Method and apparatus for adjusting for higher order intermodulation products co-located with lower order intermodulation products

Abstract

A method and apparatus are provided. an indication of a first uplink resource allocation of resource blocks for a transmission on a first carrier, and an indication of a second uplink resource allocation of resource blocks for a transmission on a second carrier are received. An indication of a downlink allocation for receiving a downlink signal is further received. A higher order intermodulation product, which is co-located with a lower order intermodulation product for the first and second allocations resulting from any respective higher order and lower order transceiver nonlinearities is identified. A determination is then made as to whether the co-located higher order intermodulation products have a region of overlap with the downlink allocation. When the co-located higher order intermodulation products have a region of overlap with the downlink allocation, adjustments in the operation are made to account for the overlap of the higher order intermodulation product and the downlink allocation.

Claims

1. A method in a user equipment comprising: receiving an indication of a first uplink resource allocation of resource blocks for a transmission on a first carrier; receiving an indication of a second uplink resource allocation of resource blocks for a transmission on a second carrier, where the second carrier is different than the first carrier; receiving an indication of a downlink allocation for receiving a downlink signal; identifying a higher order intermodulation product for the first and second uplink resource allocations, which is co-located with a lower order intermodulation product for the first and second uplink resource allocations, resulting from any respective higher order and lower order transceiver nonlinearities, where a frequency of the higher order intermodulation product falls on top of a frequency of the lower order intermodulation product; determining whether the co-located higher order intermodulation product has a region of overlap with the downlink allocation; and adjusting the reference sensitivity requirement in the region of overlap between the higher order intermodulation product and the downlink allocation, when the co-located higher order intermodulation product has a region of overlap with the downlink allocation.

2. A method in accordance with claim 1, wherein adjusting the reference sensitivity requirement in the region of overlap between the higher intermodulation product and the downlink allocation includes relaxing the reference sensitivity.

3. A method in accordance with claim 2, wherein an amount that the reference sensitivity is relaxed corresponds to an amount of the noise rise in a receiver of the user equipment resulting from the higher order intermodulation product.

4. A method in accordance with claim 1, wherein adjusting the reference sensitivity requirement in the region of overlap between the higher intermodulation product and the downlink allocation includes a suspension of the reference sensitivity requirement.

5. A method in accordance with claim 1, wherein the lower order intermodulation product corresponds to a second order intermodulation product and the higher order intermodulation product corresponds to a fourth order intermodulation product.

6. A method in accordance with claim 1, wherein the lower order intermodulation product corresponds to a third order intermodulation product and the higher order intermodulation product corresponds to a fifth order intermodulation product.

7. A method in accordance with claim 1, wherein the higher order intermodulation product is two orders higher than the lower order intermodulation product.

8. A method in accordance with claim 1, wherein a difference in an order of the lower order intermodulation product and an order of the higher order intermodulation product is an even number.

9. A method in accordance with claim 1, wherein determining whether the co-located higher order intermodulation product has a region of overlap with the downlink allocation includes instances where the lower order intermodulation product does not have a region of overlap with the downlink allocation.

10. A method in accordance with claim 1, wherein the transmission on the first carrier and the transmission on the second carrier support carrier aggregation, which includes a combination of different spectrum bands to form a larger bandwidth channel to transmit data.

11. A method in accordance with claim 1, wherein the transmission on the first carrier and the transmission on the second carrier support dual carrier operation.

12. A user equipment in a communication network, the user equipment comprising: a transceiver that sends and receives signals between the user equipment and a network entity of the communication network including receiving an indication of a first uplink resource allocation of resource blocks for a transmission on a first carrier, receiving an indication of a second uplink resource allocation of resource blocks for a transmission on a second carrier, where the second carrier is different than the first carrier, and receiving an indication of a downlink allocation for receiving a downlink signal; and a controller that identifies a higher order intermodulation product for the first and second uplink resource allocations, which is co-located with a lower order intermodulation product for the first and second uplink resource allocations, resulting from any respective higher order and lower order transceiver nonlinearities, where a frequency of the higher order intermodulation product falls on top of a frequency of the lower order intermodulation product, and determines whether the co-located higher order intermodulation product has a region of overlap with the downlink allocation; wherein, when the co-located higher order intermodulation product has a region of overlap with the downlink allocation, the controller adjusts the reference sensitivity requirement in the region of overlap between the higher order intermodulation product and the downlink allocation.

13. A user equipment in accordance with claim 12, wherein adjusting the reference sensitivity requirement in the region of overlap between the higher intermodulation product and the downlink allocation by the controller includes relaxing the reference sensitivity.

14. A user equipment in accordance with claim 13, wherein an amount that the controller relaxes the reference sensitivity, corresponds to an amount of the noise rise in the transceiver resulting from the higher order intermodulation product.

15. A user equipment in accordance with claim 12, wherein adjusting the reference sensitivity requirement in the region of overlap between the higher intermodulation product and the downlink allocation by the controller includes a suspension of the reference sensitivity requirement.

16. A user equipment in accordance with claim 12, wherein the lower order intermodulation product corresponds to a second order intermodulation product and the higher order intermodulation product corresponds to a fourth order intermodulation product.

17. A user equipment in accordance with claim 12, wherein the lower order intermodulation product corresponds to a third order intermodulation product and the higher order intermodulation product correspond to a fifth order intermodulation product.

18. A user equipment in accordance with claim 12, wherein the higher order intermodulation product is two orders higher than the lower order intermodulation product.

19. A user equipment in accordance with claim 12, wherein a difference in a rank of the lower order intermodulation product and a rank of the higher order intermodulation product is an even number.

