A Survey on Multipacket Reception for Wireless Random Access Networks

Table 1

Theoretical results on the capacity.

Metric	Condition	SPR	MPR	Works
One-hop throughput; (upper bound)	Slotted aloha	sup𝜆≥0𝑒^−𝜆	sup𝜆≥0𝑒^𝑛−𝜆∑𝑖=1𝜆^𝑖𝑅𝑖!^𝑖	[8]
Spatial throughput	Slotted aloha	^∞∑𝑥=1𝑃[𝑋=𝑥]	𝑃[𝑋=1]	[9]
Throughput (tight bound); per source-destination	Protocol model; (graph model)	Θ1𝑛	Θ^3log𝑛𝑛	[10]
Throughput (lower bound); per source-destination	Physical model; (SINR model)	Θ1𝑛log𝑛	Θloglog𝑛𝑛log𝑛	[11]
Throughput (tight bound); per source-destination	Multiflow; SINR model	Θ1𝑛	Θ(log𝑛)^(1/2)−(1/𝛼)√𝑛	[12]
Network throughput; (tight bound)	k-MPR; (arbitrary networks)	Θ(√𝑛)	Θ(√𝑘𝑛),𝑘=𝑂(𝑛)	[13]
			Θ(𝑛),𝑘=Ω(𝑛)
Network throughput; (lower bound)	k-MPR; (random networks)	Θ(𝑛)log𝑛	Ω𝑘𝑛log𝑛,𝑘=𝑂log𝑛	[13]
			Ω(√𝑛),𝑘=Ω(log𝑛)