Channel Capacity of High Altitude Platform Systems: A Case Study

Research and Development on Information and Communication Technology Channel Capacity of High Altitude Platform Systems: A Case Study Nguyen Thu Hien, Vu Van San and Nguyen Viet Hung Posts and Telecommunications Institute of Technology, Vietnam E-mail: hiennt@ptit.edu.vn, vanvv@ptit.edu.vn, hungnv@ptit.edu.vn Correspondence: Nguyen Thu Hien Communication: received 1 August 2017, revised 22 September 2017, accepted 25 September 2017 Abstract: This paper presents a model for Multiple-Input Multiple-Output (MIMO) Land High Altitude Platform chan- nels and analytical evaluation of Discrete-input Continuous- output Memoryless Channel capacity for High Altitude Plat- form (HAP)–MIMO systems, where practical transmission environments are considered. Furthermore, for HAP– Single- Input Single-Output (SISO) systems, we propose an adaptive transmission mechanism relying on the transmit power char- acterized by value at the transmitter side. Achievable channel capacity bounds are established for both idealized and real- istic adaptive coding schemes with well-adopted modulation types, namely Phase Shift Keying and Quadrature Amplitude Modulation. Keywords: High altitude platform, adaptive coded modulation, M-ary phase shift keying, M-ary quadrature amplitude modula- tion, channel capacity. I. INTRODUCTION High Altitude Platform (HAP) broadband communica- tion networks have been increasingly playing an impor- tant role in supporting broadband wireless communication systems, namely fourth generation Long Term Evolution (4G-LTE) and fifth generation (5G) networks [1]. HAPs are communication facilities situated at an altitude of 17 to 30 km and at a particular point relative to the Earth [2]. These platforms are mostly solar-powered, unmanned and remotely operated. They have the capability of carrying diverse relay payload supporting multi-purpose communi- cations. In addition, they could be in the form of full base station or, in some cases, a simple transponder, which is similar to the configuration used in satellite communication systems [2]. HAPs in a fully deployed configuration are capable of providing services and applications ranging from broadband wireless access, navigation and positioning sys- tems, remote sensing and weather observation/monitoring systems, mobile telephony as well as digital television [3]. Due to low-cost implementation, HAPs are expected to become a popular solution for the wireless communications infrastructure [4]. In 2014, two large companies, Google and Facebook, announced their investments in HAP related projects, aiming to provide internet access in the regions where communications infrastructures based on terrestrial or satellite transmissions are not available [5]. Multiple- Input Multiple-Output (MIMO) transmission promises a significant increase in the system capacity and availabil- ity of communication links in a multipath propagation environment. It is an extension of diversity principles often applied in wireless links to improve link reliability. Combining the transmit and receive diversity results in a new concept, which not only increases the link reli- ability but also offers a potential increase for the radio link capacity. The challenge nowadays is to investigate the application of MIMO techniques to the Land High Altitude Platform (LHAP) communication. Some models using multiple HAP constellations have shown that capacity can be significantly increased by using highly directional user antennas to spatially discriminate between HAPs in different parts of sky [6]. The single links in HAP systems over wireless channels typically experiences the fading and other time varying propagation losses. In such channels, adaptive transmis- sion schemes may be employed for achieving the highest throughput possible [7]. The main idea is to adapt trans- mission parameters of modulation schemes and of error- control codes, in accordance to variations of the transmis- sion channel. Adaptation strategies in [8–10] assumed that perfect channel-state information (CSI) is readily available at the transmitter or at the receiver. Other adaptive schemes considered the employment of pilot or training symbols, in order to estimate the channel state information [11]. In contrast, more practical adaptation schemes were proposed in [12] and [7], where statistics derived from the demodu- lator and decoder at the receiver may be used for providing inputs to the adaptive mechanisms. These schemes are capable of supporting nearly optimal performance, when 52 Vol. E–3, No. 14, Sep. 2017 dispensing the requirement of full-duplex transmission or the use of pilot symbols. As a reflection of these trends, different aspects of the channel capacity of