20. A user equipment in accordance with claim 12, wherein determining by the controller whether the co-located higher order intermodulation product has a region of overlap with the downlink allocation includes instances where the lower order intermodulation product does not have a region of overlap with the downlink allocation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a block diagram of an exemplary network environment in which the present invention is adapted to operate;

(2) FIG. 2 is a flow diagram in a user equipment for adjusting reference sensitivity requirement when higher order intermodulation products, which are co-located with lower order intermodulation products, overlap with a downlink allocation;

(3) FIG. 3 is a flow diagram in a network entity for selecting a downlink allocation for use by a user equipment for receiving a downlink signal, which avoids overlap with higher order intermodulation products that are co-located with lower order intermodulation products; and

(4) FIG. 4 is an exemplary block diagram of an apparatus according to a possible embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

(5) While the present disclosure is susceptible of embodiment in various forms, there is shown in the drawings and will hereinafter be described presently preferred embodiments with the understanding that the present disclosure is to be considered an exemplification of the invention and is not intended to limit the invention to the specific embodiments illustrated.

(6) Embodiments provide a method and apparatus for adjusting for higher order intermodulation products co-located with lower order intermodulation products.

(7) FIG. 1 is an example block diagram of a system 100 according to a possible embodiment. The system 100 can include a wireless communication device 110, such as User Equipment (UE), a base station 120, such as an enhanced NodeB (eNB) or next generation NodeB (gNB), and a network 130. The wireless communication device 110 can be a wireless terminal, a portable wireless communication device, a smartphone, a cellular telephone, a flip phone, a personal digital assistant, a personal computer, a selective call receiver, a tablet computer, a laptop computer, or any other device that is capable of sending and receiving communication signals on a wireless network.

(8) The network 130 can include any type of network that is capable of sending and receiving wireless communication signals. For example, the network 130 can include a wireless communication network, a cellular telephone network, a Time Division Multiple Access (TDMA)-based network, a Code Division Multiple Access (CDMA)-based network, an Orthogonal Frequency Division Multiple Access (OFDMA)-based network, a Long Term Evolution (LTE) network, a 5th generation (5G) network, a 3rd Generation Partnership Project (3GPP)-based network, a satellite communications network, a high altitude platform network, the Internet, and/or other communications networks.

(9) Recent co-existence studies for NSA NR have considered harmonics and intermodulation (IM) products up to at least 5th order to determine if they interfere with the UE downlink carrier or with other bands. One such example includes 3GPP TR 37.863-01-01 V0.3.0 (2017-11), entitled Dual connectivity (DC) band combinations of LTE 1DL/1UL+one NR band. At least one aspect which may be missing from this and other studies is the impact of higher order IM products which are co-located with lower order IM products. While these higher order IM's have less power than the lower order IM's with which they are co-located, they are wider and therefore may overlap the UE downlink or other hands even when the lower-order IM's do not. Furthermore, the higher order IM products which are co-located with the lower order IM's may have more power than the higher order IM products which are not co-located with lower order IM's. As a result, if the higher order MI products which are not co-located with lower order IM's have sufficient power to interfere with the downlink or with other bands, then it follows that the same may be true for the higher order IM products which are co-located with the lower order IM products.

(10) It can be noted that these co-located higher order IM's are implicitly addressed in the TS 36.101 spurious emission exceptions in the form of expanded regions for harmonic exceptions due to spectral “spreading”. The higher order co-located IM's are also implicitly addressed in the harmonic Refsens exceptions defined for the case when the harmonic does not overlap the UE downlink allocation but is adjacent to it.

(11) In accordance with at least one possible embodiment, the present disclosure includes defining the reference sensitivity power level (Refsens) relaxations or no Refens requirement for the user equipment (UE) in the case that a higher order intermodulation product of multiple uplink carriers is co-located with a lower order intermodulation product and the higher order intermodulation product overlaps one of the UE downlink allocations. Previously, the 3GPP RAN4 specification has defined Refsens relaxations or no Refsens requirement in the case that intermodulation products from multiple carriers fall on the UE's downlink allocation. However, RAN4 has ignored the issue of higher order intermodulation products which are co-located with lower order intermodulation products. While the higher order modulation products have less power, in general, than the lower order intermodulation products, these higher order modulation products have wider bandwidth and thus can impinge on the UE downlink allocation even when the lower order IM product does not. In the case that the lower order IM overlaps the UE's downlink, the region of overlap will be extended by the co-located higher order IM product.

(12) Historically, Refsens relaxations or no Refsens requirement may have generally been provided in the case that intermodulation products interfere with the UE's downlink receiver. However, they generally have failed to address instances, in which higher order intermodulation products are co-located with lower order intermodulation products and the higher order intermodulation products interfere with the UE's downlink receiver while the co-located lower order IM product does not. In the case that the lower order IM overlaps the UE's downlink, the region of overlap will be extended by the co-located higher order IM product. Examples of this issue can be shown by considering the fourth order intermodulation products that are co-located with the second order intermodulation products, and similarly, the fifth order intermodulation products that are co-located with third order intermodulation products. It can be noted that only ‘even’ higher order intermodulation products are co-located with ‘even’ lower order intermodulation products, and only ‘odd’ higher order intermodulation products are co-located with ‘odd’ lower order intermodulation products.

(13) According to a possible embodiment, it may be beneficial to identify the higher order intermodulation products which are co-located with lower order intermodulation products and which interfere with the UE's downlink allocation. For these higher-order intermodulation products co-located with lower order intermodulation products, it is may be beneficial to define Refsens relaxations or no Refsens requirement in the case that the higher order IM overlaps the UE's downlink allocation while the lower order IM does not. In the case that the lower order IM overlaps the UE's downlink, the region of overlap will be extended by the higher order IM and either Refsens relaxation or no Refsens requirement could be defined for this extended overlap region.

