Page 86 - 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




          Attribute update                                                  Table 1 – SC‑FDMA system setting
          In this step, the attributes of all nodes in the search tree  Parameter              Numerical Value
          T   +1  are updated based on the feedback of the measured  DFT size                  1200
                                                      
                   
          reward    in the current time slot. For LOS BA,    is the  DFT size                  2048
                                                      
          measured receive power of one sub‑band, while    is the  Cyclic pre ix length        512
          measured receive power of one subcarrier in the NLOS   Transmission band             0.1 − 0.1281 THz
          case. The details of the attribute update are shown in Al‑  Number of transmit antennas     64
          gorithm 2 from line 12 to line 22. The update of   ‑values  Number of receive antennas         2
          consists of the following steps.                                                   
          At  irst, the number of times    ℎ,   (  ) that node (ℎ,   ) has  Antenna gain    ,    ,    =        20 dBi
                                                                                
                                                                                       
                                                                                   
          been visited until time slot    is updated as          Signal constellation          4QAM
                                                               narrow its searching coverage in the highest layer. The
                    ℎ,   (  ) =    ℎ,   (   − 1) + 1, ∀(ℎ,   ) ∈    .  (37)  algorithm will be terminated, if no new node has been se‑
                                                   
                                                               lected and the selection result no longer changes, i.e.,
          Node (ℎ,   ) must have been visited one time when it is
          selected as the new node for the search tree. (ℎ,   ) will               T   +1  = T .            (41)
                                                                                             
          be visited one more time when one of its descendants is
                                   
          added to the search tree T . The average measured re‑  Then,  the  currently  selected  beam  w(   ,       
                                                                                                    
          ward    ℎ,    of (ℎ,   ) is updated by                                                      )  is  the  de‑
                                                               rived beam for the correponding sub‑band and subcarrier
                    (   ℎ,   (  ) − 1)    ℎ,   (   − 1) +        in LOS and NLOS cases, respectively. According to [9], the
              ℎ,   (  ) =        (  )        , ∀(ℎ,   ) ∈   .  computational complexity of the HBA is quadratic in the
                                                                                               2
                               ℎ,  
                                                      (38)     number of processed time slots,   (    ).
          The empirical average reward    ℎ,   (  ) of node (ℎ,   ) in
          time slot    is de ined as                           4.3  Complexity analysis
                                 2
                                           ℎ
                         (  ) + √ 2   log     +       ,  if     (  ) > 0  At time slot    , for one subcarrier or sub‑band, the deci‑
             ℎ,   (  ) = {  ℎ,       ℎ,   (  )  1  ℎ,          sion tree contains     nodes as the tree is extended by one
                     +∞,                       otherwise       node in each time slot. The attributes of all nodes in a de‑
                                                      (39)     cision tree should be updated in each time slot, and hence
                   2
          where√ 2   log     representsthecon idencemarginrelated  the run time in time slot     is linear in    ,  i.e.,    (   ).  As
                     ℎ,   (  )
                                                               the algorithm is executed for     time slots, the total com‑
          to  the  uncertainty  of  rewards,  related  to  random  data
          and  noise.  With  increasing     ℎ,   (  ),   the  uncertainty  of   putational complexity of the proposed HBA algorithm is
                                                                                    2
          the reward of (ℎ,   ) becomes lower, since there are more   quadratic in     , i.e.,   (    ) [9].
          available  observations.  The    idence  margin  is
                                                               5.   NUMERICAL RESULTS
          designed  based  on  Bayesian  principle  and  derived  in
          [26].  Here, 0  <      <  1 and    >  0 are parameters of the
                                  1
                          ℎ                                    In the following, we investigate a THz SC‑FDMA system,
          algorithm, and       speci ies the maximum variation of   whose  parameter  settings  are  provided  in  Table  1.
                        1
          the  average  reward  function  within  beam  coverage      
                                                               The transmission scenario is the indoor scenario consi-
          (w(ℎ,   )) [26], which depend on the codebook structure.
                                                               dered in [6].  The transmitter is  ixed at the center of the
          The datails re‑ garding    and    selection can be found in
                                                               room  ceiling  and  the  location  of  the  receiver  with   ixed
          [26] and [9].  If     and    is chosen based on the bounded
          diameter  prin‑  ciple  and  well‑shaped  region  principle  height ℎ  =  1.5 m is uniformly distributed within the in‑
                                                               door  environment.  The  results  are  averaged  over  500
          from  [9],  HBA  will  converge  to  the  optimal  beam  code
                                                               channel  realizations.  The  proposed  algorithm  is  com‑
          with high probability. In the initial phase of the HBA, no  pared to the following benchmarks:
          information  regarding  the  rewards  is  available.  Hence,
                                                               Optimal  SC‑FDMA  beamforming:  In  this  beamforming
             ℎ,   (  ) is initialized by in inity.  With abundant observed
          rewards  within        (ℎ,    )  available,  we  can  tighten  the  scheme,  the  CSI  is  considered  as  known  at  both  the  re‑
          upperbound   of   mean   rewards   step   by   step.  ceiver and the transmitter. Thus, an MMSE frequency do‑
                                                               main equalizer according to [10] can be designed.  This
          Finally, the estimated maximum mean reward   (ℎ,   ) in
                                                               algorithm  aims  to  minimize  the  MSE  after  equalization,
          beam coverage      (ℎ,   ) is determined as [26]
                                                               which can be formulated as a convex optimization prob‑
                    ⎧ min{   ℎ,   (  ),                        lem.  The optimal solution is derived in [10], and its per‑
                    {  max {        (  ),     (  )}},          formance can be regarded as a performance upper bound
                              ℎ+1,2  −1
              ℎ,   (  ) =  ⎨ if     (  ) > 0  ℎ+1,2    (40)    for our proposed scheme.
                    {      ℎ,  
                    ⎩ +∞, otherwise                            Random  beamforming:  In  random  beamforming,  the
                                                               beamforming vector for each subcarrier or sub‑band is a
          When the HBA algorithm has obtained a suf icient num‑  random complex vector with constant    ‑norm and ran‑
                                                                                                  2
          ber of observed rewards within the searching tree, it will  dom phase pro ile. An MMSE equalizer is employed at the
          74                                 © International Telecommunication Union, 2021
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