This　paper　addresses　a　class　of　dilation-and-modulation　(MD)　systems　in　the　space　L2(R+)　of　square　integrable　functions　defined　on　the　right　half　real　line　R+.　In　practice,　the　time　variable　cannot　be　negative.　L2(R+)　models　the　causal　signal　space,　but　it　admits　no　wavelet　and　Gabor　systems　due　to　R+　being　not　a　group　under　addition.　We　study　the　dilation-and-modulation　systems　in　L2(R+)　generated　by　characteristic　functions.　We　introduce　the　notion　of　MD-frame　sets　in　R+.　Using　＂dilation-equivalence＂　and　＂cardinality　function＂　methods　we　characterize　MD-Bessel　and　complete　sets;　obtain　two　sufficient　conditions　for　MD-Riesz　basis　sets;　and　prove　that　an　arbitrary　finite　and　measurable　decomposition　of　an　MD-Riesz　basis　set　leads　to　an　MD-frame　set.　©　2020,　Chinese　Academy　of　Sciences.　All　right　reserved.