(14) The third, fourth, and fifth powers of a two carrier signal of the form
a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t)
can be expanded, where a.sub.1(t) denotes the modulation on the first carrier at f.sub.1=ω.sub.1/2π, which has bandwidth W.sub.1, and a.sub.2(t) denotes the modulation on the second carrier at f.sub.2=ω.sub.2/2π, which has bandwidth W.sub.2.
Third Order Nonlinearity Intermodulation Products

(15) Correspondingly, the two carrier third-order nonlinearity can be represented as:
(a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t)).sup.3
which expands, as follows:
(a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t))=0.25(a.sub.1(t)).sup.3 cos(3ω.sub.1t)+0.25(a.sub.2(t)).sup.3 cos(3ω.sub.2t)+0.75(a.sub.1(t)).sup.2a.sub.2(t)cos((2ω.sub.1−ω.sub.2)t)+0.75a.sub.1(t)(a.sub.2(t)).sup.2 cos((ω.sub.1−2ω.sub.2)t)+0.75(a.sub.1(t)).sup.2a.sub.2(t)cos((2ω.sub.1+ω.sub.2)t)+0.75a.sub.1(t)(a.sub.2(t)).sup.2 cos((ω.sub.1+2ω.sub.2)t)+(0.75(a.sub.1(t)).sup.3+1.5a.sub.1(t)(a.sub.2(t)).sup.2)cos(ω.sub.1t)+(0.75(a.sub.2(t)).sup.3+1.5(a.sub.1(t)).sup.2a.sub.2(t))cos(ω.sub.2t)

(16) The harmonics and IM products which result from the expansion can be found in Table 1, below. The terms noted with an asterisk, namely IM #'s 7-10, have typically not been included in co-existence studies. However, it should be noted that multiplicative coefficients for the noted terms are at least as large as those for the IM terms normally included for the third order non-linearity.

(17) TABLE-US-00001 TABLE 1 IM Products and Harmonics due to 3.sup.nd Order Non-linearity Center Multiplicative IM # Frequency IM Bandwidth Coefficient 1 3*f.sub.1 3*W.sub.1 0.25 2 3*f.sub.2 3*W.sub.2 0.25 3 | 2*f.sub.1 − f.sub.2 | 2*W.sub.1 + W.sub.2 0.75 4 | f.sub.1 − 2*f.sub.2 | W.sub.1 + 2*W.sub.2 0.75 5 2*f.sub.1 + f.sub.2 2*W.sub.1 + W.sub.2 0.75 6 f.sub.1 + 2*f.sub.2 W.sub.1 + 2*W.sub.2 0.75  7* f.sub.1 3*W.sub.1 0.75  8* f.sub.1 W.sub.1 + 2*W.sub.2 1.5  9* f.sub.2 3*W.sub.2 0.75 10* f.sub.2 2*W.sub.1 + W.sub.2 1.5

(18) The IM products 7 and 9 are the source of adjacent channel leakage in single carrier operation. The IM products 8 and 10 occur in dual-carrier operation and unless W.sub.1 and W.sub.2 are equal, one of these IM products will be wider than the corresponding IM for single carrier operation.

(19) If the multiplicative coefficient of each term is ignored, Table 1 can be simplified slightly as in Table 1 a below.

(20) TABLE-US-00002 TABLE 1a IM Products and Harmonics due to 3.sup.nd Order Non-linearity Center IM # Frequency IM Bandwidth 1 3*f.sub.1 3*W.sub.1 2 3*f.sub.2 3*W.sub.2 3 | 2*f.sub.1 − f.sub.2 | 2*W.sub.1 + W.sub.2 4 | f.sub.1 − 2*f.sub.2 | W.sub.1 + 2*W.sub.2 5 2*f.sub.1 + f.sub.2 2*W.sub.1 + W.sub.2 6 f.sub.1 + 2*f.sub.2 W.sub.1 + 2*W.sub.2  7* f.sub.1 max(3*W.sub.1, W.sub.1 + 2*W.sub.2)  8* f.sub.2 max(3*W.sub.2, W.sub.2 + 2*W.sub.1)
Fourth Order Nonlinearity Intermodulation Products

(21) The two carrier fourth-order nonlinearity can be represented as:
(a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t)).sup.4
which expands, as follows:

(22) ${\left(a_1\left(t\right)\cos \left({\omega }_{1}t\right)+a_2\left(t\right)\cos \left({\omega }_{2}t\right)\right)}^4={\left(\frac{1}{2}{a}_1\left(t\right)\left(\exp \left(j{\omega }_{1}t\right)+\exp \left(-j{\omega }_{1}t\right)\right)+\frac{1}{2}{a}_2\left(t\right)\left(\exp \left(j{\omega }_{2}t\right)+\exp \left(-j{\omega }_{2}t\right)\right)\right)}^4=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ ijk\end{array}\right){\left(a_1\left(t\right)\exp \left(j{\omega }_{1}t\right)\right)}^i{\left(a_1\left(t\right)\exp \left(-j{\omega }_{1}t\right)\right)}^j{\left(a_2\left(t\right)\exp \left(j{\omega }_{2}t\right)\right)}^k{\left(a_2\left(t\right)\exp \left(-j{\omega }_{2}t\right)\right)}^{4-i-j-k}=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ \mathrm{ijk}\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{4-i-j}{\exp \left(j{\omega }_{1}t\right)}^i{\exp \left(-j{\omega }_{1}t\right)}^j{\exp \left(j{\omega }_{2}t\right)}^k{\exp \left(-j{\omega }_{2}t\right)}^{4-i-j-k}=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ \mathrm{ijk}\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{4-i-j}{\exp \left(j{\omega }_{1}t\right)}^{i-j}{\exp \left(j{\omega }_{2}t\right)}^{2k+i+j-4}$
and can be similarly expressed as

