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Fundamentals of 5G Design Exercise 1 Assume the following 5G New Radio (NR) communication system, as in Figure 1, where a set of N mobiles {UE1_1, UE1_2, ... ,UE1_N} are connected to a network via the transmission and reception point gNB_1 and another set of N mobiles {UE2_1, UE2_2, ... ,UE2_N} are connected to the same network via the transmission and reception point gNB_2. The system supports conversational voice with the pairing such as UE1_k is talking to UE2_k, where k is pair index and is represented by any integer value between 1 and N (N >=1). Figure 1: Assumed voice communication system (DL and UL directions are with respect to the UE1_k mobiles) Assume that a voice traffic source generates a voice packet of 296 bits size every 20 ms during full activity (typically known as talkspurt) and that the 5G NR radio operates with an OFDM sub-carrier separation of f = 15 kHz, with normal cyclic prefix and 7 symbols per slot, as illustrated in Figure 2. Hence, for each 15 kHz OFDM sub-carrier, in each 1ms sub-frame there are 4 symbols dedicated for the downlink (DL) data transmission (gNB to UEs) and 4 symbols dedicated for the uplink (UL) data transmission (UEs to gNB). Figure 2: Assumed 5G NR sub-frame and slot structure (single OFDM sub-carrier representation) Assume the following modulation schemes, as represented in Table 1. For the purpose of this exercise, transmitted bits are assumed uncoded. Acronym M1 M2 M3 M4 Questions: Modulation QPSK 16QAM 64QAM 256QAM Table 1: Assumed modulation types Uncoded (bits/s) 2 4 6 8 Q1) Assume that the only active conversational pair is (UE1_1, UE2_1) and it operates at full activity for a significant talkspurt duration, e.g. 3 seconds. Assuming that only a single OFDM sub-carrier is available, for each modulation {M1, M2, M3, M4} in Table 1, compute the number of sub-frames required to transmit a single voice packet. Hint: focus on the gNB_1 and assume that the gNB_1 to UE1_1 corresponds to the downlink transmission (for the conversation of UE2_1 with UE1_1), while the UE1_1 to gNB_1 corresponds to the uplink transmission (of the same conversation). Q2) With the assumptions from Q1, which modulation scheme(s) allow to transmit the voice packets (on a single OFDM sub-carrier) as they get generated throughout the entire talkspurt (e.g., 3 seconds) without creating any queued voice packets. Q3) Assume that there is an entire Physical Resource Block (PRB) of 12 OFDM sub- carriers available for supporting conversational voice, as illustrated in Figure 3. Figure 3: Assumed 5G NR sub-frame and slot structure (PRB representation) Assume that the only active pair is (UE1_1, UE2_1) and it operates at full activity for a significant talkspurt duration, e.g. 3 seconds. For each modulation {M1, M2, M3, M4} in Table 1, compute the number of sub-frames required to transmit a single voice packet. Q4) Assume that there is an entire Physical Resource Block (PRB) of 12 OFDM sub- carriers available for supporting conversational voice, as illustrated in Figure 3. Assume that there are several active pairs (UE1_k, UE2_k) operating at full activity for a significant talkspurt duration, e.g. 3 seconds. For each modulation {M1, M2, M3, M4} in Table 1, compute how many parallel conversations (voice conversational pairs) may be multiplexed on the same PRB without creating any queued voice packets. Exercise 2 Assume now that the 5G NR is only used for File Transfer Protocol (FTP) downloads (as in Figure 4) and that a single PRB is available for transmission, as in Figure 3. For each modulation {M1, M2, M3, M4} in Table 1, compute how many subframes are required to download a single FTP packet of size 1460 Bytes to UE1_1 (all other UEs are assumed not to be active). Exercise 3 Figure 4: Assumed data communication system Compute the total number of resource elements that are dedicated to support the control information carried through the synchronization signals and PBCH in a single SS/PBCH block (Figure 5 below). 239 192 182 Subcarrier Number 56 47 0 OFDM symbol number Figure 5: Time-frequency structure of the SS/PBCH Block P S S P B C H P B C H S S S P B C H P B C H 0123 Exercise 4 For the 5G NR numerology provided in Table 2 below, compute the respective minimum and maximum frequency bandwidths. 0 15 24 ? 275 ? 1 30 24 ? 275 ? 2 60 24 ? 275 ? 3 120 24 ? 275 ? 4 240 24 ? 138 ? 5 480 24 ? 69 ? Table 2: 5G NR Numerology Numerology (m) Sub-carrier spacing (kHz) Minimum Resource Blocks (RBs) Minimum frequency bandwidth (MHz) Maximum Resource Blocks (RBs) Maximum frequency bandwidth (MHz) Exercise 5 Figure 6 illustrates 4 slot format examples: - Slot format 1: f 15 kHz, 2 slots per sub-frame, 7 OFDM symbols per slot - Slot format 2: f 15 kHz, 1 slot per sub-frame, 14 OFDM symbols per slot - Slot format 3: f 60 kHz, 8 slots per sub-frame, 7 OFDM symbols per slot - Slot format 4: f 120 kHz, 8 slots per sub-frame, 14 OFDM symbols per slot Note that each slot should assume the standard 12 OFDM sub-carriers per Resource Block. In other words, although the figure below only shows a single OFDM sub- carrier for simple representation of each slot format, in fact each slot format diagram should be viewed expanded in the frequency domain as in Figure 3, with 12 adjacent OFDM sub-carriers separated by the corresponding f. Figure 6: 5G NR slot format examples For each slot format and each modulation type represented in Table 1 from above, compute: - Achievable downlink peak rate assuming the corresponding maximum frequency bandwidth computed in Exercise 4 (Table 2) for the respective OFDM sub-carrier separation. - Maximum spectral efficiency, which is calculated as the ratio between the downlink peak rate and the corresponding maximum spectrum bandwidth Slot format Slot format 1 Slot format 2 Slot format 3 Modulation QPSK 16QAM 64QAM 256QAM QPSK 16QAM 64QAM 256QAM QPSK 16QAM Downlink peak rate (Mbps) ? ? ? ? ? ? ? ? ? ? Maximum spectral efficiency (b/s/Hz) ? ? ? ? ? ? ? ? ? ? Slot format 4 Exercise 6 64QAM 256QAM QPSK 16QAM 64QAM 256QAM ? ? ? ? ? ? ? ? ? ? ? ? For the 5G NR as represented in Figure 4, assume that there are four active UEs {UE_1, UE_2, UE_3, UE_4} which are operating steadily at modulations {QPSK, 16QAM, 64QAM, 256QAM}, respectively. Assume that all four UEs do FTP downloads and the files they are downloading are of very large size (this is often referred as infinite backlog). Assume that the system is configured to operate with slot format 3 as displayed in Figure 6 in Exercise 5. Design/program a scheduler which gives equal downlink rate to all the four UEs (this is an equal rate scheduler). What is the common achievable FTP download rate for all the four UEs? Using a similar representation to the slot format 3 in Figure 6 of Exercise 5, illustrate two complete scheduling cycles where all four UEs are scheduled twice. Use different colors to represent the DL data transmitted for each of the four UEs. How many subframes are needed for this representation? Common note: Resource Block (RB) and Physical Resource Block (PRB) have the same meaning whenever encountered in the text from above.

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