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## Understanding Inverse Slots

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Protege-Frames User's Guide
Slots
The Slots Tab
The Slot Browser
The Slot Buttons
The Slot Editor
The Value Type Menu
The Any Value Type
The Boolean Value Type
The Class Value Type
The Float Value Type
The Instance Value Type
The Integer Value Type
The String Value Type
The Symbol Value Type
Creating a New Slot
Viewing a Slot
Editing a Top-Level Slot
Overriding Slot Properties at a Class
Editing Slot Properties
Removing a Slot from a Class
Deleting a Slot from the Project
Adding a Slot to a Class
Removing Overrides From a Slot
Understanding Inverse Slots
Creating an Inverse Slot Relationship
Working with Subslots
Finding a Slot
The Slot Hierarchy Window
The Slot Icons
The Superslots Pane
Glossary, Editing Help

This topic gives an overview of how to analyze a projectand design inverse slots in Protege-Frames.An inverse slot relationship is a reciprocal relationship between two slots.Whenever one slot is filled in at one instance,its inverse slot is automatically filled in at another instance,according to the relationship you specified.

This topic describes the most common relationship -an inverse slot relationship between two instances,including the following steps:identifying an inverse relationship,analyzing the Protege-Frames components of the relationship,implementing the relationship in Protege-Frames.

You create inverse slots using the Inverse Slot widgetin the Slot Editor.For more information on how to use the user interface,see Creating an Inverse Slot Relationship.Note that if you create an inverse slot relationshipafter one or more instances have been created,existing instances will not display the inverse slot information.

### Example

For example, suppose you want to keep track at the section levelof which editor(s) edit which section(s).There is already a slot named sections at the class Editor;it takes instances in the class Section as values:

You could create an inverse slot named editor at the class Sectionwhich takes instances in the class Editor as values:

Now, when you edit the instance Mr. Scienceto assign the value Science to the slot sections,the inverse relationship is tracked by Protege-Frames.At the instance Science, Mr. Science automatically appearsas a value for the slot editor.

### Identifying the Relationship

First, you must determine if an inverse slotwill appropriately represent the structure of your knowledge base.An inverse slot represents a reciprocal relationship that always occurs.For example, if Mr. Science edits the Science section,the Science section is edited by Mr. Science.Protege-Frames supports several different types of inverse relationships:

1. The relationship must be reciprocal.

2. The relationship can be a one-to-one correspondence, or one or both of the slots can have multiple values. For example, Chief Honcho edits a number of sections.

3. The relationship can be between instances in different classes or instances in the same class. For example, likes and is_liked_by would be a relationship where the slot and its inverse slot are both attached to Person.

4. A slot can be its own inverse. shares_ an_ office_ with would be a candidate for an inverse relationship where the inverse slot was identical with the original slot. This is a stronger tie than simply having instances in the same class.

### Analyzing the Relationship for Protege-Frames

Once you have identified the relationship in your ontology,you need to analyze it in terms of your Protege-Frames project.For an inverse slot relationship between Instance slots,determine the following:

• What Protege-Frames class(es) do you want for the first set of instances? We will call this first list of classes Class_List_A.

• Make sure to choose a class or classes that are appropriate for the project.

• It is most important to choose a class list that is not too small; that is, you need to select a list of classes such that every possible instance is in one of those classes.

• At the same time, for simplicity, you want the class list to be focused on the instances and not be too broad.

• This list may consist of a single class. For example, in the newspaper project, one of the reporters, Larry Tennis-Nut, is an eager beaver and sometimes edits the Sports section. It would make sense to expand the list of classes to Editor and Reporter. However, no salesmen or columnists are allowed to edit a section. Therefore, while it would be possible to simply use the class Employee, it is cleaner not to.

• If the second set of instances is different from the first, perform the same analysis for the second set of instances. Call this second list of classes Class_List_B.

• As before. this list may be a single class.

• This list may be identical to Class_List_A.

### Steps Required for Implementing the Relationship

In this example, we will restrict ourselves to instances in the class Section.