(23) ${\left(a_1\left(t\right)\cos \left({\omega }_{1}t\right)+a_2\left(t\right)\cos \left({\omega }_{2}t\right)\right)}^4=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ ijk\end{array}\right){\left(a_1\left(t\right)\exp \left(j{\omega }_{1}t\right)\right)}^j{\left(a_1\left(t\right)\exp \left(-j{\omega }_{1}t\right)\right)}^i{\left(a_2\left(t\right)\exp \left(j{\omega }_{2}t\right)\right)}^{4-i-j-k}{\left(a_2\left(t\right)\exp \left(-j{\omega }_{2}t\right)\right)}^k=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{4-i-j}{\exp \left(j{\omega }_{1}t\right)}^j{\exp \left(-j{\omega }_{1}t\right)}^i{\exp \left(j{\omega }_{2}t\right)}^{4-i-j-k}{\exp \left(-j{\omega }_{2}t\right)}^k=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{4-i-j}{\exp \left(j{\omega }_{1}t\right)}^{j-i}{\exp \left(j{\omega }_{2}t\right)}^{4-i-j-2k}$

(24) Summing the two expressions and dividing by two yields

(25) ${\left(a_1\left(t\right)\cos \left({\omega }_{1}t\right)+a_2\left(t\right)\cos \left({\omega }_{2}t\right)\right)}^4=\frac{1}{32}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{4-i-j}\left({\exp \left(j{\omega }_{1}t\right)}^{i-j}{\exp \left(j{\omega }_{2}t\right)}^{2k+i+j-4}+{\exp \left(j{\omega }_{1}t\right)}^{j-i}{\exp \left(j{\omega }_{2}t\right)}^{4-i-j-2k}\right)=\frac{1}{16}\underset{i=0}{\overset{4}{.Math.}}\underset{j=0}{\overset{4-i}{.Math.}}\underset{k=0}{\overset{4-i-j}{.Math.}}\left(\begin{array}{c}4\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{4-i-j}\cos \left(\left(\left(i-j\right){\omega }_1+\left(2k+i+j-4\right){\omega }_2\right)t\right)$

(26) Performing the summation and combining terms yields the following expansion:
(a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t).sup.4=0.125(a.sub.1(t)).sup.4 cos(4ω.sub.1t)+0.125(a.sub.2(t)).sup.4 cos(4ω.sub.2t)+0.5(a.sub.1(t)).sup.3a.sub.2(t)cos((3ω.sub.1−ω.sub.2)t)+0.5a.sub.1(t)(a.sub.2(t)).sup.3 cos((ω.sub.1−3ω.sub.2)t)+0.5(a.sub.1(t)).sup.3a.sub.2(t)cos((3ω.sub.1+ω.sub.2)t)+0.5a.sub.1(t)(a.sub.2(t)).sup.3 cos((ω.sub.1+3ω.sub.2)t)+0.75(a.sub.1(t)).sup.2(a.sub.2(t)).sup.2 cos((2ω.sub.1−2ω.sub.2)t)+0.75(a.sub.1(t)).sup.2(a.sub.2(t)).sup.2 cos((2ω.sub.1+2ω.sub.2)t)+1.5((a.sub.1(t)).sup.3a.sub.2(t)+a.sub.1(t)(a.sub.3(t)).sup.3)cos((ω.sub.1−ω.sub.2)t)+1.5((a.sub.1(t)).sup.3a.sub.2(t)+a.sub.1(t)(a.sub.3(t)).sup.3)cos((ω.sub.1+ω.sub.2)t)+(0.5(a.sub.1(t)).sup.4+1.5(a.sub.1(t)).sup.2(a.sub.2(t)).sup.2 cos(2ω.sub.1t)+(0.5(a.sub.2(t))+1.5(a.sub.1(t)).sup.2(a.sub.2(t)).sup.2)cos(2ω.sub.2t)+0.375(a.sub.1(t)).sup.4+1.5(a.sub.1(t)).sup.2(a.sub.2(t)).sup.2+0.375(a.sub.2(t)).sup.4

(27) The harmonics and IM products which result from the expansion can be found in Table 2, below. The terms noted with an asterisk (direct current terms are excluded), namely IM #'s 9-16, have typically not been included in co-existence studies. However, it should be noted that multiplicative coefficients for the noted terms are at least as large as those for the IM terms normally included for the fourth order non-linearity.

(28) The IM terms 13 and 15 at 2*f.sub.1 and 2*f.sub.2, respectively, occur also in single carrier operation and may have been addressed previously by allowing for spectral “spreading” when defining spurious exceptions for the second harmonic and also for defining Refsens relaxations for harmonics adjacent to the downlink allocation. This spectral spreading is actually due to an IM term generated by a 4th order (or higher even order) non-linearity falling on top of the second harmonic.

(29) TABLE-US-00003 TABLE 2 IM Products and Harmonics due to 4.sup.th Order Non-linearity Center Multiplicative IM # Frequency IM Bandwidth Coefficient 1 4*f.sub.1 4*W.sub.1 0.125 2 4*f.sub.2 4*W.sub.2 0.125 3 | 3*f.sub.1 − f.sub.2 | 3*W.sub.1 + W.sub.2 0.5 4 | f.sub.1 − 3*f.sub.2 | W.sub.1 + 3*W.sub.2 0.5 5 3*f.sub.1 + f.sub.2 3*W.sub.1 + W.sub.2 0.5 6 f.sub.1 + 3*f.sub.2 W.sub.1 + 3*W.sub.2 0.5 7 | 2*f.sub.1 − 2*f.sub.2 | 2*W.sub.1 + 2*W.sub.2 0.75 8 2*f.sub.1 + 2*f.sub.2 2*W.sub.2 + 2*W.sub.1 0.75  9* | f.sub.1 − f.sub.2 | 3*W.sub.1 + W.sub.2 1.5 10* | f.sub.1 − f.sub.2 | W.sub.1 + 3*W.sub.2 1.5 11* f.sub.1 + f.sub.2 3*W.sub.1 + W.sub.2 1.5 12* f.sub.1 + f.sub.2 W.sub.1 + 3*W.sub.2 1.5 13* 2*f.sub.1 4*W.sub.1 0.5 14* 2*f.sub.1 2*W.sub.1 + 2*W.sub.2 1.5 15* 2*f.sub.2 4*W.sub.2 0.5 16* 2*f.sub.2 2*W.sub.1 + 2*W.sub.2 1.5 17  0 4*W.sub.1 0.375 18  0 2*W.sub.1 + 2*W.sub.2 1.5 19  0 4*W.sub.2 0.375

(30) If the multiplicative coefficient of each term is ignored and the direct current terms are removed, Table 2 can be simplified slightly as in Table 2a below.

