Performance Evaluation of Multiterminal Backhaul Compression for Cloud Radio Access Networks
In cloud radio access networks (C-RANs), the baseband processing of the available macro- or pico/femto-base stations (BSs) is migrated to control units, each of which manages a subset of BS antennas. The centralized information processing at the control units enables effective interference management. The main roadblock to the implementation of C-RANs hinges on the effective integration of the radio units, i.e., the BSs, with the backhaul network. This work first reviews in a unified way recent results on the application of advanced multiterminal, as opposed to standard point-to-point, backhaul compression techniques. The gains provided by multiterminal backhaul compression are then confirmed via extensive simulations based on standard cellular models. As an example, it is observed that multiterminal compression strategies provide performance gains of more than 60% for both the uplink and the downlink in terms of the cell-edge throughput.
Cloud radio access network, constrained backhaul, distributed compression, multivariate compression, network MIMO.
A promising architecture for next-generation wireless cellular systems prescribes the separation of localized and distributed radio units from remote and centralized information processing, or control, nodes. This architecture is often referred to as a cloud radio access network (C-RAN) . The centralization of information processing afforded by C-RANs potentially enables effective interference management at the geographical scale covered by the distributed radio units. The main roadblock to the realization of this potential hinges on the effective integration of the wireless interface provided by the radio units with the backhaul network . Current solutions, which are the object of various standardization efforts , prescribe the use of standard analog-to-digital conversion (ADC) techniques in the uplink and standard digital-to-analog conversion (DAC) techniques in the downlink. With these standard solutions, backhaul capacity limitations are known to impose a formidable bottleneck to the system performance (see, e.g., ).
In order to alleviate the performance bottleneck identified above, recent efforts by a number of wireless companies have targeted the design of more advanced backhaul compression schemes. These are based on various ad hoc combinations of ADC and DAC techniques and proprietary point-to-point compression algorithms (see, e.g., ). However, as it is well known from network information theory, point-to-point techniques generally fail to achieve the optimal performance in even the simplest multiterminal settings . Recent works have hence explored the performance of multiterminal, as opposed to standard point-to-point, backhaul compression techniques for the uplink - and the downlink  of C-RAN systems. In this paper, we first review these works in Sec. 3 for the uplink and in Sec. 4 for the downlink in a unified fashion. We then provide extensive simulation results based on standard cellular models  to lend evidence to the gains provided by multiterminal backhaul compression as compared to standard point-to-point techniques in Sec. 5.
Notation: For random variables , and , we adopt standard information-theoretic definitions for the mutual information , conditional mutual information , differential entropy and conditional differential entropy . Given a sequence , we define a set for a subset . For random vectors and , we define the following correlation matrices , and .
2 System Model
We consider the two-dimensional hexagonal cellular layout with 19 macro cells shown in Fig. 1. We assume that each macro-base station (BS) uses three sectorized antennas, and each pico-BS and mobile station (MS) uses a single omni-directional antenna. In each macro-cell, MSs and pico-BSs are uniformly distributed. Fig. 1 illustrates an example with MSs and pico-BS.
In a C-RAN system, the baseband processing of the available macro- or pico/femto-BSs is migrated to control units, each of which manages a subset of BS antennas. For example, in Fig. 1, a control unit manages the three sectors of cell 1 and hence the corresponding sectorial antennas of the three relevant macro-BSs and the available pico-BS. We refer to a subset of BS antennas connected to the same control unit, and to the corresponding covered area, as a cluster.
Every th BS is connected to the corresponding control unit via a backhaul link with capacity bps/Hz  where the normalization is done with respect to the bandwidth of the wireless uplink/downlink channels. For instance, if BS communicates with the corresponding control unit at a date rate of 100 Mbps and the wireless uplink/downlink channels have a 10 MHz bandwidth, the normalized backhaul capacity is given as bps/Hz.
According to the C-RAN principle, the data exchanged on the backhaul links between BSs and control units consists of compressed baseband signals -. Specifically, in the uplink, the baseband signal received by each BS is compressed and forwarded to the connected control unit, where decoding takes place. Instead, in the downlink, the baseband signals are produced and compressed by the control units, and then upconverted and transmitted by the BSs.
