Busy Bursts for Trading off Throughput and Fairness in Cellular OFDMA-TDD

To mathematically describe BB-enabled interference avoidance, let define a transmitter or receiver (either BS or MS) of user within cell . With this notation, the channel gain of the intended link at chunk becomes . The channel gain of an interfering link, between transmitter of user located in an adjacent cell and receiver , is denoted by . In case two links compete for resources, the CCI between transmitter and receiver amounts to . (The term is equivalent to the CCI as defined in (1). While the notation is preferred for intercellular interference management, the latter is used for intracell resource allocation. The same rule applies for related quantities that denote transmitted and received signal powers.) Likewise, and are the transmit power of the BB transmitter (data receiver) and the interfering BB power received at data transmitter (BB receiver), respectively.

Exploiting TDD channel reciprocity [18], transmitter can ascertain , the potential amount of interference it causes to an existing link , by measuring at the associated BB minislot [13]. Applying the channel reciprocity property of TDD, , yields

The maximum CCI that a candidate transmitter may cause to an active receiver is determined by the interference threshold , which is constant and known to the entire network. When , transmitter is located outside the exclusion range of . Provided that is known to the candidate transmitter , (6) enables to verify whether by invoking the threshold test [13, 14]

In case , condition (7) reduces to

By tuning , the maximum CCI in (2) is adjusted, which determines the size of the exclusion range around active receivers.

In a multicell scenario, signals from multiple links superimpose at the receiver. The total interference at data receiver amounts to

where is the set of simultaneously active transmitters. Likewise, the received BB at the data transmitter (BB receiver) yields

where is the set active receivers (BB transmitters).

Unlike the case when two links compete for resources, is no longer equivalent to in the threshold test (8). This is because in (9) the interference powers from multiple transmitters add up. Consequently, the total CCI at data receiver may exceed the tolerable threshold such that , although the BB power (10) observed by the individual interferers is below the threshold, . On the other hand, in (10) the interfering BB powers from multiple simultaneously active receivers observed at add up. It is, therefore, possible that , so that link is prohibited from accessing chunk , although its individual CCI contribution, would be below . Note that the former effect partly compensates the latter. Moreover, in many cases the interference is dominated by one strong interfering source. Therefore, the threshold test (8) provides a good approximation to the level of interference potentially caused to the active receivers.

Initial access of unreserved slots in BB-OFDMA is carried out in contention. During contention, two or more transmitters from adjacent cells may access chunk simultaneously. As a result, one or several links may encounter a collision on chunk where the SINR target is not met. To reduce the occurrence of simultaneously accessed chunks in contention, a -persistent chunk allocation procedure is applied to BB-OFDMA, where chunk in cell is accessed with probability . Denoting the outcome of the -persistent chunk allocation with the binary random variable , the access probability yields . The impact of on the system performance is investigated in Section 6.1.

The BB-OFDMA protocol enables a link to contend for a chunk once it is ensured that the CCI caused to the coexisting links in the neighbouring cells is below a given threshold (8). Prior to accessing chunk , transmitter listens to the associated BB minislot. Whether a user within cell may contend for chunk in (4) is controlled by

Chunks, where in (4), are allocated to user . Those chunks where the achieved SINR is above a required SINR target, , are reserved by setting the reservation indicator in (4), and are subsequently protected from CCI by BB broadcast. The BB broadcast from the intended data receiver is observed as a surge in the received BB power [14], which effectively notifies the transmitter that the data of chunk has been correctly received. User then reserves chunk in the next frame by setting in (5). On the other hand, if the transmitter does not detect a BB surge, it is understood that the SINR target was not met due to high CCI. These chunks are released by a reset of the reservation indicator to and setting , so that chunk may be assigned to other users.

Cell-edge users are particularly affected by CCI for two reasons. First, the desired signal levels are, on average, much weaker compared to users in close vicinity to the desired BS due to relatively low channel gains on their intended links . Second, cell-edge users suffer from high CCI in the downlink, or cause high CCI to the adjacent cells in the uplink.