(31) TABLE-US-00004 TABLE 2a IM Products and Harmonics due to 4.sup.th Order Non-linearity Center IM # Frequency IM Bandwidth 1 4*f.sub.1 4*W.sub.1 2 4*f.sub.2 4*W.sub.2 3 | 3*f.sub.1 − f.sub.2 | 3*W.sub.1 + W.sub.2 4 | f.sub.1 − 3*f.sub.2 | W.sub.1 + 3*W.sub.2 5 3*f.sub.1 + f.sub.2 3*W.sub.1 + W.sub.2 6 f.sub.1 + 3*f.sub.2 W.sub.1 + 3*W.sub.2 7 | 2*f.sub.1 − 2*f.sub.2 | 2*W.sub.1 + 2*W.sub.2 8 2*f.sub.1 + 2*f.sub.2 2*W.sub.2 + 2*W.sub.1  9* | f.sub.1 − f.sub.2 | max(3*W.sub.1 + W.sub.2, W.sub.1 + 3*W.sub.2) 10* f.sub.1 + f.sub.2 max(3*W.sub.1 + W.sub.2, W.sub.1 + 3*W.sub.2) 11* 2*f.sub.1 max(4*W.sub.1, 2*W.sub.1 + 2*W.sub.2) 12* 2*f.sub.2 max(4*W.sub.2, 2*W.sub.1 + 2*W.sub.2)
Fifth Order Nonlinearity Intermodulation Products

(32) The two carrier fifth-order nonlinearity can be represented as:
(a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t)).sup.5
which expands, as follows:

(33) ${\left(a_1\left(t\right)\cos \left({\omega }_{1}t\right)+a_2\left(t\right)\cos \left({\omega }_{2}t\right)\right)}^5={\left(\frac{1}{2}{a}_1\left(t\right)\left(\exp \left(j{\omega }_{1}t\right)+\exp \left(-j{\omega }_{1}t\right)\right)+\frac{1}{2}{a}_2\left(t\right)\left(\exp \left(j{\omega }_{2}t\right)+\exp \left(-j{\omega }_{2}t\right)\right)\right)}^5=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\exp \left(j{\omega }_{1}t\right)\right)}^i{\left(a_1\left(t\right)\exp \left(-j{\omega }_{1}t\right)\right)}^j{\left(a_2\left(t\right)\exp \left(j{\omega }_{2}t\right)\right)}^k{\left(a_2\left(t\right)\exp \left(-j{\omega }_{2}t\right)\right)}^{5-i-j-k}=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{5-i-j}{\exp \left(j{\omega }_{1}t\right)}^i{\exp \left(-j{\omega }_{1}t\right)}^j{\exp \left(j{\omega }_{2}t\right)}^k{\exp \left(-j{\omega }_{2}t\right)}^{5-i-j-k}=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{5-i-j}{\exp \left(j{\omega }_{1}t\right)}^{i-j}{\exp \left(j{\omega }_{2}t\right)}^{2k+i+j-5}$
and can similarly be expressed as

(34) ${\left(a_1\left(t\right)\cos \left({\omega }_{1}t\right)+a_2\left(t\right)\cos \left({\omega }_{2}t\right)\right)}^5=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\exp \left(j{\omega }_{1}t\right)\right)}^j{\left(a_1\left(t\right)\exp \left(-j{\omega }_{1}t\right)\right)}^i{\left(a_2\left(t\right)\exp \left(j{\omega }_{2}t\right)\right)}^{5-i-j-k}{\left(a_2\left(t\right)\exp \left(-j{\omega }_{2}t\right)\right)}^k=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{5-i-j}{\exp \left(j{\omega }_{1}t\right)}^j{\exp \left(-j{\omega }_{1}t\right)}^i{\exp \left(j{\omega }_{2}t\right)}^{5-i-j-k}{\exp \left(-j{\omega }_{2}t\right)}^k=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{5-i-j}{\exp \left(j{\omega }_{1}t\right)}^{j-i}{\exp \left(j{\omega }_{2}t\right)}^{5-i-j-2k}$

(35) Summing the two expressions and dividing by two yields

(36) ${\left(a_1\left(t\right)\cos \left({\omega }_{1}t\right)+a_2\left(t\right)\cos \left({\omega }_{2}t\right)\right)}^5=\frac{1}{64}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{1+j}{\left(a_2\left(t\right)\right)}^{5-i-j}\left({\exp \left(j{\omega }_{1}t\right)}^{i-j}{\exp \left(j{\omega }_{2}t\right)}^{2k+i+j-5}+{\exp \left(j{\omega }_{1}t\right)}^{j-i}{\exp \left(j{\omega }_{2}t\right)}^{5-i-j-2k}\right)=\frac{1}{32}\underset{i=0}{\overset{5}{.Math.}}\underset{j=0}{\overset{5-i}{.Math.}}\underset{k=0}{\overset{5-i-j}{.Math.}}\left(\begin{array}{c}5\\ ijk\end{array}\right){\left(a_1\left(t\right)\right)}^{i+j}{\left(a_2\left(t\right)\right)}^{5-i-j}\cos \left(\left(\left(i-j\right){\omega }_1+\left(2k+i+j-5\right){\omega }_2\right)t\right)$