HAP based systems were analysed in [13], where the Continuous-Input Continuous-Output Memoryless Channel (CCMC) capacity of HAP based systems were investigated for the additive white Gaussian noise (AWGN) channel in different path loss scenarios. As compared to the above-mentioned studies and ex- tensive research in [14] that focuses on channel capacity of HAP-Single-Input Single-Output (SISO) systems, the original contributions of this paper are as follows. First, we first clarify a framework of the HAP based systems, where we focus on characterizing the fading channel model, where the effects of both fast fading and slow fading are taken into consideration along with different pathloss scenarios. Second, we compute the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity for HAP-MIMO for benchmarking the design of HAP based systems em- ploying specific coherent modulation schemes. Third, we present an analytical evaluation of channel capacity bounds for HAP-SISO links invoking adaptive coded modulation schemes in realistic channel conditions and establishing achievable channel capacity bounds for both idealized and realistic adaptive coding schemes associated with both pop- ular modulation types, namely Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM). We also propose the adaptive mechanism relying on the transmit power ratio transmitted from the transmitter to the noise power encountered at the receiver. The rest of the paper is organized as follows. In Sec- tion II, a review of the HAP propagation channel model is provided. In Section III, the channel capacity associ- ated with the HAP-MIMO employing different modulation schemes is described. In Section IV, the adaptive channel capacity for the HAP-SISO links is derived for the corre- sponding adaptive coded modulation mechanisms. Finally, our conclusions are given in Section V. II. HAP PROPAGATION CHANNEL MODEL From the system architecture point of view, HAP com- munication system can be used in different configurations. In the simplest configuration HAPs are used as standalone platforms, providing broadband wireless access to terminals located in their coverage area. In the case of multi-platform constellation, HAPs can be interconnected via ground sta- tions or by inter-platform links (IPL) forming a network of HAPs, thus arbitrarily extending the system coverage. Furthermore, a HAP system can be deployed as a stan- dalone network or it can be connected to external networks via gateways providing suitable interworking functionality. HAP 1 HAP 2 inter-platform link Stratosphere Troposphere Gases, water, vapour, rainy,... y = hx + n y = h x + n y = hx + n y = hx + n Mobile User 1 Mobile User 2 Range R(Ptindex) Figure 1. Channel model for HAP operating environment. In order to investigate also the potential gain offered by exploiting space and platform diversity, we consider a configuration with two HAPs and two mobile users (MUs) (Figure 1). The principle of diversity is to provide two or more statistically independent channels for transmission of the same information. In the case of space diversity, independent channels are provided by receiving the same signal using multiple antennas suitably separated in space. Due to limited availability of space, weight and power for the communication payload on the platform, space diversity in the sky segment can only be achieved by transmitting the same signal from multiple platforms. From the perspective of space and platform diversity, the HAP system architecture enables four operating sce- narios: (i) single HAP-single MU (SISO), (ii) single HAP- two MUs (Single-Input Multiple-Output: SIMO), (iii) two HAPs-single MU (Multiple-Input Single-Output: MISO), and (iv) two HAPs-two MUs (MIMO). As seen in Figure 1, transmission links in the HAP system are affected by various influences of the propagation environment such as free space loss, attenuation due to meteorological effects and multipath fading. Let us now consider a single transmission link in the HAP system of Figure 1 associated with the transmitted and received signals of x and y, respectively. It should be noted that x and y are two complex numbers representing a symbol transmitted and received in the context of the single trans- mission link, respectively. Accordingly, the received signal can be represented as y = hx + n (1) where h = Ahsh f is the complex-valued fading coefficient that comprises three components. The first component, A, is the path loss, which includes free space loss and attenu- ations associated with above-mentioned weather scenarios. 