Table 1 Most commonly used symbols and parameters

N _RA

Number of receiving antennas

M = 2N_RA

Collision recovery factor / number of

tags the reader is capable of resolving

J

Maximum number of tags

the reader acknowledges

J _C

Maximum number of tags with

colour C the reader acknowledges

R∈[0..N]

Number of tags active in the same slot

$R_C\in \left[0‥\frac{N}{C}\right]$

Number of tags per slot

with colour C

j∈[1..R]

Tag index per slot for R>0

i∈[1..N_RA]

Receive antenna index

r _c (t)

Received signal vector $\in {\mathbb{C}}^{N_{\text{RA}}\times 1}$

H _c

Channel matrix $\in {\mathbb{C}}^{N_{\text{RA}}\times R}$

a(t)

Modulation vector $\in {\mathbb{R}}^{R\times 1}$

N

Number of tags within the reader range

F

Number of slots in a frame

r _i [k]

Sample of the received signal from i th antenna

taken within duration of the first preamble bit t_1bit

s _l

Collision scenario l = 1,2,…,S(R)