(37) Performing the summation and combining terms yields the following expansion:
(a.sub.1(t)cos(ω.sub.1t)+a.sub.2(t)cos(ω.sub.2t)).sup.5=0.0625(a.sub.1(t)).sup.5 cos(5ω.sub.1t)+0.3125(a.sub.1(t)).sup.4a.sub.2(t)cos((4ω.sub.1−ω.sub.2)t)+0.3125(a.sub.1(t)).sup.4a.sub.2(t)cos((4ω.sub.1+ω.sub.2)t)+0.625(a.sub.1(t)).sup.3(a.sub.2(t)).sup.2 cos((3ω.sub.1−2ω.sub.2)t)+0.625(a.sub.1(t)).sup.3(a.sub.2(t)).sup.2 cos((3ω.sub.1+2ω.sub.2)t)+0.625(a.sub.1(t)).sup.2(a.sub.2(t)).sup.3 cos((3ω.sub.2−2ω.sub.1)t)+0.625(a.sub.1(t)).sup.2(a.sub.2(t)).sup.3 cos((3ω.sub.2+2ω.sub.1)t)+0.3125a.sub.1(t)(a.sub.2(t)).sup.4 cos((4ω.sub.2−ω.sub.1)t)+0.3125a.sub.1(t)(a.sub.2(t)).sup.4 cos((4ω.sub.2+ω.sub.1)t)+0.0625(a.sub.2(t)).sup.5 cos(5ω.sub.2)+(0.3125(a.sub.1(t)).sup.5+1.25(a.sub.1(t)).sup.3(a.sub.2(t)).sup.2)cos(3ω.sub.1t)+(1.25(a.sub.1(t)).sup.4a.sub.2(t)+1.875(a.sub.1(t)).sup.2(a.sub.2(t)).sup.3)cos((2ω.sub.1−ω.sub.2)t)+(1.25(a.sub.1(t)).sup.4a.sub.2(t)+1.875(a.sub.1(t)).sup.2(a.sub.2(t)).sup.3)cos((2ω.sub.1+ω.sub.2)t)+(1.875(a.sub.1(t)).sup.3(a.sub.2(t)).sup.2+1.25a.sub.1(t)(a.sub.2(t)).sup.4)cos((2ω.sub.2−ω.sub.1)t)+(1.875(a.sub.1(t)).sup.3(a.sub.2(t)).sup.2+1.25a.sub.1(t)(a.sub.2(t)).sup.4)cos((2ω.sub.2+ω.sub.1)t)+(1.25(a.sub.1(t)).sup.2(a.sub.2(t)).sup.3+0.3125(a.sub.2(t)).sup.5)cos(3ω.sub.2t)+(0.625(a.sub.1(t)).sup.5+3.75(a.sub.1(t)).sup.3(a.sub.2(t)).sup.2+1.875a.sub.1(t)(a.sub.2(t)).sup.4)cos(ω.sub.1t)+(1.875(a.sub.1(t)).sup.4a.sub.2(t)+3.75(a.sub.1(t)).sup.2(a.sub.2(t)).sup.3+0.625(a.sub.2(t)).sup.5)cos(ω.sub.2t)

(38) The harmonics and IM products which result from the expansion can be found in Table 3, below. The terms noted with an asterisk, namely IM #'s 11-28, have typically not been included in co-existence studies. However, it should be noted that multiplicative coefficients for the noted terms are at least as large as those for the IM terms normally included for the fifth order non-linearity.

(39) The IM terms 11 and 13 at 3*f.sub.1 and 3*f.sub.2, respectively, occur also in single carrier operation and have been addressed previously by allowing for spectral “spreading” when defining spurious exceptions for the third harmonic and also for defining Refsens relaxations for harmonics adjacent to the downlink allocation. This spectral spreading is actually due to an IM term generated by a 5.sup.th order (or higher odd order) non-linearity falling on top of the third harmonic.

(40) TABLE-US-00005 TABLE 3 IM Products and Harmonics due to 5.sup.nd Order Non-linearity Center Multiplicative IM # Frequency IM Bandwidth Coefficient 1 5*f.sub.1 5*W.sub.1 0.0625 2 5*f.sub.2 5*W.sub.2 0.0625 3 | 4*f.sub.1 − f.sub.2 | 4*W.sub.1 + W.sub.2 0.3125 4 | f.sub.1 − 4*f.sub.2 | W.sub.1 + 4*W.sub.2 0.3125 5 4*f.sub.1 + f.sub.2 4*W.sub.1 + W.sub.2 0.3125 6 f.sub.1 + 4*f.sub.2 W.sub.1 + 4*W.sub.2 0.3125 7 | 3*f.sub.1 − 2*f.sub.2 | 3*W.sub.1 + 2*W.sub.2 0.625 8 | 2*f.sub.1 − 3*f.sub.2 | 2*W.sub.2 + 3*W.sub.1 0.625 9 3*f.sub.1 + 2*f.sub.2 3*W.sub.1 + 2*W.sub.2 0.625 10  2*f.sub.1 + 3*f.sub.2 2*W.sub.2 + 3*W.sub.1 0.625 11* 3*f.sub.1 5*W.sub.1 0.3125 12* 3*f.sub.1 3*W.sub.1 + 2*W.sub.2 1.25 13* 3*f.sub.2 5*W.sub.2 0.3125 14* 3*f.sub.2 2*W.sub.1 + 3*W.sub.2 1.25 15* | 2*f.sub.1 − f.sub.2 | 4*W.sub.1 + W.sub.2 1.25 16* | 2*f.sub.1 − f.sub.2 | 2*W.sub.1 + 3*W.sub.2 1.875 17* | f.sub.1 − 2*f.sub.2 | W.sub.1 + 4*W.sub.2 1.25 18* | f.sub.1 − 2*f.sub.2 | 3*W.sub.1 + 2*W.sub.2 1.875 19* 2*f.sub.1 + f.sub.2 4*W.sub.1 + W.sub.2 1.25 20* 2*f.sub.1 + f.sub.2 2*W.sub.1 + 3*W.sub.2 1.875 21* f.sub.1 + 2*f.sub.2 W.sub.1 + 4*W.sub.2 1.25 22* f.sub.1 + 2*f.sub.2 3*W.sub.1 + 2*W.sub.2 1.875 23* f.sub.1 5*W.sub.1 0.625 24* f.sub.1 3*W.sub.1 + 2*W.sub.2 3.75 25* f.sub.1 W.sub.1 + 4*W.sub.2 1.875 26* f.sub.2 5*W.sub.2 0.625 27* f.sub.2 2*W.sub.1 + 3*W.sub.2 3.75 28* f.sub.2 4*W.sub.1 + W.sub.2 1.875

(41) If the multiplicative coefficient of each term is ignored, Table 3 can be simplified slightly as in Table 3a below.

