The LTE network architecture is designed with the goal of supporting packet-switched traffic with seamless mobility, quality of service (QoS) and minimal latency. A packet-switched approach allows for the supporting of all services including voice through packet connections. The result in a highly simplified flatter architecture with only two types of node namely evolved Node-B (eNB) and mobility management entity/gateway (MME/GW). This is in contrast to many more network nodes in the current hierarchical network architecture of the 3G system. One major change is that the radio network controller (RNC) is eliminated from the data path and its functions are now incorporated in eNB. Some of the benefits of a single node in the access network are reduced latency and the distribution of the RNC processing load into multiple eNBs. The elimination of the RNC in the access network was possible partly because the LTE system does not support macro-diversity or soft-handoff.

In this chapter, we discuss network architecture designs for both unicast and broadcast traffic, QoS architecture and mobility management in the access network. We also briefly discuss layer 2 structure and different logical, transport and physical channels along with their mapping.

Network architecture

All the network interfaces are based on IP protocols. The eNBs are interconnected by means of an X2 interface and to the MME/GW entity by means of an S1 interface as shown in Figure 2.1. The S1 interface supports a many-to-many relationship between MME/GW and eNBs.

A major design goal for the LTE system is flexible bandwidth support for deployments in diverse spectrum arrangements. With this objective in mind, the physical layer of LTE is designed to support bandwidths in increments of 180 kHz starting from a minimum bandwidth of 1.08 MHz. In order to support channel sensitive scheduling and to achieve low packet transmission latency, the scheduling and transmission interval is defined as a 1 ms subframe. Two cyclic prefix lengths namely normal cyclic prefix and extended cyclic prefix are defined to support small and large cells deployments respectively. A subcarrier spacing of 15 kHz is chosen to strike a balance between cyclic prefix overhead and robustness to Doppler spread. An additional smaller 7.5 kHz subcarrier spacing is defined for MBSFN to support large delay spreads with reasonable cyclic prefix overhead. The uplink supports localized transmissions with contiguous resource block allocation due to single-carrier FDMA. In order to achieve frequency diversity, inter-subframe and intra-subframe hopping is supported. In the downlink, a distributed transmission allocation structure in addition to localized transmission allocation is defined to achieve frequency diversity with small signaling overhead.

Channel bandwidths

The LTE system supports a set of six channel bandwidths as given in Table 8.1.We note that the transmission bandwidth configuration BWconfig is 90% of the channel bandwidth BWchannel for 3–20 MHz. For 1.4 MHz channel bandwidth, the transmission bandwidth is only 77% of the channel bandwidth. Therefore, LTE deployment in the small 1.4 MHz channel is less spectrally efficient than the 3 MHz and larger channel bandwidths.

Like other 3G systems, the current HSPA system uses turbo coding as the channel-coding scheme. The LTE system supports peak data rates that are an order of magnitude higher than the current 3 G systems. It is therefore fair to ask the question, can the turbo coding scheme scale to data rates in excess of 100 Mb/s supported by LTE, while maintaining reasonable decoding complexity? This question is particularly important as other coding schemes, which offer inherent parallelism and therefore provide very high decoding speeds such as Low Density Parity Check (LDPC) codes, have recently become available. A major argument against turbo coding schemes is that they are not amenable to parallel implementations thus limiting the achievable decoding speeds. The problem, in fact, lies in the turbo code internal interleaver used in the current HSPA system, which creates memory contention among processors in parallel implementation. Therefore, if the turbo code internal interleaver can somehow be made contention free, it becomes possible for turbo code to benefit from parallel processing and hence achieve high decoding speeds.

LDPC codes

Similar to turbo codes, LDPC codes are near-Shannon limit error correcting codes. More recently, LDPC codes have been adopted in standards including IEEE 802.16e wireless MAN, IEEE 802.11n wireless LAN and digital video broadcast DVB-S2. The LDPC codes allow an extremely flexible code design that can be tailored to achieve efficient encoding and decoding. The interest in LDPC codes comes from their potential to achieve very high throughput (due to the inherent parallelism of the decoding algorithm) while maintaining good error-correcting performance and low decoding complexity.

In cellular systems, the wireless communication service in a given geographical area is provided by multiple Node-Bs or base stations. The downlink transmissions in cellular systems are one-to-many, while the uplink transmissions are many-to-one. A one-to-many service means that a Node-B transmits simultaneous signals to multiple UEs in its coverage area. This requires that the Node-B has very high transmission power capability because the transmission power is shared for transmissions to multiple UEs. In contrast, in the uplink a single UE has all its transmission power available for its uplink transmissions to the Node-B. Typically, the maximum allowed downlink transmission power in cellular systems is 43 dBm, while the uplink transmission power is limited to around 24 dBm. This means that the total transmit power available in the downlink is approximately 100 times more than the transmission power from a single UE in the uplink. In order for the total uplink power to be the same as the downlink, approximately 100 UEs should be simultaneously transmitting on the uplink.