By tuning the interference threshold in (8), the amount of CCI caused to the receiver of a preestablished and coexisting link is adjusted. Lowering enforces a larger exclusion region around a vulnerable receiver. This enables cell-edge users to meet their SINR target with a greater likelihood. On the other hand, by augmenting , the number of simultaneously served links increases, giving rise to an enhanced system throughput. However, the cell-edge users are less likely to maintain their SINR target as interference protection is gradually eliminated. The chunks are released where the SINR target is not met, which means that these chunks are no longer reserved. Since the cell-centre users are less exposed to CCI, the chunks released by the cell-edge users are likely to be reallocated to the cell-centre users. As the allocation of the resources is shifted from the cell-edge users towards the cell-centre users, fairness is compromised. Hence, by adjusting , system throughput is traded off for fairness.

A common measure to quantify fairness is Jain's fairness index [22], defined by

where is the number of users in a given cell . The user throughput accounts for the number of successfully transmitted/received bits by user , as defined in (5). A fairness index of represents a perfectly fair system where all users achieve the same throughput. On the other extreme, a fairness index of represents an unfair system where one user is served while all other users starve. We note that the fairness definition (12) is a relative measure, which ignores the absolute achieved throughput per user. To this end, a good fairness index may coincide with poor spectrum utilisation. For instance, a system where two users achieve Mbps and Mbps would result in a poorer fairness index than a system where both users achieve only Mbps. When analysing fairness, the fairness definition (12) should therefore be considered jointly with user throughput results.

(1) Consequences for the Downlink In the downlink, MSs at the cell edge are exposed to high CCI from transmitters in adjacent cells (see Figure 2(a)). Note that the CCI observed at a given cell (cell 1 in Figure 2(a)) is independent of the user distribution in adjacent cells (cell 2 in Figure 2(a)), assuming a constant transmit power . This implies that if BS₂ lies within the exclusion region of MS₁, resources reserved by MS₁ cannot be spatially reused by any of the links in cell 2. However, if is increased such that BS₂ is located outside the exclusion region of MS₁, all links in cell 2 qualify for a spatial reuse of the resources reserved by MS₁. However, the SINR target at MS₁ is less likely to be met. Should the SINR target at MS₁ not be met, this would cause the chunk allocated to MS₁ to be released and reallocated to another user served by BS₁- possibly a user that is located closer to the the serving BS₁. Therefore, the cell-edge throughput would suffer.

(2) Consequences for the Uplink In the uplink, the transmitters (MSs) are distributed uniformly over the coverage area of the BS (see Figure 2(b)). Unlike the downlink, the CCI at the tagged BS depends on which MS transmits in the adjacent cell. To this end, the CCI observed at BS₁ in Figure 2(b) depends on whether MS₂ or MS₃ transmits to BS₂. Suppose that in cell 2 both MS₂ and MS₃ contend with MS₁ in cell 1 for chunks and . In case MS₂ and MS₁ simultaneously access chunk , while MS₃ and MS₁ simultaneously access chunk , the SINR at BS₁ tends to be superior on chunk due to the lower CCI caused by MS₃. While MS₂ causes excessive CCI to BS₁, MS₁ and MS₃ may share chunk , although both users might be located near the cell boundary. Thus the uplink benefits from interference diversity due to the distributed location of mobile users. As a result, the degradation of performance at the cell edge at high in uplink mode is less severe compared to the downlink.

With fixed power BB signalling, the same level of interference protection is given to all links, disregarding the quality of the intended link. In case two receivers MS₁ and MS₂ with respective channel gains are exposed to the same interference, as illustrated in Figure 3, the SINR target is more likely met for MS₁ than for MS₂. By allowing MS₁ and MS₂ to transmit a BB with variable power, the individual amount of interference that can be tolerated by MS₁ and MS₂ is signalled to candidate transmitters in adjacent cells. Exclusion regions of different size are effectively formed around MS₁ and MS₂, as illustrated in Figure 3.

For busy burst with interference tolerance signalling (BB-ITS), the objective is that a given SINR target, , is maintained for an active receiver . This means that the maximum allowable interference depends on the intended link quality . Let denote the interference limit, for which the SINR (2) approaches . Then the tolerable interference at receiver is upper bounded by

Adjusting the tolerable interference level (13) implies that larger exclusion regions are formed for links with weak desired signal levels and vice versa.