(42) TABLE-US-00006 TABLE 3a IM Products and Harmonics due to 5.sup.nd Order Non-linearity Center IM # Frequency IM Bandwidth 1 5*f.sub.1 5*W.sub.1 2 5*f.sub.2 5*W.sub.2 3 | 4*f.sub.1 − f.sub.2 | 4*W.sub.1 + W.sub.2 4 | f.sub.1 − 4*f.sub.2 | W.sub.1 + 4*W.sub.2 5 4*f.sub.1 + f.sub.2 4*W.sub.1 + W.sub.2 6 f.sub.1 + 4*f.sub.2 W.sub.1 + 4*W.sub.2 7 | 3*f.sub.1 − 2*f.sub.2 | 3*W.sub.1 + 2*W.sub.2 8 | 2*f.sub.1 − 3*f.sub.2 | 2*W.sub.2 + 3*W.sub.1 9 3*f.sub.1 + 2*f.sub.2 3*W.sub.1 + 2*W.sub.2 10  2*f.sub.1 + 3*f.sub.2 2*W.sub.2 + 3*W.sub.1 11* 3*f.sub.1 max(5*W.sub.1, 3*W.sub.1 + 2*W.sub.2) 12* 3*f.sub.2 max(5*W.sub.2, 2*W.sub.1 + 3*W.sub.2) 13* | 2*f.sub.1 − f.sub.2 | max(4*W.sub.1 + W.sub.2, 2*W.sub.1 + 3*W.sub.2) 14* | f.sub.1 − 2*f.sub.2 | max(W.sub.1 + 4*W.sub.2, 3*W.sub.1 + 2*W.sub.2) 15* 2*f.sub.1 + f.sub.2 max(4*W.sub.1 + W.sub.2, 2*W.sub.1 + 3*W.sub.2) 16* f.sub.1 + 2*f.sub.2 max(W.sub.1 + 4*W.sub.2, 3*W.sub.1 + 2*W.sub.2) 17* f.sub.1 max(5*W.sub.1, 3*W.sub.1 + 2*W.sub.2, W.sub.1 + 4*W.sub.2) 18* f.sub.2 max(5*W.sub.2, 2*W.sub.1 + 3*W.sub.2, 4*W.sub.1 + W.sub.2)

(43) As such, the two-carrier third, fourth and fifth order nonlinearities have been expanded in order to enumerate the intermodulation terms and harmonics resulting from these nonlinearities. Recent co-existence studies for NSA NR have generally not included the IM products generated by higher order non-linearities which fall on top of IM products generated by lower order non-linearities. However, as these co-located higher order IM products may have more power than the higher order IM products which are not co-located with lower order IM's, they should also be included in the NSA NR co-existence studies. Thus, it would be beneficial for the noted IM products in Tables 1, 2, and 3 be considered for inclusion in the dual-carrier self-defense analysis, such as for non-standalone (NSA) fifth generation (5G) standards, and corresponding reference sensitivity relaxations be defined, if necessary, including where the IM products fall in a downlink allocation.

(44) FIG. 2 illustrates a flow diagram 200 in a user equipment for adjusting reference sensitivity requirement when higher order intermodulation products, which are co-located with lower order intermodulation products overlap with a downlink allocation. More specifically, the flow diagram 200 is illustrative of a method, and includes receiving 202 an indication of a first uplink resource allocation of resource blocks for a transmission on a first carrier, and receiving 204 an indication of a second uplink resource allocation of resource blocks for a transmission on a second carrier. An indication of a downlink allocation for receiving a downlink signal is further received 206. A higher order intermodulation product, which is co-located with a lower order intermodulation product for the first and second allocations resulting from any respective higher order and lower order transceiver nonlinearities is identified 208. A determination 210 is then made as to whether the co-located higher order intermodulation products have a region of overlap with the downlink allocation. When the co-located higher order intermodulation products have a region of overlap with the downlink allocation, the reference sensitivity requirement in the region of overlap between the higher order intermodulation product and the downlink allocation is adjusted 212.

(45) A method consistent with flow diagram 200 illustrated in FIG. 2 can further provide for where adjusting the reference sensitivity requirement in the region of overlap between the higher intermodulation product and the downlink allocation includes relaxing the reference sensitivity. In some instances, an amount that the reference sensitivity is relaxed can correspond to an amount of the noise rise in a receiver of the user equipment resulting from the higher order intermodulation product. In some instances, adjusting the reference sensitivity requirement in the region of overlap between the higher intermodulation product and the downlink allocation can include a suspension of the reference sensitivity requirement.

(46) In some instances, the lower order intermodulation product can correspond to a second order intermodulation product and the higher order intermodulation product can correspond to a fourth order intermodulation product. In some instances, the lower order intermodulation product can correspond to a third order intermodulation product and the higher order intermodulation product can correspond to a fifth order intermodulation product. In some instances, the higher order intermodulation product can be two orders higher than the lower order intermodulation product. In some instances, a difference in an order of the lower order intermodulation product and an order of the higher order intermodulation product can be an even number.