The following steps are necessary to create an inverse slot relationshipin a Protege-Frames project:

1. Create a slot of type Instance whose allowed classes are Class_List_A. We'll call this the original_slot.

2. Create another slot of type Instance whose allowed classes are Class_List_B. We'll call this the inverse_slot. If the information is important in your ontology, it is likely that one or both of these slots already exist in the project.

3. Attach your Protege-Frames slots to the appropriate classes.

• First, add original_slot to every class in Class_List_B. Recall that the target values of original_slot are in Class_List_A. Assigning the slot to Class_List_B is what creates the cross-connection between the classes.

• Similarly, assign inverse_slot to every class in Class_List_A.

4. Create the inverse relationship between inverse_slot and original_slot. (You can actually do this as soon as both slots are created.)

If you already have a slot original_slot of type Instance in your projectand it already has the desired allowed classes and domain,you can create a new slot specifically as the inverse of original_slot.In this case, the inverse_slot has the following properties;you can edit them after creation if necessary:

• inverse_slot is automatically attached to all classes in the list of allowed classes for original_slot.

• its allowed classes automatically includes the list of all the classes where original_slot is attached.

For information on how to use the Protege-Frames interface to make an inverse slot,see Creating an Inverse Slot Relationship.

## Synchronization Signals (PSS and SSS)

In LTE, there are two downlink synchronization signals which are used by the UE to obtain the cell identity and frame timing.

• Primary synchronization signal (PSS)

• Secondary synchronization signal (SSS)

The division into two signals is aimed to reduce the complexity of the cell search process.

### Cell Identity Arrangement

The physical cell identity, ${N}_{ID}^{cell}$, is defined by the equation:

• ${N}_{ID}^{\left(1\right)}$ is the physical layer cell identity group (0 to 167).

• ${N}_{ID}^{\left(2\right)}$ is the identity within the group (0 to 2).

This arrangement creates 504 unique physical cell identities.

### Synchronization Signals and Determining Cell Identity

The primary synchronization signal (PSS) is linked to the cell identity within the group (${N}_{ID}^{\left(2\right)}$). The secondary synchronization signal (SSS) is linked to the cell identity group (${N}_{ID}^{\left(1\right)}$) and the cell identity within the group (${N}_{ID}^{\left(2\right)}$).

You can obtain ${N}_{ID}^{\left(2\right)}$ by successfully demodulating the PSS. The SSS can then be demodulated and combined with knowledge of ${N}_{ID}^{\left(2\right)}$ to obtain ${N}_{ID}^{\left(1\right)}$. Once you establish the values of ${N}_{ID}^{\left(1\right)}$ and ${N}_{ID}^{\left(2\right)}$, you can determine the cell identity (${N}_{ID}^{cell}$).

### Primary Synchronization Signal (PSS)

The primary synchronization signal (PSS) is based on a frequency-domain Zadoff-Chu sequence.

Zadoff-Chu sequences are a construction of Frank-Zadoff sequences defined by D. C. Chu in [1]. These codes have the useful property of having zero cyclic autocorrelation at all nonzero lags. When used as a synchronization code, the correlation between the ideal sequence and a received sequence is greatest when the lag is zero. When there is any lag between the two sequences, the correlation is zero. This property is illustrated in this figure.

#### PSS Generation

The PSS is a sequence of complex symbols, 62 symbols long.

The sequence ${d}_{u}\left(n\right)$ used for the PSS is generated according to these equations:

In the preceding equation, u is the Zadoff-Chu root sequence index and depends on the cell identity within the group ${N}_{ID}^{\left(2\right)}$.

${N}_{ID}^{\left(2\right)}$Root index u
025
129
234

#### Mapping of the PSS

The PSS is mapped into the first 31 subcarriers either side of the DC subcarrier. Therefore, the PSS uses six resource blocks with five reserved subcarriers each side, as shown in this figure.

As the DC subcarrier contains no information in LTE this corresponds to mapping onto the middle 62 subcarriers within an OFDM symbol in a resource grid. d(n) is mapped from lowest subcarrier to highest subcarrier. The PSS is mapped to different OFDM symbols depending on which frame type is used. Frame type 1 is frequency division duplex (FDD), and frame type 2 is time division duplex (TDD).