In the following, we detail the signal and channel model by focusing on one specific cluster, e.g., cell 1 in Fig. 1. For notational convenience, we index the BSs in the cluster as and the MSs in the cluster as , and define the sets and .
2.1 Uplink Channel
The signal received by BS in the cluster under study in the uplink is given by
where is the vector of symbols transmitted by all the MSs in the cluster, with being the symbol transmitted by MS ; the noise models thermal noise and the interference signals arising from the other clusters; and the channel vector from all the MSs in the cluster toward BS is given by with denoting the uplink channel response from the th MS and to the th BS. The signal is subject to the per-MS power constraint, which is stated as for .
2.2 Downlink Channel
In the downlink, each MS in the cluster under study receives a signal given as
where we have defined the aggregate transmit signal vector by all the BSs in the cluster as with denoting the signal transmitted by the th BS; the additive noise accounts for thermal noise and interference from the other clusters; and the channel vector from all the BSs in the cluster toward MS is given as with denoting the downlink channel gain from BS to MS . Finally, we have the per-BS power constraints , for .
For both uplink and downlink, the channel vectors and remain constant for the entire coding block duration and are known to the corresponding control unit. As discussed in Sec. 1, the main goal of this paper is to provide a realistic evaluation of the advantages of the multiterminal backhaul compression strategies proposed in  for the uplink and in  for the donwlink. In the next two sections, we review these strategies.
3 Multiterminal Compression for the Uplink of C-RAN
In the uplink of C-RAN, each MS within the cluster under study encodes its message to produce a transmitted signal for each channel use. This signal is taken from a conventional Gaussian codebook and is hence distributed as where satisfies the per-MS power constraint . Note that, since the MSs cannot cooperate with each other, the transmitted signals are independent across the MS index .
Each th BS communicates with the control unit by providing the
latter with a compressed version of the
received signal . The control unit first decompresses
the signals , ,
and then, based on all signals ,
decodes the MSs’ messages
where the quantization noise is independent of the signal and distributed as .
Point-to-Point Backhaul Compression : In a conventional system, the control unit decompresses the descriptions in parallel as shown in Fig. 2-(a). In this case, the signal can be recovered at the control unit if the condition
is satisfied where with (see, e.g., [6, Ch. 3]).
Multiterminal Backhaul Compression -: Standard point-to-point compression does not leverage the statistical correlation among the signals received at different BSs. Based on this observation, distributed compression was proposed in  to utilize such correlation. Following , this can be done as follows. For a given ordering of the BS indices, the control unit decompresses in the order as shown in Fig. 2-(b). Therefore, when decompressing , the control unit has already retrieved the signals . These signals can be hence treated as side information available at the decoder, namely the control unit, but not to the encoder, namely BS . As a result, using the Wyner-Ziv theorem [6, Ch. 3], the descriptions for can be recovered at the control unit if the conditions
are satisfied, where we have defined vectors and , and the conditional variance is given by
with . The matrices and are given by
where we have defined the matrix .
We assume that the control unit performs single-user decoding of the messages sent by MSs based on all the descriptions , so that each message is decoded by treating the interference signals for as noise (see  for the analysis with joint decoding of all MSs and  for successive interference cancellation). Under this assumption, the achievable rate for MS is given by
where the conditional covariance with is given as
We are interested in evaluating the performance of the standard proportional-fair scheduler. This scheduler, at each time slot, select the power allocation and the quantization noise powers and the order so as to maximize the weighted sum-rate
with being a fairness constant and represents the average data rate of MS until the previous time slot (see, e.g., ). After each time slot, the rate is updated as where is a forgetting factor. We recall that increasing the constant encourages fairness among the MSs, while the objective function reduces to the sum-rate when . This problem is formulated as
To tackle the non-convex problem (12), we propose a separate design of the power control variables and the compression noise powers for a fixed permutation . Specifically, at Step 1, the power coefficients are optimized assuming ideal backhaul links (i.e., for ). This problem is stated as
or, equivalently, in the epigraph form
Albeit still non-convex, it is seen that the problem (14) belongs to the class of different-of-convex (DC) problems (see, e.g., ). Thus, we can leverage the iterative majorization minimization (MM) algorithm, which is known to converge to a locally optimal point of (14) (see, e.g., [16, Sec. 1.3.3]). The MM algorithm solves a sequence of convex problems obtained by linearizing the non-convex constraints (14b). With the so-obtained power variables , at Step 2, we optimize the quantization noise powers . It can be seen that the optimal quantization power , for fixed powers , is simply given by imposing equality in the backhaul constraint (12b), leading to
for with given in (6).