(47) In some instances, determining whether the co-located higher order intermodulation products have a region of overlap with the downlink allocation can include instances where the lower order intermodulation products do not have a region of overlap with the downlink allocation.

(48) In some instances, the transmission on the first carrier and the transmission on the second carrier can support carrier aggregation, which includes a combination of different spectrum bands to form a larger channel to transmit data. In some instances, the transmission on the first carrier and the transmission on the second carrier can support dual carrier operation.

(49) FIG. 3 is a flow diagram 300 in a network entity for selecting a downlink allocation for use by a user equipment for receiving a downlink signal, which avoids overlap with higher order intermodulation products that are co-located with lower order intermodulation products. The flow diagram 300 is similarly illustrative of a method. The flow diagram 300 includes selecting 302 a first uplink resource allocation of resource blocks for a transceiver of a user equipment on a first carrier, and selecting 304 a second uplink resource allocation of resource blocks for the transceiver of the user equipment on a second carrier. A higher order intermodulation product, which is co-located with a lower order intermodulation product for the first and second uplink resource allocations resulting from any respective higher order and lower order transceiver nonlinearities in the transceiver of the user equipment is then identified 306. A downlink allocation for receiving a downlink signal is then selected 308, such that the selected downlink allocation avoids overlapping with any higher order intermodulation products, which is identified as being co-located with a lower order intermodulation product for the first and second uplink resource allocations. An indication of the first uplink resource allocation, the second uplink resource allocation, and the downlink allocation is then transmitted 310 to the user equipment for use in communicating with the network entity.

(50) FIG. 4 is an exemplary block diagram of an apparatus 400, such as the wireless communication device 110, according to a possible embodiment. The apparatus 400 can include a housing 410, a controller 420 within the housing 410, audio input and output circuitry 430 coupled to the controller 420, a display 440 coupled to the controller 420, a transceiver 450 coupled to the controller 420, an antenna 455 coupled to the transceiver 450, a user interface 460 coupled to the controller 420, a memory 470 coupled to the controller 420, and a network interface 480 coupled to the controller 420. The apparatus 400 can perform the methods described in all the embodiments

(51) The display 440 can be a viewfinder, a liquid crystal display (LCD), a light emitting diode (LED) display, a plasma display, a projection display, a touch screen, or any other device that displays information. The transceiver 450 can include a transmitter and/or a receiver. The audio input and output circuitry 430 can include a microphone, a speaker, a transducer, or any other audio input and output circuitry. The user interface 460 can include a keypad, a keyboard, buttons, a touch pad, a joystick, a touch screen display, another additional display, or any other device useful for providing an interface between a user and an electronic device. The network interface 480 can be a Universal Serial Bus (USB) port, an Ethernet port, an infrared transmitter/receiver, an IEEE 1394 port, a WLAN transceiver, or any other interface that can connect an apparatus to a network, device, or computer and that can transmit and receive data communication signals. The memory 470 can include a random access memory, a read only memory, an optical memory, a solid state memory, a flash memory, a removable memory, a hard drive, a cache, or any other memory that can be coupled to an apparatus.

(52) The apparatus 400 or the controller 420 may implement any operating system, such as Microsoft Windows®, UNIX®, or LINUX®, Android™, or any other operating system. Apparatus operation software may be written in any programming language, such as C, C++, Java or Visual Basic, for example. Apparatus software may also run on an application framework, such as, for example, a Java® framework, a .NET® framework, or any other application framework. The software and/or the operating system may be stored in the memory 470 or elsewhere on the apparatus 400. The apparatus 400 or the controller 420 may also use hardware to implement disclosed operations. For example, the controller 420 may be any programmable processor. Disclosed embodiments may also be implemented on a general-purpose or a special purpose computer, a programmed microprocessor or microprocessor, peripheral integrated circuit elements, an application-specific integrated circuit or other integrated circuits, hardware/electronic logic circuits, such as a discrete element circuit, a programmable logic device, such as a programmable logic array, field programmable gate-array, or the like. In general, the controller 420 may be any controller or processor device or devices capable of operating an apparatus and implementing the disclosed embodiments. Some or all of the additional elements of the apparatus 400 can also perform some or all of the operations of the disclosed embodiments.

(53) The flow diagrams and/or methods of this disclosure can be implemented on a programmed processor. However, the controllers, flowcharts, and modules may also be implemented on a general purpose or special purpose computer, a programmed microprocessor or microcontroller and peripheral integrated circuit elements, an integrated circuit, a hardware electronic or logic circuit such as a discrete element circuit, a programmable logic device, or the like. In general, any device on which resides a finite state machine capable of implementing the flowcharts shown in the figures may be used to implement the processor functions of this disclosure.

(54) While this disclosure has been described with specific embodiments thereof, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art. For example, various components of the embodiments may be interchanged, added, or substituted in the other embodiments. Also, all of the elements of each figure are not necessary for operation of the disclosed embodiments. For example, one of ordinary skill in the art of the disclosed embodiments would be enabled to make and use the teachings of the disclosure by simply employing the elements of the independent claims. Accordingly, embodiments of the disclosure as set forth herein are intended to be illustrative, not limiting. Various changes may be made without departing from the spirit and scope of the disclosure.

(55) In this document, relational terms such as “first”, “second”, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. The phrase “at least one of”, “at least one selected from the group of”, or “at least one selected from” followed by a list is defined to mean one, some, or all, but not necessarily all of, the elements in the list. The terms “comprises”, “comprising”, “including”, or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “a”, “an”, or the like does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. Also, the term “another” is defined as at least a second or more. The terms “including”, “having”, and the like, as used herein, are defined as “comprising”. Furthermore, the background section is written as the inventor's own understanding of the context of some embodiments at the time of filing and includes the inventor's own recognition of any problems with existing technologies and/or problems experienced in the inventor's own work.