) and Multiple Input Multiple Output (MIMO) are considered as promising solutions to meet the huge increase in data traffic for 5G system predicted in the near future. In addition to providing larger bandwidth as compared to the 4G systems, antenna arrays can be packed into a smaller size due to the use of mmWave frequencies.
Thus, the spectral efficiency can be improved considerably as large MIMO elements compensate for the high path loss experienced by high frequencies [1].The higher spectral efficiency of MIMO is achieved when separate signal paths are provided by each pair of transmitting and receiving antennas. This increases the diversity in the wireless communication system [2,3].
As the new systems started adopting mmWave spectrum, carrier frequencies having values of 28 GHz, 38 GHz, and 73 GHz or more are apparently become available for future wireless systems [4]. General introduction to mmWave systems and its integrated antennas for 60 GHz system are already presented [5,6]. References [7,8] also presented measurements for path loss and wideband propagation for mmWave frequencies using highly directional horn antennas. Their findings are: mmWave transmission causing more signal loss with path loss proportional to the square of the frequency, while demonstrating rich multipath scattering when considering narrow angles. Theoretical studies of the spectral efficiency and outage probability analysis of mmWave transmissions are covered in references [9][10][11]. At higher frequencies, rain, foliage and atmospheric absorption are seriously in mmWave mobile communication, with rain and Oxygen causing attenuation around 10 to 20 dB/km. Such issues can be dealt with by considering reduced cell sizes of about 50 to 200 m, especially at 28 GHz and 38 GHz, to give an attenuation of about 1.4 dB over 200m cell [12]. The main challenge presented in 5G system, apart from the limited frequency band, is the degradation in Bit Error Rate (BER) performance. So, searching for new techniques to improve BER performance for new generation networks is desirable by using powerful error correction codes such as polar code [13]. Polar code is proposed for 60 GHz systems where promising BER performance is achieved in the presence of either linear power amplifier (PA) or nonlinear PA compared with Low-Density Parity Check (LDPC) coding scheme [13]. Detection and decoding algorithm is proposed for polar coded signal when used with massive MIMO using graphs of MIMO [14]. The proposed scheme and architecture achieved the advantages of both MIMO and polar codes.
A scheme of adaptive polar coded signal is proposed for indoor mmWave propagation which affected by the blockage with the capacity of the underlying channel is achieved [15]. The simulation results showed that the proposed adaptive transmission scheme has better error performance compared to the traditional fixed-rate transmission scheme. The authors in reference [16] studied the polar encoding process for standard 5G wireless communication systems. The study covered the polar encoding and decoding implementations which occurred to be within the feasible complexity and work within required latency in addition to its rate flexibility.
In the above mentioned references, the transmission of polar code signal using mmWave band is based on single input single output (SISO), so the present work deals with the use of MIMO technology instead of SISO. The aim here is to evaluate the performance of the transmission system when the combination of polar code signal being transmitted in mmWave band with MIMO technology to improve the BER performance of the system.
The remaining parts of the paper are organized as follows: Section-II presents the system model where polar code used is described followed by the modulation, the MIMO system, and the channel models. The results of the simulation tests and their analysis are presented in Section-III. Finally, the main concluding remarks are given in Section-V. Figure 3 shows the transmission system model. The data source produces binary independent and equal probable bits.

II. SYSTEM MODEL
The encoder is forward error correction that add check bits to assist in correcting possible errors introduced by the channel.
The modulator maps the coded bits into modulated symbols. This is followed by the MIMO encoder with its output linked to the transmission channel. Additive white Gaussian noise (AWGN) is added at the channel output. The details of the system components just mentioned are given next.

A. Polar Coding
The forward error correction code adopted in the model is the polar code which is considered as candidate for 5G system [17]. Polar code is a list of codes that utilizing the channel polarization by using the fact that channel can be polarized into reliable and unreliable channels. This code can achieve the capacity limit for infinite block lengths. Polar code has a recursive structure with low complexity making this code desirable for hardware implementation [18]. Successive Cancellation List  [14]. To enhance the error correction performance, polar codes are concatenated with a high rate Cyclic Redundancy Check (CRC) code [17]. A polar code with (N, K) of (256,128) resulting in coding rate of Âoe is used in the model with CRC as given in reference [20]. SCL decoding with list size L=8 is used as polar decoder at the receiver side.

