I would like to remotely control my Linux desktop via an ssh connection (connected through my phone).

Fortunately, we can use xdotool.

I created a simple command-interpreter that maps keys to xdotool. I used standard video game controls (wasd) for large mouse movements (100px), with smaller movements available (ijkl 10px). It can toggle between mouse and keyboard, which allows you to somewhat easily open a browser and type URLs.

I use this to control my HD television from my phone, and so far it works great.

#!/bin/bash
#
#
: ${DISPLAY:=":0"}
export DISPLAY

echo "xmouse! press q to quit, h for help"

function print_help() {
  echo "xmouse commands:
  h - print help

  Mouse Movements
  w - move 100 pixels up
  a - move 100 pixels left
  s - move 100 pixels down
  d - move 100 pixels right

  Mouse Buttons
  c - mouse click
  r - right mouse click
  u - mouse wheel Up
  p - mouse wheel Down

  Mouse Button dragging
  e - mouse down (start dragging)
  x - mouse up (end dragging)

  Mouse Movements small
  i - move 10 pixels up
  j - move 10 pixels left
  k - move 10 pixels down
  l - move 10 pixels right

  Keyboard (experimental)
  Press esc key to toggle between keyboard and mouse modes
  
"
}

KEY_IN="Off"
IFS=''
while read -rsn1 input; do
  #
  # toggle mouse and keyboard mode
  case "$input" in
  $'\e') if [ "$KEY_IN" = "On" ]; then
           KEY_IN="Off"
           echo "MOUSE mode"
         else
           KEY_IN="On"
           echo "KEYBOARD mode"
         fi
     continue
     ;;
  esac
  #
  # keyboard mode
  if [ "$KEY_IN" = "On" ]; then
  case "$input" in
  $'\x7f') xdotool key BackSpace ;;
  $' ')  xdotool key space ;;
  $'')   xdotool key Return ;;
  $':')  xdotool key colon ;;
  $';')  xdotool key semicolon ;;
  $',')  xdotool key comma ;;
  $'.')  xdotool key period ;;
  $'-')  xdotool key minus ;;
  $'+')  xdotool key plus ;;
  $'!')  xdotool key exclam ;;
  $'"')  xdotool key quotedbl ;;
  $'#')  xdotool key numbersign ;;
  $'$')  xdotool key dollar ;;
  $'%')  xdotool key percent ;;
  $'&')  xdotool key ampersand ;;
  $'\'') xdotool key apostrophe ;;
  $'(')  xdotool key parenleft ;;
  $')')  xdotool key parenright ;;
  $'*')  xdotool key asterisk ;;
  $'/')  xdotool key slash ;;
  $'<')  xdotool key less ;;
  $'=')  xdotool key equal ;;
  $'>')  xdotool key greater ;;
  $'?')  xdotool key question ;;
  $'@')  xdotool key at ;;
  $'[')  xdotool key bracketleft ;;
  $'\\') xdotool key backslash ;;
  $']')  xdotool key bracketright ;;
  $'^')  xdotool key asciicircum ;;
  $'_')  xdotool key underscore ;;
  $'`')  xdotool key grave ;;
  $'{')  xdotool key braceleft ;;
  $'|')  xdotool key bar ;;
  $'}')  xdotool key braceright ;;
  $'~')  xdotool key asciitilde ;;
  *)     xdotool key "$input" ;;
  esac
  #
  # mouse mode
  else
  case "$input" in
  q) break ;;
  h) print_help ;;
  a) xdotool mousemove_relative -- -100 0 ;;
  s) xdotool mousemove_relative 0 100 ;;
  d) xdotool mousemove_relative 100 0 ;;
  w) xdotool mousemove_relative -- 0 -100 ;;
  c) xdotool click 1 ;;
  r) xdotool click 3 ;;
  u) xdotool click 4 ;;
  p) xdotool click 5 ;;
  e) xdotool mousedown 1 ;;
  x) xdotool mouseup 1 ;;
  j) xdotool mousemove_relative -- -10 0 ;;
  k) xdotool mousemove_relative 0 10 ;;
  l) xdotool mousemove_relative 10 0 ;;
  i) xdotool mousemove_relative -- 0 -10 ;;
  *) echo "$input - not defined in mouse map" ;;
  esac
  fi
done