To signal the variable interference tolerance level of a victim receiver to candidate transmitters in adjacent cells, the BB transmit power is adjusted, such that the simple threshold test in (8) is retained. Hence no additional information for channel sensing is required for BB-ITS. The received BB power approaches a fixed threshold, , if the CCI approaches . Inserting and into (6) yields the variable BB power . Assuming that is fixed and denoted by , the BB transmit power is adjusted as follows [23]:

where is the maximum BB transmit power. The operator ensures that . Note that when , we get . In this situation, the chunk is released and no BB is transmitted. Therefore, it is ensured that in (14) always has a positive value. We note that and . It can be checked by plugging (14) into (8) that the threshold test (8) effectively checks if , regardless of the threshold used, as long as the BB transmit power is not clipped. In this paper, we choose dBm because the probability of BB transmit power being clipped was found to be lower than 0.05 for the given deployment scenario with  dB used. Furthermore, with this threshold, the received BB at the intended transmitter (the lower bound of which is approximated by ) remains well above the noise floor  dBm, such that it can be reliably detected.

Receiver feedback based on BB-ITS (see Section 4.6) allows for receiver-driven link adaptation, where the chosen transmission rate is adapted to the instantaneous channel conditions. Let be the set of supported modulation schemes. Associated to each modulation scheme is an SINR target that must be achieved to satisfy a given frame error rate (FER).

Provided that the channel response does not change between successive frames, changes in may be signalled from receiver to transmitter through (14), since any fluctuation in received BB power is due to a change of in (14). In summary, BB-ITS serves two important objectives. First, by adjusting the SINR target , the receiver implicitly signals to the transmitter through BB-ITS that the transmission format should be changed; second, by varying the BB power in (14), the size of the exclusion region around the active receiver is adjusted, so that the required SINR target is met in successive frames.

Link adaptation with BB-ITS is carried out in two phases: the contention phase, where the link is established and the link adaptation (LA) phase, where the receiver adjusts its transmission format to the current channel conditions.

Contention Phase

In contention, multiuser chunk allocation is carried out as described in Section 4.3. To contend for an unreserved chunk , transmitter initially uses the modulation scheme with the lowest spectral efficiency . Chunks that satisfy are reserved in the next frame by BB signalling (see Section 4.4), where the transmit power in (14) is set using . Then the transmission proceeds to the link adaptation phase.

Link Adaptation Phase

The objective of the link adaptation phase is to select the modulation scheme for chunk , which yields the highest spectral efficiency, for which holds. By utilising BB-ITS link, adaptation is accomplished without any explicit feedback. The receiver executes the following algorithm.

The transmitter senses the BB minislot associated to chunk . In order to determine the modulation scheme requested by the receiver, the transmitter executes the following algorithm.

Estimation errors due to channel variations and noise may cause detection errors, so that . Mismatch between the selected modulation schemes at transmitter and receiver can be mitigated if the transmitter announces together with payload data on chunk .

Full-frequency reuse with adaptive score-based chunk allocation (ASCA) is considered as the benchmark system. This means that neither chunk reservation nor interference avoidance mechanisms is in place. In order to maintain a fair comparison, the same fair scheduling algorithm (3) as in BB-OFDMA is applied. With ASCA, the score-based scheduler assigns chunk to user whose score (3) is minimised

Chunk allocation for ASCA (17) corresponds to (4) by setting the reservation indicator to zero, , and by allowing a cell to access all chunks, which is achieved by setting for all in (3).

The likelihood of achieving the SINR target during the initial access in contention is depicted in Figure 5 for with dB, where is the number of bits per symbol. The cell-edge region suffers from collisions (SINR target not met) both in the uplink (Figure 5(a)) and the downlink (Figure 5(b)). Decreasing the access probability substantially reduces the occurrence of collisions, since the probability of simultaneous access of chunks in contention reduces (see Section 4.3). In the downlink, cell-edge users suffer from weaker desired signal power and at the same time experience strong CCI. Furthermore, the users located at the street crossings at m are exposed to strong LoS interference from BSs in the perpendicular streets. In the uplink, however, these users cause CCI to the neighbouring cells; which may impact either users at the cell-edge or users closer to the intended BS. Consequently, the SINR target is met with less likelihood at street crossings and the cell edge in the downlink mode compared to the uplink mode.

