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January 17, 2018

This paper was given at the Ka and Broadband Communication Conference – 2015 – It is presented here as in the original proceedings’ submission and conference PDF distribution. [proceedings]

This post is the second in a three parts series. The last part will be published next. you can see part 1 and part 3 (follow links)
Part 1 – is an introduction and abstract and use cases of beam hopping system design.
Part 2 – covers beam hopping basic system consideration and illumination strategies.
Part 3 – covers beam hopping adaptation to demand, summary and conclusion.

3. Beam Hopping Basic System Considerations and illumination strategies

In this paper, the following terminology is used:

• Beam: the directional radio signal transmitted from a satellite
• Cell: an area on the ground illuminated by a beam
• Transmission channel or just Transmitter: The power amplifier and additional components handling the transmission, and shared among beams
• Cluster: A set of beams served by one transmitter
• Dwell time: the time duration in which a given transmission channel is allocated to a given beam.
• Off time: the time duration in which a given cell is not illuminated
• Transmission Packet: The transmission that occurs during the dwell time
• Beam Hopping Transmission plan: the absolute transmission times and dwell times allocated for each beam
• Revisit time: The maximal time -period in which a terminal is revisited
• Cycle: The period of time during which a transmitter covers all the beams within its allocated cluster.

Those terms refer, for the sake of simplicity, to the downlink direction, namely transmissions from the satellite to the Earth stations. In the uplink direction, a similar can be applied, with interchanging the transmitters to receivers.

As beam-hopping is a time domain technique, the timing diagrams can best describe its operation. Figure 1 shows a timing diagram for a transparent payload case. The diagram shows the timing of transmissions from two gateways, each feeding four beams for two cycles. The different colors and patterns indicate to which beam the payload is destined.

Figure 1: Timing Diagram- Transparent Payload

Gateways transmissions (GW-TX) are to be timed such that they arrive at a known time instant at the payload, taking into account the propagation delay each goes through ( τ_p1 τ_p2 in the diagram, drawn extremely out of scale). For that purpose, gateways may be required to apply a time advance (t_A). The payload distributes the transmissions to the different beams, after some inherent delay τ_pld. Time should be allocated in the payload for the switching of the transmitters to the beams, or for the antennas to settle in the relevant direction. This time, denoted t_s in Fig.1 is to be allocated at every beam hop. t_s also includes the uncertainly in synchronization between the gateways and payload, measured at the payload.

The switching time is one of the more important parameters in determining the system efficiency and it directly affects the mode of operation. The penalty in system efficiency due to beam-hopping can be expressed as a factor (<1) by which the system effective data rate should be multiplied by. If we further denote by tĀ_dw the average dwell time, the efficiency factor of a beam-hopping system can be expressed as:

Equation #1

Another important parameter is the time it takes a transmitter to illuminate all the beams allocated to it. This time, denoted T_w in the figure, is the beam-hopping cycle, and it is the upper bound for the revisit time- the maximal time duration for a terminal in any beam to be revisited. This time is a result of various constraints in the system including:

• Terminal stability and ability for re-acquisition after a period of no- reception.
• Worst case latency allowed for a message to arrive to destination.

Each transmitter performs a cycle of transmissions to the beams it covers per each Tw cycle, where the illumination time per beam is determined by the known statistics of the demand in each. In this case, in which the illumination is periodic, t_dw = N_clt_s / T_W , N_cl is the number of cells in a cluster.

In addition, one may also observe that the upper bound, η_BH^UB, and the lower bound, η_BH^LB, on the efficiency would be:

Equation #2

where T_min is the minimal dwell time.

Another source of inefficiency might be the case where the instantaneous traffic is not enough to fill up the transmission packet for the entire dwell time. As incoming traffic is statistical in nature, margins must be taken to reduce overflows (which may cause extended latencies) so statistically empty room is unavoidable. Exact analysis of this case highly depends on the application and traffic model.

In addition to system efficiency, another important parameter to be considered is the overall latency, a data packet undergoes to. Obviously, in any data communications network, packets incur delays resulting from propagation delays, queuing and buffering, and a satellite beam-hopping communication system is no exception. However, the beam-hopping technique gives rise to further delays.