53 Research and Development on Information and Communication Technology The second component, hs , is the block fading coefficient, which is also known as slow fading, large-scale shadow fading or quasi-static fading, which may be deemed to be unchanged for all symbols within a frame duration. The third component, h f , is the fast fading or small- scale fading, which fluctuates on a symbol-by-symbol basis. Finally, n is the AWGN process having a variance of N0/2 per dimension, where N0 is the power spectral density of the noise. Considering the frequency of f = 28 GHz and f = 30 GHz typically used in an Asian region, Table I lists magnitudes of path loss that subject to the free space loss and attenuation pertaining to different weather conditions occurring on the single transmission link, when measured at an elevation angle of θ = 12◦, a temperature of t◦ = 7◦C, the water vapour concentration of ρ = 6 g/m3, the absolute humidity of 10 g/m3 and the average rain density of 0.01%/year [13]. Values of the path loss A may be calculated as A = Afs + Aa, (2) where Afs is the free-space loss and Aa is the atmospheric attenuation due to influences of the clear air, fog, cloud as well as rain at Ka-band frequencies that depends on weather conditions: clear-sky, Aa cs (in dB), or rainy, Aa r (in dB). Expressing the free space loss Afs in dB, with frequency f in MHz and distance from HAP to user r in km, depending on elevation angle, θ (i.e., r = hHAP/sin θ, where hHAP is the platform height in km), we obtain Afs = 32.4 + 20 log r + 20 log f . (3) In order to assess the channel capacity degradation due to atmosphere, the total equivalent conditionally fading is required. Establishing the total equivalent conditionally fading is somewhat more complicated. We have calculated the attenuation due to atmosphere for different weather conditions, by combining the attenuations due to influences of the clear air, mixed cloud and rain. Thus, the atmospheric attenuation in clear sky condition Aa cs in dB may be calculated as Aa cs = Aw + Ao, (4) where Aw is the attenuation due to water vapor, and Ao is the attenuation due to oxygen. Similarly, the atmospheric attenuation in rainy condition Aa r(dB) in dB may be computed as Aa r = Aw + Ao + Acloud + Arain0.01%, (5) where Acloud is the attenuation due to mixed cloud, and Arain0.01% is the attenuation due to rain exceeded for 0.01% of an year. Details on computing these attenuation can be refer to [13]. TABLE I PATHLOSS MAGNITUDE OF THE SINGLE TRANSMISSION LINK IN DIFFERENT WEATHER CONDITIONS Pathloss (dB) f = 28 GHz f = 31 GHz Clear-Sky 157.4020 dB 158.5402 dB Rainy 200.9416 dB 206.8696 dB III. DCMC CHANNEL CAPACITY FOR HAP-MIMO SYSTEMS When a fixed modulation scheme is activated in the HAP system, the associated DCMC capacity may be achieved by invoking an idealized channel coding scheme [15]. With- out loss of generality, let us assume that the information transmitted over the channel has uniform distribution. By employing the classic Monte Carlo simulation method for averaging the expectation terms, the DCMC capacity in BPS of the transmission link may be calculated as [16]: CDCMC(η) (R) = η − 1 M M∑ l=1 E [ log2 M∑ z=1 exp ( ψl,z )  Xl ] , (6) where R is the information rate, M = 2η is the number of modulation levels, while η is the number of modulated bits and E [A|Xl] is the expectation of A conditioned on the M- ary signals Xl . More specically, Equation (6) represents the capacity of the MIMO DCMC that can be reached when employing a channel code such as Space Time Block Code (STBC) [17]. Note that ψl,z is a function of both the transmitted signal and of the channel as defined in [16, Equation (21)]. For the system relying on a single transmit and a single receiver antenna, we have ψl,z = −h(xl − xz) + n2 + |n|2 N0 . (7) Let us define the faded signal to noise power ratio at the transmitter side as SNRt = E [ 1 |h |2 SNRr ] , where SNRr is the faded signal to noise power ratio at the receiver side. Following the approach in [18, 19], where N0, is assumed to be constant, then on average we have SNRt = SNRr +A. (8) At a given information rate R, we readily identify the corresponding signal to noise power ratio SNRt |R. So SNRt |R is defined as the SNRt value associated with the capacity CDCMC(η) = R on the C DCMC (η) -versus-SNRt capacity curve represented by Equation (6) and plotted in Figure 2, where an information rate of R may be maintained. 