The impact of the choice of interference threshold on the mean system throughput is shown in Figure 6 for fixed 16-QAM modulation with . It is seen that for lower values of , the amount of allocated resources (Set ) and the achieved throughput (Set ) are approximately equal. This is because at low , larger exclusion regions around active receivers are enforced. Thus, CCI is mitigated at the expense of spatial reuse. By increasing , the system throughput gradually improves until the maximum is reached. However, increasing introduces additional links that cause more CCI to the existing links. As a result, some of the links (mainly cell-edge users) are less likely to meet the SINR target. Although it is desirable to maximise the spectral efficiency, it may be necessary to maintain a fair distribution of resources to all users. Achieving a balance between maximising spectral efficiency and enhancing fairness is addressed in Section 6.3.

Figure 7 shows the average user throughput versus distance from the serving BS. It is observed that the performance of BB-OFDMA is sensitive to the chosen threshold . The system throughput is maximised for dBm in the downlink and for dBm in the uplink (see Figure 6). However, these thresholds severely affect cell-edge user throughput. Increasing interference protection by lowering enhances user throughput at the cell edge at the expense of system throughput. In the uplink (Figure 7(a)), the cell edge throughput (measured at m from the desired BS) improves from 1.5 Mbps ( dBm) to 3.08 Mbps (  dBm), an approximately onefold increase, whereas in the downlink (Figure 7(b)), user throughput increases from 267 kbps ( dBm) to 2.9 Mbps ( dBm), an approximately tenfold increase. At m, MSs are exposed to LOS interference from BSs in perpendicular streets in the downlink. Consequently, high CCI compromises throughput for these users. In the uplink, MSs located at street crossings at m transmit, so that these users are not exposed to LOS interference. Hence the uplink throughput of ASCA is not affected at m. For BB-OFDMA, however, MSs located at street crossings are exposed to strong BB signals from BSs in perpendicular streets, which reduces the number of chunks such users can compete for, causing a drop of throughput for users located at street crossings.

Fairness is numerically quantified using Jain's fairness index (12). The cdf of the fairness distribution is presented in Figure 8(a) for the uplink and Figure 8(b) for the downlink. Applying the interference threshold that maximises system throughput, dBm in the downlink and dBm in the uplink, results in median fairness index of and respectively. Increasing the interference protection by lowering improves fairness, as this enables cell-edge users to meet their SINR target. To this end, using dBm in the uplink and dBm in the downlink, approximately 22% of system throughput, is traded off for median fairness indices of . In the uplink, the median fairness index can be further improved to 0.78 by setting dBm. However, the improved fairness significantly degrades system throughput (see Figure 6).

On the other hand, with BB-ITS, median fairness indices of 0.7 are achieved. The corresponding average uplink and downlink user throughputs at the cell edge amount to 2.57 Mbps and 2.99 Mbps, respectively. The corresponding reduction in system throughput compared to the respective optimal thresholds with fixed power BB is only 1% in the uplink and 8% in the downlink. Note that BB-OFDMA with fixed BB power requires a 22% reduction in system throughput for a comparable performance at the cell edge. In light of this, BB-ITS results in a better tradeoff between system throughput and fairness.

For comparison, the median fairness resulting from ASCA is in the uplink and in the downlink. The corresponding average user throughputs at the cell edge are 2.278 Mbps and 208 kbps, respectively. This means that ASCA is more fair in the uplink compared to the downlink. The reason is that in the downlink cell-edge users are exposed to high CCI, while in the uplink cell-edge users cause high CCI to adjacent cells. Hence the detrimental effects of interference on the uplink tend to be more equally distributed among all users.