The total latency budget of a packet arriving at a gateway is expressed in

Equation #3

• τ _delay is the total delay
• τ _Bg is the buffering delay in the gateway needed to accumulate the data to fill out the transmission packet.
• τ _wg is the waiting time from the point the transmission packet is ready till transmission. In a worstcase scenario, this value may reach the cycle time (or even beyond that, in case of traffic surges)
• τ _pgs is the propagation delay between the gateway and the satellite
• τ _pld is the inherent delay in the payload, mentioned above.
• τ _Ag is the time needed to align the downlink transmissions to transmissions from other gateways.
  (typically compensated for by advancing the gateway transmission time)
• τ _Bs is further buffering that might be needed aboard the satellite, might be relevant for regenerative payloads.
• τ _pst is the propagation delay between the satellite and the terminal.

The scheme presented in Fig. 1 is basically pre-defined according to prior information on the expected load. It is not necessarily the only possible strategy in the design of the beam-hopping illumination plan. Other strategies determine the hopping plan according to the data arrival time, thus avoiding mismatch between the actual demand distribution and the BHTP. The most extreme example would be a “point-and-shoot” approach where each packet is routed directly to its destination cell on a first comes – first served basis., thus avoiding buffering delays. On the other hand, each transmission would be tolled by an additional switching time and if data packets are small, it might substantially reduce the total efficiency.

Figure 2 shows an example for the timing diagram of an illumination strategy, based on fixed transmission time intervals. In this strategy the packets for each cell are queued. At constant instants, beams are transmitted to the cells with the longest queues, or, to cells for which the revisit time constraint has expired. Figure 2 shows an example for one beam serving 4 cells, arranged per their load.

Another possible strategy would call for a constant transmission packet size (in bits, or in symbols). As above, packets for each cell are queued and once the set transmission packet size is met, the packet is routed for transmission, again with re-visit time constraints. Variants of this scheme might be to set different transmission packet size for each beam, according to the demand in that beam. In this case, the dwell time matches the demand data rate, similarly to the periodic predefined structure described in Fig. 1.

Figure 2: Beam Illumination Timing Diagram – Point and Shoot

If the cycle and dwell times are selected optimally, the performance, in terms of efficiency and latency, of both method would be similar. However, they differ from implementation point of view. While in the first scheme transmissions are made according to a predefined scheme, in the second case transmissions depend on the arriving traffic. The periodic scheme would be preferable for the case of a transparent payload. In this case the gateways and payload should maintain an acceptable level of synchronization, and exchange beam-hopping timing plan information when necessary. In the data driven approaches are to be implemented over a transparent payload, each transmission should be tagged with the routing information, to be decoded at the payload, for the relevant beam. The periodic scheme has an advantage from the point of view of the terminal, which can be switched off at predictable times. The data driven strategy would be more adequate for a regenerative payload, where the routing decision is made on-board, thus saving on buffering time.

3.1 Fixed Transmission Time Strategy- Latency and Beam Utilization

To learn the effect of transmission interval size as a function of data rate on the resulting latency and beam utilization a simulation was performed with the following parameters:

• 10 cells, 4 Beams, 100 users
• Users are distributed exponentially among cells
• BW= 100 MHz
• SNR per user (in dB) is randomly selected from a Gaussian distribution ~ N (10,3) dB
• Spectral efficiency per user- as per Shannon’s formula (with 2dB penalty)
• Load: 0.25 and 0.5 of Total Capacity
• Demand data rate per user, randomly selected from a truncated Gaussian distribution, with average bit rate commensurate with the mean SNR. Simulations were run with data rate equal to 0.25 and to 0.5 of the SNR
• Packet arrival rate: randomly selected from a Gaussian distribution ~ N (20,10) packets/sec, correlated with the data rate per use (with correlation factor of 0.8). The arrival process per user is Poisson, with the random arrival rate.
• Revisit time: 30 msec

The resulting beam utilization and average waiting time for each data rate case, as a function of the transmission interval size are given in Figure 3 (a) and (b) respectively.

(a) Beam Utilization	(b) Average Waiting Tim
Figure 3: Constant Transmission Interval- Performance

Clearly, the lower the transmission interval, the better is the beam utilization and the lower is the waiting time. However, the result does not reflect switching time effect, which causes a reduction of efficiency as the interval gets lower. Notably, beam utilization gets flat above approximately 2msec, which is the point where most of the arrival data packets are smaller than transmission packet interval. The waiting time grows linearly with the interval time for low load scenario. When the load is higher the slope of the decrease is higher.