**3. Effect of UWB Interference on the portable WiMAX downlink range**

For each WiMAX downlink channel, the UWB interfering signal is due to only a given part of the total UWB spectrum. To account for UWB interference, an extra source of interference is added to the WiMAX noise. Here we consider the UWB interference as a Gaussian signal. The WiMAX technology is based on Orthogonal Frequency Division Multiplex (OFDM) technique. Thus we will calculate the Signal to interference plus noise (SINR) on a single subcarrier, not in the overall bandwidth.

The interference power is calculated by assuming an UWB interfering source at different distances from the WiMAX receiver. Therefore, the interference power generated by a UWB device, IUWB, is given (in dBm) by:

$$I\_{\rm LIVB} = P\_{\rm LIVB} - L\_{\rm LIVB} \text{(d)} + G\_{\rm RX\\_WMAX} \tag{1}$$

UWB Coexistence with 3G and 4G Cellular Systems 319

• A is the free space propagation loss at a distance of 100 m.

• s is the shadowing margin assumed to be 10 dB. • Lglass is the wall insertion loss assumed to be 5 dB.

• Bc is the WiMAX band width of a single carrier.

The WiMAX received power per subcarrier SWiMAX\_sc is given as:

• PWiMAX\_sc is the WiMAX transmitted power per subcarrier.

that exists within the three nearest clusters of 4 macrocells is given by:

dB (antenna for a macrocell with 3 sectors).

−

*SINR*

IUWB is the UWB interference all given in real numbers.

where R is the radius of the WiMAX macrocell.

WiMAX bandwidth of 20 MHz.

where:

where:

given by:

• hRX is the WiMAX antenna height in the receiving end.

• γ is the propagation exponent with a typical value of 3.9 to 4.7.

• f is the operating frequency of the WiMAX system given in MHz.

The thermal noise of the WiMAX receiver Nrec\_sc per subcarrier is given by:

( ) \_ <sup>10</sup> ( ) 114 10 log *rec sc <sup>c</sup> MHz*

• NF is the WiMAX receiver noise figure in dB assumed to be constant within the

• GTX\_WiMAX is the antenna gain of the WiMAX in the transmitting end assumed to be 18

The WiMAX cochannel interference due to the macrocells using the same frequency band

\_ <sup>10</sup> 10log 3 <sup>12</sup> *cc WiMAX WiMAX sc <sup>d</sup> I S*

<sup>4</sup> ( ) 20log 10 log ( ) 4 *UWB L d n d* π

 ≈ +−

λ

10 log *WiMAX sc*

where Icc-WiMAX is the WiMAX cochannel interference, Nrec is the receiver thermal noise, and

For the WiMAX receiver, the signal to interference plus noise ratio SINR per subcarrier is

For the UWB system the propagation loss with 99.995% confidence is given by:

10

≈ +

10 10

*S*

\_

*CC WiMAX rec sc UWB*

+ +

*I NI* <sup>−</sup> <sup>=</sup>

\_

*N dBm* =− + *B NF* + (4)

*WiMAX sc WMAX sc Tx WiMAX WiMAX Rx WiMAX* \_ \_\_ \_ *S P G LG* = + −+ (5)

*R*

γ

σ (6)

(7)

(8)

• d is the distance between the WiMAX transmitter and the WiMAX receiver.

where:


Taking into account that UWB devices are short range, the quasi free space path-loss model with shadowing is often most appropriate, especially when the distance between the UWB transmitter and the mobile receiver is lower than 8 m. Thus, in the WiMAX downlink frequency band, the UWB signal propagation loss LUWB(d), measured in dB at a distance d in meters from the UWB transmitter, is calculated as:

$$L\_{\rm IIVB}(d) = 20\log\_{10}\left(\frac{4\pi}{\lambda}\right) + 10\ln\log\_{10}(d) + N\left(0, \sigma\right) \tag{2}$$

Where λ is the operating wavelength at the WiMAX frequency, n is the indoor propagation exponent (1.8 to 2.0) and N(0, σ) is a Gaussian variable of zero mean and a standard deviation of σ, representing the deviation from the path loss mean value (shadowing). Practical values of σ are in the range 1.8 to 3 dB in the line of sight LOS environment. Here we assume that the Gaussian variable N(0, σ) is truncated at ±4σ. In our case σ is assumed to be 2 dB.