4 Multiterminal Compression for the Downlink of C-RAN
In the downlink of a C-RAN, the control unit first encodes each message for MS via a separate channel encoder, which produces a coded signal for each channel use. Each coded symbol is taken from a conventional Gaussian codebook and hence it is distributed as . The signals are further processed by the control unit in two stages, namely precoding and compression.
1. Precoding: In order to allow for interference management both across the MSs and among the data streams for the same MS, the signals in vector are linearly precoded via multiplication of a complex matrix . The precoded data can be written as
where the matrix can be factorized as with denoting the precoding vector corresponding to MS . The precoded data can be written as , where the signal is the precoded signal corresponding to the th BS and is given as with the vector having all zero elements except for the th element that contains 1.
2-(a). Point-to-Point Backhaul Compression : Each precoded data stream for must be compressed in order to allow the control unit to deliver it to the th BS through the backhaul link of capacity bps/Hz. Each th BS then simply forwards the compressed signal obtained from the control unit. Using standard rate-distortion considerations, we adopt a Gaussian test channel to model the effect of compression on the backhaul link. In particular, we write the compressed signals to be transmitted by BS as
where the compression noise is modeled as a complex Gaussian noise. With conventional backhaul compression, as shown in Fig. 3-(a), the signal corresponding to different BSs are compressed separately, which leads to independent quantization noises . Similar to the uplink, the compressed signal (17) can be transmitted to the th BS if the condition
2-(b). Multiterminal Backhaul Compression : The main idea of the multiterminal backhaul compression for the downlink is to control the effect of the additive quantization noises at the MSs by designing their correlation across the BSs within the cluster. This is made possible by multivariate compression [6, Ch. 7], which requires joint compression of all signals as in Fig. 3-(b). A successive compression implementation, which is dual to the successive decompression implementation of distributed source coding shown in Fig. 2-(b) for the uplink, is detailed in [11, Sec. IV-D].
To elaborate, we write the vector of compressed signals for all the BSs as
In (19), the compression noise is modeled as a complex Gaussian vector , where the covariance matrix consists of elements defining the correlation between the quantization noises of BS and BS .
Using the multivariate compression lemma in [6, Ch. 9], reference  shows that the signals obtained via the test channel (19) can be reliably transferred to the BSs on the backhaul links if the condition
is satisfied for all subsets , where the matrix is obtained by stacking the vectors for horizontally. We observe that the inequalities (18) for standard point-to-point compression are obtained by substituting into (20).
With the described precoding and compression operations and assuming that the interference signals are treated as noise signals at MSs, the achievable rate for MS is computed as
Similar to the uplink, our goal is to implement the proportional fairness scheduler, which requires to optimize the weighted sum-rate over the precoding matrix and the quantization covariance matrix , subject to the backhaul constraints (20) and the per-BS power constraints . The weighted sum-rate is defined as in Sec. 3. This problem is formulated as
5 Performance Evaluation
In this section, we discuss the performance advantages of multiterminal backhaul compression for the uplink and downlink of C-RAN systems on a standard cellular model based on . We focus on the performance evaluation in macro-cell 1 in Fig. 1, which is served by the three sectorized antennas from the corresponding macro-BSs and by pico-BSs. A control unit is connected to all BS antennas that serve cell 1 as in Fig. 1, which is to be hence considered as a cluster. The backhaul links to each macro-BS antenna and to each pico-BS have the capacities of and bps/Hz, respectively. All interference signals from other macro-cells, denoted by cell 2, cell 3,, cell 19, are treated as independent noise signals. We used the system parameters suggested in  and summarized in Table 1, and adopted the LTE rate model proposed in [18, Annex A]. We assume that the fairness is measured during time slots in which the locations of pico-BSs and MSs are fixed and small-scale fading channels change independently from slot to slot.