54 Vol. E–3, No. 14, Sep. 2017 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Ca pa ci ty [B PS ] 140 145 150 155 160 165 170 175 180 185 SNRt [dB] SISO SIMO1x2 MISO2x1 MIMO2x2 SNRt ( ) Ca pa ci ty (B PS ) Figure 2. Capacity curves of the DCMC calculated by Equation (6) for the above four operating scenarios HAP-MIMO experiencing uncorrelated Rayleigh (fast or small-scale) fading channel, when employing QPSK in clear-sky at frequency of f = 28 GHz. As a direct result of having formulated the DCMC ca- pacity for the HAP transmission link presented in Figure 2 and Figure 3, one may roughly predict the differences in the performance of transmission link in HAP systems. For example, depending on the value of SNRt given at the transmitter reflecting the transmit power, the HAP system may provide infinitesimally low Bit Error Rate/Frame Error Rate (BER/FER) performance. Additionally, if SNRt value is given, the transmitter may decide the most beneficial modulation scheme that should be activated, as seen in Fig- ure 2 and Figure 3. In HAP-MIMO system if any one path is faded, there is a high probability that the other paths are not, so the signal still gets through. The channel capacity of a MIMO antenna system can be improved without using additional transmit power and spectral bandwidth over SISO antenna system. Specifically in Figure 2, the channel capacity in HAP- MIMO2×2 increased by 2 times compared to HAP-SISO system when employing QPSK modulation scheme. Con- sequently, MIMO is an IEEE 802.11n standard for world- wide [20]. However, MIMO systems are more costly and more complex. Therefore, depending on the requirements of the system design, the choice of antenna configuration (MIMO, MISO, SIMO or SISO) and modulation scheme is appropriate. Moreover, the SNRt value determined for a given sce- nario may be used for determining the maximum gain that may be obtained by further optimizing a given system. 1 2 3 4 5 6 7 8 Ca pa ci ty [B PS ] 140 145 150 155 160 165 170 175 180 185 SNRt [dB] BPSK QPSK 8PSK 16PSK SNRt (d ) Ca pa ci ty (B PS ) Figure 3. Capacity curves of the DCMC calculated by Equation (6) for a HAP-MIMO2×2 experiencing uncorrelated Rayleigh (fast or small-scale) fading channel, when employing M-ary PSK in clear-sky at frequency of f = 28 GHz. The principle of how to calculate the maximum gain was illustrated in [21], where that principle can be further developed for applying into existing systems of [22]. IV. ADAPTIVE CODED MODULATION CHANNEL CAPACITY FOR THE HAP TRANSMISSION LINK We consider a downlink transmission between HAP and MU. At the time i, the transmitter sends signal x[i] via LHAP channel that is affected by fading coefficient h[i] and AWGN noise n[i]. The receiver is capable of calculating the channel quality based on the outputs of demodulation or decoding, as seen in Figure 4. This information reflecting the channel quality experienced by the system may be used for supporting adaptive mechanisms, which facilitate the transmitter to select appropriate transmission parameters applied for the next frames. Important transmission param- eters that can be adapted are the rate of the error correction code and the modulation level, as listed in Table II. Let the set of error-control codes available at the transmitter be denoted by { Rcl , 1 ≤ i ≤ Nc } , where Nc is the number of coding rates that can be activated by both transmitter and receiver. The set of modula- tion schemes available at the transmitter is denoted by{ ηj(in BPS), 1 ≤ j ≤ Nm } , where Nm is the number of bits per symbol pertaining to the modulation scheme. The information rate R (or the rate of coded modulation schemes) available at both the transmitter and receiver may be represented by Rν = Rclηj , where we have 1 ≤ ν ≤ NcNm. Accordingly, there may be two main 55 Research and Development on Information and Communication Technology X + Transmitter LHAP Channel Receiver HAP w[i] Adaptive Coding Rcl [i] Adaptive Modulation ηj[i] x[i] h[i] n[i] y[i] Demodulation & Decoding Channel Estimate Mobile User w′[i] Feedback: SNR, Distance Statictis, Error Count Range R(Ptindex) Figure 4. Adaptive coded modulation principle. TABLE II SNRt INTERVALS, CODE RATE Rc AND INFORMATION RATE R, WHEN APPLYING THE ADAPTATION MECHANISM RELYING ON M -ARY PSK MODULATION SCHEMES FOR HAP-TO-GROUND TRANSMISSION OVER RAYLEIGH FADING CHANNEL AT f = 28 GHZ IN A CLEAR-SKY CONDITION. SNRt intervals (dB) Mod. scheme Code rate, Rc Information rate, R (BPS) [137.4, 147.4) BPSK 0.01 to 0.12 0.01 to 0.12 4QAM 0.005 to 0.18 0.15 to 0.36 [147.4, 157.4) QPSK 0.07 to 0.4 0.12 to 0.8 8QAM 0.12 to 0.28 0.36 to 0.8 [157.4, 162.4) 8PSK 0.27 to 0.5 0.8 to 1.51 16QAM 0.2 to 0.42 0.8 to 1.66 [162.4, 167.4) 16PSK 0.38 to 0.58 1.51 to 2.33 32QAM 0.3 to 0.55 1.66 to 2.74 ≥ 167.4 32PSK ≥0.5 ≥2.33 64QAM ≥ 0.45 ≥ 2.74 approaches for optimizing the transmission performance, namely transmit power per information bit [7] and channel capacity [23]. However, we only concentrate on the second approach here. As seen in Figure 4, the measurement of channel quality statistics is carried out at the receiver, in order to provide feedback information to the transmitter. Based on the feedback information, the beneficial modulation scheme is activated for the transmission of the next frame. To illustrate the