B. The Modulator
The modulation considered in the work is Quadrature Phase Shift Keying (QPSK). The symbol rate considered here is 2.5 M Symbols/sec, thus the resultant bit rate is 5 Mbps. The baseband equivalent representation of QPSK is used in the simulation tests.

C. The MIMO System Model
In MIMO transmission system, the signal is fed to the Nt antennas at the transmitter and received by Nr antennas at the receiver. Considering the Nt-component transmitted vector X and the Nr-component noise vector N, the received Nr-component vector Y is given by [21]; Where the noise components zero mean AWGN samples with fixed variance, and H is the fading channel matrix with dimensionality of (N r x N t ). Considering Alamouti Space Time Block Coded (STBC) for 2x2 MIMO, the transmitted signal is by [3,21]; and the channel matrix H is; The estimate of the transmitted symbol in the absence of noise is given by [21]; Where is transpose conjugate of H H . Similarly, one may apply the above analysis to find the demodulated signals at the receiver for 4x4 MIMO or higher MIMO dimensionality. The MIMO antenna elements spacing is taken to beˇ/2 witȟ is determined by the carrier frequency fc=28 GHz.

D. The MIMO System Model
Three types of wireless transmission channel models are considered in the work. These are:

2-Flat Fading Channel Model:
The channel is known as flat fading if the bandwidth of the transmitted signal is smaller than the coherence bandwidth of the channel. The effect of flat fading channel can be seen as a decrease in the signal-to-noise power ratio (SNR) [22]. In flat fading channel model, the received sample is given by: Where α is a complex quantity represents the signal path gain. This is only single path from Saleh Valenzuela (S V) model that is modeled as [23]; where α 1 is the complex gain of the lth path,α T and α R are steering vectors at the receiver and transmitter, respectively.θ l and ϕ l are angle of arrival and departure with, θ l [0, 2Π] and ϕ l [0,2Π].

3-Millimeter Wave Channel Model:
Due to the small wavelength of signals at mmWave frequency bands, MIMO dimensionality is used in order to get the strongest received power. There is limited spatial selectivity or scattering characteristic in indoor scenarios with mmWave channel caused by high path loss. To represent the impulse response of a multipath channel, a tapped delay line (TDL) model is used [4,12,24]; where C i (t) are channel coefficients (average path gain) which is varied with time t, and T P is the number transmission paths. An indoor channel model is considered here with three paths. Other channel parameters used in the work are presented in Table I [21,24].

III. SIMULATION TEST AND RESULTS
The model described in previous section is used to measure the BER performance of the system under different test conditions regarding the MIMO size, channel model, and the use of polar code. Fig. 2 presents BER performance for SISI, 2x2 MIMO, and 4x4 MIMO over AWGN channel. It is clear that 4x4 MIMO system provides superior BER performance as compared to others. Fig. 3 shows the results of polar code with (N,K) of (256,128) resulting in coding rate of (Âoe). The list size for the SCL decoder is of 8. It is clear that the coded results with 4x4 MIMO provided better BER performance as compared to SISO and other 2x2 MIMO cases due to the additional gain provided by the 4x4 MIMO arrangement.

IV. CONCLUSIONS
In this paper, we have introduced an arrangement of polar coded signal with MIMO system operating over a model of mmWave channel. The BER performances of different system arrangements are obtained via simulation tests. The results show that both the MIMO system and the polar code improved bit error rate performance over the channel models considered in the work. These models are AWGN, flat fading, and an indoor multipath fading mmWave channel operating at 30 GHz carrier frequency. Polar coded signal performed better over AWGN channel as compared to other two channel models. The advantages of using MIMO arrangement are enhanced by using the polar code signal. Thus, with the expected higher bandwidth provided by mmWave frequency band and hence higher bit rate, polar coded MIMO system improved the performance by at least 6 dB at BER of 10 −4 for the assumed test conditions and mmWave channel model considered in the work. Thus, it is expected to have further BER performance improvements when using higher dimensionality MIMO system.