Figures 9(a)–9(d) depict the cumulative distribution function (cdf) of the user throughput and the system throughput. The results shown in Figures 9(a)-9(b) demonstrate that BB-enabled interference avoidance exhibits a gain in median system throughput of up to 50% compared to ASCA, both in uplink and downlink. Using a modulation format of  bits per symbol and a -rate convolutional code, the upper bound on system throughput achieved in an isolated cell (CCI free system) is 111.8 Mbps. With dBm in the uplink and dBm in the downlink, a median system throughput of about % and % of the upper bound (CCI free system) is achieved.

Figures 9(c)-9(d) show the cdf of the user throughput for BB-OFDMA and ASCA. When fairness is the primary concern, dBm in the uplink and dBm in the downlink are preferable. Then the 10%-ile of the achieved user throughput amounts to Mbps in the uplink (see Figure 9(c)) and Mbps in the downlink (see Figure 9(d)). In contrast, ASCA fails to deliver any downlink throughput to more than 20% of the users. In the uplink, the 10%-ile of the user throughput of BB-OFDMA is improved by 40% compared to ASCA. With these uplink and downlink thresholds of dBm and dBm, the median system throughput of BB-OFDMA is still 15% and 18% higher than that achieved with ASCA (see Figures 9(a)-9(b)).

The results of BB-OFDMA with variable BB power, termed BB-ITS, are also included in Figures 9(a)–9(d). With BB-ITS, the lower 10%-ile of user throughput achieved is 1.04 Mbps in uplink and 1.416 Mbps in downlink (see Figures 9(c)-9(d)), at a modest degradation in system throughput (see Figures 9(a)-9(b)) compared to BB-OFDMA with fixed threshold that maximises the respective system throughput. BB-ITS, therefore, not only avoids the need for tuning the interference threshold so as to match a certain interference scenario (e.g., in uplink or downlink), but also achieves a preferable compromise between maximising system throughput and maintaining fairness.

Figures 10(a)-10(b) compare the system and user throughput achieved by performing link adaptation (LA) with BB-ITS and ASCA. Both BB-ITS and ASCA utilise the same link adaptation algorithm presented in Section 4.7; the only difference is that for ASCA interference protection is omitted. The results shown in Figure 10(a) reveal that BB-ITS with link adaptation attains an improvement of 50% (uplink) and 13% (downlink) in median system throughput compared to ASCA with link adaptation. Furthermore, Figure 10(b) shows that the BB-ITS outperforms ASCA by a factor of 2.75 in terms of the lower 10%-ile of the downlink user throughput. On the other hand, the cell-edge user throughput of BB-ITS and ASCA in the UL is comparable, while significant improvements of up to 70% are observed for higher percentiles of the user throughput in Figure 10(b).

By performing link adaptation with BB-ITS, the cell-edge users benefit in the downlink, whereas the users that are closer to their desired BS benefit in the uplink. The reason for this opposite trend for the uplink and the downlink is elaborated in the following. Due to the specific point-to-multipoint structure in the downlink, the CCI observed by the cell-edge users is dominated by the interference originating from the closest BS. When a chunk is assigned to a cell-edge user in the downlink, interference tolerance signalling enforces that this chunk cannot be spatially reused by the closest BS in an adjacent cell. By ensuring that, this dominant interferer does not access this chunk, the achieved SINR is greatly improved, potentially enough to meet the higher SINR target(s), thus allowing for the higher-order modulation schemes. In the uplink, on the other hand, the chunks assigned to the cell-edge users are more likely to be reused in the adjacent cells due to the distributed location of the MSs transmitters (see Section 4.5). Consequently, it is less likely that a more spectrally efficient modulation scheme can be used by the cell-edge users. Furthermore, in the uplink, the distance between the MSs (transmitters) and the victim BSs (receivers) in neighbouring cells is larger for the cell-centre MSs than the cell-edge users. Hence the cell-centre users are more likely to be located outside the exclusion range of BSs receivers (BB transmitters). This results in a larger number of chunks that are available to be spatially reused for the cell-centre users. Lastly, the cell-centre users also benefit from higher SINRs as a result of which throughput is particularly boosted by performing link adaptation.