4.6.1 Track parameter extraction
The resulting blocks from the clustering algorithm, which may or may not con-tains cluster centers, are patched together on a single map. A square map with the same number of single-bit signals as squares on the active region of the Hough map is formed. Its element goes high whenever a midpoint is spotted in the corre-sponding square region. Starting from the central row, each square is checked, in the order from small 𝜙0to big 𝜙0, for an active high signal. If it is not spotted, then the row above, and then the row below, the 2nd row above, the 2nd row below, etc. are checked, until the whole square map is exhausted.
A new signal square map with only the first found active square on is produced.
Each element on the new map enters XOR logic with the original square map. The output is a square map with the first found square off–otherwise the same as the original map. The same procedure is performed on this square map to extract a new signal square map with only the second found square on, and it is performed repeatedly to extract 6 squares with the smallest |𝜔|. This algorithm originates from Zheng-Xian Chen’s study [107], the difference being that it now works on the square map, and that it extracts highest-transverse-momentum tracks regardless of their charge.
Finally, the indices of all the signal square maps is extracted using the same decomposition method mentioned in Sec. 4.5.4. The 𝜙0coordinate is encoded into a 7-bit unsigned binary number, the 𝜔 a 7-bit signed binary number.
The number of tracks to find in this step is implemented as an adjustable pa-rameter from 1 to 6 in the HDL source code. Currently, a 2D tracker finds 4 tracks in each quarter of the 𝑟–𝜙 plane of the tracking detector. The iterative process is pipelined, so the total latency increases with the number of output tracks.
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4.6.2 TS association
The fine map indices of each signal peak are extracted alongside with the track parameters. The corresponding Hough map cells are turned on. If the signal is in the center of a Hough map cell, only the cell is turned on. If the signal is on an edge or a corner, 2 or 4 adjacent Hough map cells are turned on.
The resulting single-track Hough map is inversely transformed onto the track segment hit maps of all 5 axial superlayers. All the common track segment hits on both the single-track, inversely transformed hit map and the registered, persisted track segment hit maps become a track segment candidate. A candidate with a first priority cell hit will be selected if it exists. Otherwise, a second-priority TS is selected. In the presence of multiple first or second priority TS candidates, the one with the largest track segment ID, namely the largest 𝜙, is selected.
The levels of logic to select the TS candidates are large, so this process is pipelined into 2 steps. In the first step, every 14 candidates are grouped together. Each group checks whether there is a candidate inside respectively. The group which has a candidate with the largest ID is selected. In the second step, the candidate with the largest TS ID within the candidate group is selected. This procedure is performed for both the first-priority position and second-priority position infor-mation. At the cost of increased latency, the level of logic is significantly reduced, which helps the design to meet timing more easily. Figure 4.11and 4.12display the levels of logic with each method.
4.6.3 Persistence suppression
It is described in section 4.4that the 2D tracker works by finding tracks in the overlapping period between the persisted track segment hit signals in different superlayers. Since the search is performed at every clock, there will be a track signal at every clock within the overlapping period. Apparently, all the signals after the first clock should be suppressed. Some track signals coming from the timing clones can also be suppressed in this step. As simple as it might sound,
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Figure 4.11: Technology schematic diagram of the TS linking process using 2 clock cycles. Each data path has a similar level of logic, and no path is significantly longer.
Figure 4.12: Technology schematic diagram of the TS linking process using only 1 clock cycle. The level of logic in the timing-critical path is much larger, and thus the data path is much longer.
.. there is no easy way to suppress the clones and retain all track segments without increasing latency.
After signal track parameters 𝜔 and 𝜙0 are extracted, they are stored in reg-isters. The associated track segment information are obtained as described in section 4.6.2, registered, and synchronized with the track parameters. Then, a watcher compares these registered values with their old values in the last clock.
If any of the associate track segment information appears, changes, or disappears, a new signal is sent with the updated information. However, all the TS informa-tion disappear when a signal track simply goes out of persistence. In this case, the output signal is not sent. On the other hand, if the track parameters appear or change, an output signal is sent8. As in the case of the TS information, when the track parameters disappear, the output is not sent.
track 1 TSF0 TSF2 TSF4 TSF6 TSF8 track 2 TSF0 TSF2 TSF4 TSF6 TSF8 track 3 TSF0 TSF2 TSF4 TSF6 TSF8 track 4 TSF0 TSF2 TSF4 TSF6 TSF8
TSF info storage
watcher watcher watcher watcher
Figure 4.13: Persistence suppression
TS info 0,2,4,6,8 appears/changes/disappears (TS ID, L/R, priority position)
cluster center cell indices appear/change
but not all disappear
send output
Figure 4.14: Rules regarding whether to send new output
8It is possible for the track parameters to change as the associate TS information remains the same. When new neighboring track segment with smaller ID get hit, the cluster shape changes, and so does the track parameters.
.. Under this rule, no additional latency is introduced, but there will be many clones whenever a track segment (within the acceptance of the found track) with larger ID gets hit, or the incoming track segment hits shift the cluster center by changing the cluster shape. It is possible for the 2D tracker to postpone the out-put by a fixed period and wait for new incoming track segment hits, but this in-crease the latency. If the 2D tracker ignores subsequent track segment hits to a signal track, the clone rate can be reduced, but then the 3D tracker cannot get the most precise information for reconstructing the 𝑧−vertex. The final strategy will depend on the performance study with realistic data input.