• FDD — The PSS is mapped to the last OFDM symbol in slots 0 and 10, as shown in this figure.

• TDD — The PSS is mapped to the third OFDM symbol in subframes 1 and 6, as shown in this figure.

### Secondary Synchronization Signal (SSS)

The secondary synchronization signal (SSS) is based on maximum length sequences (m-sequences).

#### M-Sequence Definition

An m-sequence is a pseudorandom binary sequence which can be created by cycling through every possible state of a shift register of length m, resulting in a sequence of length 2m–1. Three m-sequences, each of length 31, are used to generate the synchronization signals denoted $\stackrel{˜}{s}$, $\stackrel{˜}{c}$ and $\stackrel{˜}{z}$.

#### SSS Generation

Two binary sequences, each of length 31, are used to generate the SSS. Sequences s0(m0) and s1(m1) are different cyclic shifts of an m-sequence, $\stackrel{˜}{s}$. The indices m0 and m1 are derived from the cell-identity group, NID(2) and determine the cyclic shift. The values can be read from table 6.11.2.1-1 in [2].

The two sequences are scrambled with a binary scrambling code (c0(n), c1(n)), which depends on NID(2).

The second SSS sequence used in each radio frame is scrambled with a binary scrambling code (z1(m0), z1(m1)) corresponding to the cyclic shift value of the first sequence transmitted in the radio frame.

## Ug Slots

The sequences s0(m0) and s1(m1) are given by these equations:

$\stackrel{˜}{s}$ is generated from the primitive polynomial ${x}^{5}+{x}^{2}+1$ over the finite field GF(2).

c0(n) and c1(n are given by these equations:

$\stackrel{˜}{c}$ is generated from the primitive polynomial ${x}^{5}+{x}^{3}+1$ over the finite field GF(2).

z1(m0) and z1(m1) are given by these equations:

## Ug Slot

$\stackrel{˜}{z}$ is generated from the primitive polynomial ${x}^{5}+{x}^{4}+{x}^{2}+x+1$ over the finite field GF(2).

#### Mapping of the SSS

The scrambled sequences are interleaved to alternate the sequence transmitted in the first and second SSS transmission in each radio frame. This allows the receiver to determine the frame timing from observing only one of the two sequences; if the first SSS signal observed is in subframe 0 or subframe 5, synchronization can be achieved when the SSS signal is observed in subframe 0 or subframe 5 of the next frame.

As with PSS, the SSS is mapped to different OFDM symbols depending on which frame type is used:

• FDD — The SSS is transmitted in the same subframe as the PSS but one OFDM symbol earlier. The SSS is mapped to the same subcarriers (middle 72 subcarriers) as the PSS.

• TDD — The SSS is mapped to the last OFDM symbol in slots 1 and 11, which is three OFDM symbols before the PSS.

The SSS is constructed using different scrambling sequences when mapped to even and odd resource elements.

• Even resource elements:

• Subframe 0: $d\left(2n\right)={s}_{0}^{\left({m}_{0}\right)}\left(n\right){c}_{0}\left(n\right)$

• Subframe 5: $d\left(2n\right)={s}_{1}^{\left({m}_{1}\right)}\left(n\right){c}_{0}\left(n\right)$

• Odd resource elements:

• Subframe 0: $d\left(2n+1\right)={s}_{1}^{\left({m}_{1}\right)}\left(n\right){c}_{1}\left(n\right){z}_{1}^{\left({m}_{0}\right)}\left(n\right)$

• Subframe 5: $d\left(2n+1\right)={s}_{0}^{\left({m}_{0}\right)}\left(n\right){c}_{1}\left(n\right){z}_{1}^{\left({m}_{1}\right)}\left(n\right)$

d(n) is mapped from lowest subcarrier to highest subcarrier.

## References

[1] Chu, D. C. “Polyphase codes with good periodic correlation properties.” IEEE Trans. Inf. Theory. Vol. 18, Number 4, July 1972, pp. 531–532.

[2] 3GPP TS 36.211. “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.

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