Page 18 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 7 – Terahertz communications
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ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 7





          where     (  ,      (ℎ ,    ,    ),    (ℎ ,    ,    ))  is  the  atmospheric   where    is the Boltzmann’s constant,                is the mole-
                                                                        
                                    
                          
          medium’s  transmittance.  We  employ  Line‑By‑Line   cular noise temperature obtained as               (  , ℎ ,   ,   )  =
                                                                                                          
          Radiative  Transfer  Model  (LBLRTM)  for  obtaining        (  , ℎ ,   ,   ).   Here,    is the reference temperature (in
                                                                                    0
                                                                 0
                                                                        
          realistic  transmittance  values  across  various  atmospheric   Kelvin), and    is the channel’s emissivity,   (  , ℎ ,   ,   )  = 1
                                                                                                         
          altitudes  [39,  40].      (ℎ ,    ,    )  and    (ℎ ,    ,    )  are  the   −    (  ,      (ℎ ,    ,    ),    (ℎ ,    ,    ))  [14].  Hence,                  is  a
                                
                                                                            
                                                                                      
                                               
          atmospheric  temperature  (in  Kelvin)  and  water  vapor   function  of  transmittance,     ,   which  is  obtained  using
          concentration  (in  %),  respectively,  for  the  link  between   LBLRTM.  In  the  results  provided  in  this  paper,  for  cap‑
          the Tx drone hovering at ℎ and Rx drone at ℎ .       turing  the  absorption  effect  across  the  THz  band
                                  
                                                  
                                                               (0.75‑10 THz), US Standard 1976 weather pro ile is set
          In  regard  to  the  impact  of  the  mobility  of  the
                                                               in  LBLRTM  [12].  For  computing  the  capacity  of  THz
          communicating drones and the resulting Doppler spread,
                                                               drone‑to‑drone links under ideal, no fading channel, the
          thanks to the very high operating frequency in the order
                                                                                                 
          of THz, mobile drones observe minimized Doppler effect   total  channel  gain  is  set  as,      =     .   In  this  paper,  we
                                                               consider the standard narrowband capacity computation
          [15],  promising  high  rate  links  between  communicating
                                                               in [14, 45]:
          drones.  It  has  been  shown  in  [41,  42]  that  for  a  typical
          drone  relative  velocity,     =  10  m/s,  the  maximum                                   2
                                   
                                                                                            |  (      ,ℎ    ,  ,  )|      
          Doppler shift is negligible. As an example, by considering     (ℎ ,   ,   ) = ∑ Δ          [1 +           (      ,ℎ    ,  ,  ,(Δ  ))  ] ,  (8)
                                                                        
                                                                                     2
                                                                               =1
             =  0.75  THz,  and     =  10  m/s,  the  maximum  Doppler
                              
            
          shift is:      .        =    .  /   = 25017.31 Hz, which is negligible   where  total  transmit  power,     ,  and  total  antenna  gain
                                                                                            
                          
          in terms of the inter‑carrier interference. Moreover, since   (from Tx and Rx antennas),    are set to practical values
                                                                                          
          we  are  con‑  sidering  drone  to  drone  communications,   as    = 24 dBm (0.25 W) [46] and    = 60 dBi [47, 48],
                                                                     
                                                                                                 
          where a swarm (group) of drones move together,    can   respectively.  For power allocation, we consider both the
                                                        
          be less than 10 m/s (up to 0 m/s) and      .        will be even   Water‑Filling (WF) and Equal‑Power (EP) schemes [14].
          smaller than the example provided above. Therefore, we   In WF allocation, the total transmit power,    is optimally
                                                                                                      
          neglect  the  effect  of  the  Doppler  spread  in  our  capacity   distributed across the THz band (0.75‑10 THz) compris‑
          computations.                                        ing  of  constant  narrowbands,      =  1,  2,  3,  ...,    ,   each
          For  beam  misalignment  fading,  we  consider  the   0.3 GHz wide (i.e., LBLRTM’s spectral resolution), as:
          following probability density function for the BM fading
          coef icient,    ,  [43]:                                        1  −  1  ,    ≥    s.t. ∑        ≤   
                       
                                                                                                      
                                     2  2                              = {     ∘             ∘    =1          (9)
                            (  ) =         −1  ,       (5)               0        ,    <    ,
                                      2                                                 ∘
                                    0
          where    =           ,          is the equivalent Tx beam width,  where             is  the  optimal  power  for  the  constant  nar‑
                     2     
             denotes the jitter (BM) standard deviation, and    is  rowband,   ,     is the threshold SNR,    is the SNR of   .     ∘
                                                                                                
                                                                           ∘
             
                                                       0
                                                                                
                                                                                       1
                                                                                   1
          the fraction of power collected at Rx at no beam misalign‑  is obtained by ∑   =1  (     ∘  −         ) = 1 [49].
          ment. This BM fading model has been widely employed in  In EP allocation,     is distributed equally within all   
                                                                                  
          many studies of free space optical systems. For more de‑  across the entire THz band (0.75‑10 THz) [12].
          tails of the BM fading model, we refer to our earlier work
          [12] and also [43].                                  For the channel under fading, involvingBM and MP fading,
          Finally, for incorporating multipath fading, we consider  the channel gain is set as    =          , and we evaluate
                                                                                             
                                                                                                  
                                                                                               
          the famous   ‑   model as follows [44]:              the ergodic capacity by averaging results over 100 real‑
                                                               izations, as follows:
                                                                                    
                    (  ) =             −1        (−    ) ,  (6)                                     |  (      ,ℎ    ,  ,  )|      
                                                                                                       2
                          ̂
                                               ̂                   (ℎ ,   ,   ) = Δ      (∑        [1 +      ]) ,
                                                                                       2
                                                                      
                               Γ(  )                                                =1             (      ,ℎ    ,  ,  ,(Δ  ))
          where     (  ) is the pdf of the MP fading coef icient,    ,                                      (10)
                                                           
             is the fading parameter,    is the normalized variance of   where   (. ) denotes the expectation taking over channel
                                                               realizations under fading.
          the channel envelope under fading, and   ̂ is the   ‑ root
                                                
          mean  value.  The    ‑     model  is  a  common  model  of   Next, we present the capacity and ergodic capacity results
          several famous  fading  distributions.  For  instance,      =  2   speci ically for drone scenarios, considering various prac‑
                                                               tical settings of Tx and Rx drone altitudes, zenith angles
          and    = 1 represents Rayleigh fading, etc.
                                                               and  transmission  ranges.  Fig.  4(a)‑(c)  depict  the  chan‑
          For computing noise power,     ,   we consider a constant   nel capacity as the function of transmission range under
                                     
          narrowband  approach  [14]  across  the  THz  band   ideal, i.e., under no fading channel.  The capacity results
          (0.75‑10 THz), where each narrowband, Δ   is 0.3 GHz   with no fading (ideal) channel are included in our analy‑
          wide,  which  is  the  spectral  resolution  of  LBLRTM.   sis as the benchmark to compare how much of the capa-
          Numerically,                                         city is degraded when realistic beam misalignment fading
               (  , ℎ ,   ,   , Δ  ) =    ∫               (  , ℎ ,   ,   )    ,  (7)  and multipath fading are introduced into the channel, as
                    
                                 
               
                                               
                                 Δ                             provided in the subsequent discussion.  Three drone Tx
          6                                  © International Telecommunication Union, 2021
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