In the calculation of the propagation loss of the WiMAX signal we use the two-slope propagation loss model. Thus, for a distance higher than 100 m, the WiMAX signal propagation loss in dB is given as:

$$L\_{\rm WMAX} = A + 10\ \chi \log\_{10} \left(\frac{d}{d\_o}\right) + s + L\_{\rm glass} + 6\log\_{10} \left(\frac{f}{1900}\right) - 10.8\log\_{10} \left(\frac{h\_{\rm RX}}{2}\right) \tag{3}$$

Where:


The thermal noise of the WiMAX receiver Nrec\_sc per subcarrier is given by:

$$N\_{rec\\_sc}(dBm) = -114 + 10\log\_{10}\left(B\_c\right)\_{MHz} + NF \tag{4}$$

where:

318 Ultra Wideband – Current Status and Future Trends

subcarrier, not in the overall bandwidth.

with the separation distance d in m.

meters from the UWB transmitter, is calculated as:

device, IUWB, is given (in dBm) by:

where:

be 2 dB.

Where:

propagation loss in dB is given as:

*WiMAX glass*

γ

*o*

*d*

bandwidth.

**3. Effect of UWB Interference on the portable WiMAX downlink range** 

For each WiMAX downlink channel, the UWB interfering signal is due to only a given part of the total UWB spectrum. To account for UWB interference, an extra source of interference is added to the WiMAX noise. Here we consider the UWB interference as a Gaussian signal. The WiMAX technology is based on Orthogonal Frequency Division Multiplex (OFDM) technique. Thus we will calculate the Signal to interference plus noise (SINR) on a single

The interference power is calculated by assuming an UWB interfering source at different distances from the WiMAX receiver. Therefore, the interference power generated by a UWB

\_ ( ) *UWB UWB UWB RX WiMAX I P L dG* =− + (1)

• PUWB is the UWB Effective Isotropic Radiation Power (EIRP) in dBm in the WiMAX

• LUWB(d) is the path-loss between the UWB device and the WiMAX receiver which varies

Taking into account that UWB devices are short range, the quasi free space path-loss model with shadowing is often most appropriate, especially when the distance between the UWB transmitter and the mobile receiver is lower than 8 m. Thus, in the WiMAX downlink frequency band, the UWB signal propagation loss LUWB(d), measured in dB at a distance d in

> <sup>4</sup> ( ) 20log 10 log ( ) 0, *UWB L d n dN* π

Where λ is the operating wavelength at the WiMAX frequency, n is the indoor propagation exponent (1.8 to 2.0) and N(0, σ) is a Gaussian variable of zero mean and a standard deviation of σ, representing the deviation from the path loss mean value (shadowing). Practical values of σ are in the range 1.8 to 3 dB in the line of sight LOS environment. Here we assume that the Gaussian variable N(0, σ) is truncated at ±4σ. In our case σ is assumed to

In the calculation of the propagation loss of the WiMAX signal we use the two-slope propagation loss model. Thus, for a distance higher than 100 m, the WiMAX signal

*<sup>d</sup> <sup>f</sup> <sup>h</sup> L A s L*

<sup>10</sup> <sup>10</sup> <sup>10</sup> 10 log 6 log 10.8log <sup>1900</sup> <sup>2</sup>

= + ++ + <sup>−</sup>

λ

 ≈ ++

( ) <sup>10</sup> <sup>10</sup>

σ

*RX*

(3)

(2)

• GRX\_WiMAX is the antenna gain of the WiMAX system in the receiving end.


The WiMAX received power per subcarrier SWiMAX\_sc is given as:

$$\mathbf{S}\_{\text{WiMAX\\_sc}} = \mathbf{P}\_{\text{WMAX\\_sc}} + \mathbf{G}\_{\text{Tx\\_WMAX}} - \mathbf{L}\_{\text{WiMAX}} + \mathbf{G}\_{\text{Rx\\_WMAX}} \tag{5}$$

where:


The WiMAX cochannel interference due to the macrocells using the same frequency band that exists within the three nearest clusters of 4 macrocells is given by:

$$I\_{cc-WiMAX} = S\_{WiMAX\\_sc} + 10\log\_{10} 3 \left(\frac{d}{\sqrt{12} \, R}\right)^{\gamma} \tag{6}$$

where R is the radius of the WiMAX macrocell.

For the UWB system the propagation loss with 99.995% confidence is given by:

$$L\_{\rmcupWB}(d) = 20\log\_{10}\left(\frac{4\pi}{\lambda}\right) + 10\ln\log\_{10}(d) - 4\,\sigma\tag{7}$$

For the WiMAX receiver, the signal to interference plus noise ratio SINR per subcarrier is given by:

$$SINR = 10\log\_{10}\left(\frac{S\_{\text{WiMAX\\_sc}}}{I\_{\text{CC\\_WiMAX}} + N\_{\text{rec\\_sc}} + I\_{\text{LIVB}}}\right) \tag{8}$$

where Icc-WiMAX is the WiMAX cochannel interference, Nrec is the receiver thermal noise, and IUWB is the UWB interference all given in real numbers.