|System bandwidth||10 MHz|
|Path-loss (macro-BS)||, : distance in kilometers|
|Path-loss (pico-BS)||, : distance in meters|
|Antenna pattern for sectorized macro-BS antennas||, ,|
|Lognormal shadowing (macro-BS)||10 dB standard deviation|
|Lognormal shadowing (pico-BS)||6 dB standard deviation|
|Antenna gain after cable loss (macro-BS)||15 dBi|
|Antenna gain after cable loss (pico-BS and MS)||0 dBi|
|Noise figure||5 dB (macro-BS), 6 dB (pico-BS), 9 dB (MS)|
|Transmit power||46 dBm (macro-BS), 24 dBm (pico-BS), 23 dBm (MS)|
As shown in , with frequency reuse factor , the advantages of intra-cluster cooperation are masked by the effects of the interference coming from the adjacent clusters. Thus, we consider the frequency reuse pattern with proposed in  in which the available bandwidth is partitioned into three bands , and , which are allocated so as to minimize the resulting inter-cluster interference as illustrated in Fig. 4. As a result, cell 1 of interest suffers from the interference signals only from cells (8,10,12,14,16,18).
In this subsection, we examine the advantage of the multiterminal compression scheme based on distributed source coding reviewed in Sec. 3 for the uplink of the C-RAN described above. In Fig. 5, the CDF of the sum-rate is plotted with MSs, bps/Hz and . For the order on the BS, we assume that the control unit first retrieves the signals compressed at the macro-BSs and then decompresses the signals received from the pico-BSs. It is observed that, as compared to standard point-to-point compression, multiterminal compression provides performance gains of 17%, 27% and 42% for , and pico-BSs, respectively, in terms of the 50%-ile sum-rate. Thus, the performance gain of the multiterminal compression is most pronounced when a large number of pico-BSs are located in the same cluster. This suggests that a sophisticated design of backhaul compression provides relevant gain if many radio units are concentrated in given areas.
In Fig. 6, we plot the cell-edge throughput, i.e., the 5%-ile rate, versus the average spectral efficiency. The curve is obtained by varying the fairness constant in the utility function (11) (see, e.g., [14, Fig. 5]). We fix pico-BSs, MSs, bps/Hz, and . As we increase the constant , the 5%-ile rate increases due to the enhanced fairness among the MSs. We observe that spectral efficiencies larger than 1.01 bps/Hz are not achievable with point-to-point compression, while they can be obtained with multiterminal compression. Moreover, it is seen that multiterminal compression provides 1.6x gain in terms of cell-edge throughput for spectral efficiency of 2.9 bps/Hz.
In this subsection, we turn to the advantage of the multiterminal compression technique as described in Sec. 4 for the downlink. Fig. 7 plots the cell-edge throughput versus the average spectral efficiency for pico-BSs, MSs, bps/Hz, and . As for the uplink, it is seen that spectral efficiencies larger than 1.05 bps/Hz are not achievable with point-to-point compression, while they can be obtained with multiterminal compression. Specifically, multiterminal compression provides about 2x gain in terms of cell-edge throughput for spectral efficiency of 1 bps/Hz.
In this work, we have studied the advantage of multiterminal backhaul compression techniques over standard point-to-point compression for the uplink and downlink of cloud radio access networks. The extensive simulations are based on standard cellular models and the results focused on performance metrics such as sum-rate, proportional-fairness utility and cell-edge throughput. As an example, we observed that multiterminal compression techniques provide performance gains of more than 60% for both the uplink and the downlink in terms of the cell-edge throughput.
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