Wimax standards and Security The Wimax

Measured Signal-Aware Mechanism

The power received from a transmitter at separation distance d will directly impact the received signal-to-noise ratio (SNR). The desired signal level is represented as received power P_r in milliwatt and is given by

=_r
P [mW] ^PtGtGr
PL(d)L
[valid if d 2D²/λ] (7.5)

≥

=

= ×
where P_t is the transmitted power, G_t and G_r are the transmitter and receiver antenna gains, PL(d) is the path loss (PL) with distance d, L the system loss factor (L 1, transmission lines, etc., but not due to propagation), D the maximum dimension of transmitting antenna, and λ the corresponding wavelength of the propagating signal [23]. The antenna gain G 4πA_e/λ²; A_e is the effective aperture of the antenna. The length of λ can be obtained by c/f 3 10⁸/f in meters, where f is the frequency the signal carries. Besides, P_r can be represented in dBm units as
P_r [dBm] = 10 log(P_r [mW])
= P_t + G_t + G_r − PL(d) − L (7.6)
In the free space propagation model, the propagation condition is assumed idle and there is only one clear line-of-sight (LOS) path between the trans- mitter and receiver (T-R). On unobstructed LOS path between T-R, PL(d) can be evaluated as (4π)²d²/λ² or when powers are measured in dBm units as

+ +
92.4 20 log( f ) 20 log(d). We can get the desired T-R separation distance in meters

4π

4πf
d = ^{λ ,}PL(d) = ^{c ,}PL(d) (7.7)


However, in street canyon scenario or urban environment, the PL model can be demonstrated through measurements using the parameter σ to denote the rule between distance and received power [2] and be expressed as

d₀

σ
PL(d) = PL(d₀) + 10ρ log ^d + X
+ C_f + C_H (7.8)

=
where the term PL(d₀) is for the free space PL with a known selection in refer- ence distance d₀, which is in the far field of the transmitting antenna (typically 1 km for large urban mobile systems, 100 m for microcell systems, and 1 m for indoor systems) and measured by PL(d₀) 20 log(4πd₀/λ). The term X_σ denotes a zero-mean Gaussian distributed random variable (with units in dB) that reflects the variation in an average received power, which naturally occurs when PL model of this type is used [13]. The ρ is the path loss expo- nent, where ρ = 2 for free space and is generally higher for wireless channels.

=

≤ ≤

= − +

= − ≤ ≤
It can be measured as ρ (a bH_b c/H_b), where a, b, and c are constants for each terrain category. The numerical values for these constants are studied in Ref. 12, where H_b is the height of the base station and 10 m Hb 80 m. The term C_f , which is measured by C_f 6 log ( f/1900) [10], stands for the frequency correction factor; it accounts for a change in diffraction loss for different frequencies. Owing to the diffraction loss, a C_f is a simple frequency dependent factor. C_H is the receiver antenna height correction factor and H the receiver antenna height. C_H 10.7 log(H/2) when 2 m H 8 m. This correction factor closely matches the Hata–Okumura mobile antenna height correction factor for a large city [14].
We know that the audio or video quality of a receiver is directly related to the SNR. The limiting factor on a wireless link is the SNR required by the receiver for useful reception

SNR [dB] = P_r [dBm] − N₀ [dBm] (7.9)

where N₀ is the noise power in dBm. Assuming the carrier bandwidth is B, the receiver noise figure F, the spectral efficiency r_b/B, and the coding gain G_c, the SNR for coded modulation with data rate r_b can be obtained by

N₀ B
SNR [dB] = 10 log ^{Pr rb} − G_c (7.10)

= − + +
where N₀ [dBm] 174 [dBm] 10 log B F [dB]. To obtain a criterion mea- surement of the received SNR, we force each MSS to use the lowest frequency to contend the channel with a predefined transmission power. The BS, after receiving a RNG-REQ message from the MSS, calculates the estimated dis- tance between BS and MSS according to the received SNR. Assume that the BS needs a minimum receiving power or sensitivity P_r,min, which corresponds to a minimum required SNR, denoted as SNR_min, from each MSS to successfully receive the signal. According to Equations 7.6 and 7.10, we have


^SNRmin ^{= P}r,min ^{− N}0
= P_t + G_t + G_r − PL(d) − L − N₀ (7.11)

Substituting Equation 7.8 in Equation 7.11 leads to

c

d₀
SNR_min = P_t + G_t + G_r − 20 log ^4πd0f − 10ρ log ^d

— X_σ − C_f − C_H − L − N₀ (7.12)

B = 20 MHz, F = 7, G_t = 15, G_r = 18, P_t = 16 W, L = 5 dB.
20

18

16



Maximum distance (km)
14

12

10

8

6

4

2

0
2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66

Frequency (GHz)