What is the meaning of mathematical operator ℝ{.} in Equation (14) of the attached paper?

In the attached paper titled, "Approximate expressions for BER performance in downlink mmWave MU-MIMO hybrid systems with different data detection approaches", mathematical operator ℝ{.} is used with minus sign in Equation (14). Can anybody help explain the meaning of this operator? Why minus sign is used?

Approximate expressions for BER performance in downlink mmWave MU‐MIMO hybrid syste
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Mathematics

Hybrid Systems

Neeraj Sharma

Panjab University

Daniyel Yaacov Bilar Thank you so much so such detailed reply. May I ask more? I shall be highly obliged.

1. BER is normally expressed as Q-function of sqrt(SNR). In Eq 15, what is signal power and noise power?

2. How to interpret Eq (13)?

3. You have well explained Eq (14). But how does it lead to Eq (15)?

4. In Eq. (17), will simply putting K=1 make it applicable for SU-MIMO case?

5. Data vector s belongs to some constellation Q . In Eq. (17), M is defined as number of possible transmitted symbol vectors. Is there any connection between Q and M? Is it related to the modulation technique used? For example, in 16-QAM modulation, 16 possible combinations of bits are generated.

I am eagerly waiting for your reply.