principle, we use SNRt as the indicator of the channel quality. Accordingly, the SNRt intervals shown in Table II may be employed for selecting the bene- ficial modulation scheme that allows the system to transmit at the highest information rate possible. It should be noted that in order to approach the capacity both adaptive coding and modulation have to be activated. As a result, we have the modulation scheme, SNRt intervals, the coding rate Rc and the ultimate information rate R detailed in Table II. Moreover, it was proved that the channel capacity cor- responding to the idealized channel coding may be ap- proached when a highly complex decoder is affordable at the transmitter [24]. To strike the trade-off between complexity and near-capacity performance, the realistic coding schemes of [21] may be used for providing an arbitrary coding rate Rc and an infinitesimally low BER at the SNRt value that is d = 0.5 dB away from the corresponding channel capacity. Accordingly, given a transmit power represented by SNRt value, the maximum channel capacity C may be calculated based on the corresponding curves plotted in Fig- ures 5 and 6. Concerning the maximum channel capacity, the most beneficial modulation scheme and the associated channel coding rate can also be determined. Ultimately, the results for both well-adopted modulation types, M-ary PSK and M-ary QAM, are presented in Table II. As a result, we have the channel capacity for the HAP transmission link employing adaptive coding and modulation scheme plotted in Figures 5 and 6 for both modulation categories over the entire SNRt range of our interest. It should be noted that there is a gap of 0.5 dB between channel capacity in the scenario of invoking an idealised channel coding scheme and a realistic channel coding scheme, as seen in Figures 5 and 6. V. CONCLUSIONS In this paper, we have presented the results of analytical evaluation of channel capacity for HAP-MIMO systems 56 Vol. E–3, No. 14, Sep. 2017 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Ca pa ci ty [B PS ] 140 150 160 170 180 190 SNRt [dB] BPSK QPSK 8-PSK 16-PSK 32-PSK Bound-Idealized Code Bound-Realistic Code SNRt (dB) Ca pa ci ty (B PS ) Figure 5. DCMC capacity bound for the M-ary PSK adaptive transmission schemes in HAP-SISO system over Rayleigh fading channel in clear-sky at frequency of f = 28 GHz. 1 2 3 4 5 6 Ca pa ci ty [B PS ] 140 150 160 170 180 190 SNRt [dB] 4-QAM 8-QAM 16-QAM 32-QAM 64-QAM Bound-Idealized Code Bound-Realistic Code SNRt (dB) Ca pa ci ty (B PS ) Figure 6. DCMC capacity bound for the M-ary QAM adaptive trans- mission schemes in HAP-SISO system over Rayleigh fading channel in clear-sky at f = 28 GHz. employing specific modulation schemes at Ka-band fre- quencies under practical transmission environment. 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Kanatas, “Mobile-to-mobile communications via strato- spheric relays: Relay selection and performance analysis,” in Proceedings of the International Conference on Commu- nications (ICC). IEEE, 2015, pp. 916–921. [23] T. Keller and L. Hanzo, “Adaptive multicarrier modulation: a convenient framework for time-frequency processing in wireless communications,” Proceedings of the IEEE, vol. 88, no. 5, pp. 611–640, May 2000. [24] C. E. Shannon, “A mathematical theory of communication,” ACM SIGMOBILE Mobile Computing and Communications Review, vol. 5, no. 1, pp. 3–55, 2001. Nguyen Thu Hien was born in 1976 in Lao Cai. She received the B.Eng. and M.Eng degrees from the Posts and Telecommuni- cations Institute of Technology in 2004 and 2010, respectively. Her research interests include wireless communications, informa- tion and communication system, signal pro- cessing, image and video processing. Vu Van San received Ph.D. degree in 2000. In 1983, he joined in the Research Institute of Posts and Telecommunications (RIPT). He is now working at Posts and Telecommunications Institute of Technol- ogy (PTIT). His research interests are in the areas of high-speed optical communi- cations, access networks, and digital trans- mission systems, wireless communications systems and signal processing. He is currently the Editor in Chief of Journal of Science and Technology on Information and Communications. He is also serving as a member of science and technology committee of the Ministry of Information and Communications. Nguyen Viet Hung was born in 1977 in Ha Nam Ninh. He received the B.Eng. from Hanoi University of Science and Technol- ogy (HUST), Hanoi, in 1999, the M.Eng. degree from Asian Institute of Technology (AIT), Bangkok, Thailand, in 2002, and the Ph.D. degree from the University of Southampton, UK, in 2013. His research interests include cooperative communications, channel coding, network coding and quantum communications. 58