Most modern cellular systems also support power control, which allows, for example, allocating more power to the cell-edge users than the cell-center users. This way, the cell range in the downlink can be extended because the Node-B can always allocate more power to the coverage-limited UE. However, in the uplink, the maximum transmission power is constrained by the maximum UE transmission power.

The Global system for mobile communications (GSM) is the dominant wireless cellular standard with over 3.5 billion subscribers worldwide covering more than 85% of the global mobile market. Furthermore, the number of worldwide subscribers using high-speed packet access (HSPA) networks topped 70 million in 2008. HSPA is a 3 Gevolution of GSM supporting high-speed data transmissions using WCDMA technology. Global uptake of HSPA technology among consumers and businesses is accelerating, indicating continued traffic growth for high-speed mobile networks worldwide. In order to meet the continued traffic growth demands, an extensive effort has been underway in the 3G Partnership Project (3GPP) to develop a new standard for the evolution of GSM/HSPAtechnology towards a packet-optimized system referred to as Long-Term Evolution (LTE).

The goal of the LTE standard is to create specifications for a new radio-access technology geared to higher data rates, low latency and greater spectral efficiency. The spectral efficiency target for the LTE system is three to four times higher than the current HSPA system. These aggressive spectral efficiency targets require pushing the technology envelope by employing advanced air-interface techniques such as low-PAPR orthogonal uplink multiple access based on SC-FDMA (single-carrier frequency division multiple access) MIMO multiple-input multiple-output multi-antenna technologies, inter-cell interference mitigation techniques, low-latency channel structure and single-frequency network (SFN) broadcast. The researchers and engineers working on the standard come up with new innovative technology proposals and ideas for system performance improvement.

In this chapter we study dynamics at the general level of s-categories. It is based upon Section 2.2 and Chapter 4, and is independent of the intervening work on bigraphs.

Recall from Chapter 2 the distinction between concrete and abstract bigraphs; the former have their nodes and edges as support, while the latter have no support. In s-categories, this distinction is less sharp; an spm category is just an s-category with empty supports. Much of the work of this chapter therefore applies to both. However, when we introduce behavioural equivalence in Section 7.2, we first make sure it is robust (i.e. that the equivalence is preserved by context) in the case where the s-category possesses RPOs; we are then able to retain this robust quality when the s-category is quotiented, or abstracted, in a certain way – even if RPOs are thereby lost.

We begin in Section 7.1 with a notion of a basic reactive system, based upon an s-category equipped with reaction rules. This determines a basic reaction relation which describes how agents may reconfigure themselves. We refine this definition to a wide reactive system, with a notion of locality based on the width of objects in a wide s-category, introduced in Definition 2.14. We are then able to describe where each reaction occurs in an agent, and thus to define a wide reaction relation that permits reactions to occur only in certain places.

In Section 7.2 we introduce labelled transition systems, which refine reactive systems by describing the reactions that an agent may perform, possibly with assistance from its environment.

In Section 2.1 we define bigraphs formally, together with fundamental ways to build with them.

In Section 2.2, using some elementary category theory, we introduce a broader mathematical framework in which bigraphs and their operations can be expressed. The reader can often ignore this generality, but it will yield results which do not depend on the specific details of bigraphs.

In Section 2.3 we explain how the concrete place graphs, link graphs and bigraphs over a basic signature each form a category of a certain kind. We then use the tools of the mathematical framework to introduce abstract bigraphs; they are obtained from the concrete ones of Section 2.1 by forgetting the identity of nodes and edges.

Throughout this chapter, when dealing with bigraphs we presume an arbitrary basic signature Κ.

Bigraphs and their assembly

Notation and terminology We frequently treat a natural number as a finite ordinal, the set of all preceding ordinals: m = {0, 1, …, m − 1}. We write S # T to mean that two sets S and T are disjoint, i.e. S ∩ T = ∅.

This chapter refines the structural analysis of concrete bigraphs. In Section 5.1 we establish some properties for concrete bigraphs, including RPOs. In Section 5.2 we enumerate all IPOs for a given span. Finally, in Section 5.3 we show that RPOs do not exist in general for abstract bigraphs.

RPOs for bigraphs

We begin with a characterisation of epimorphisms (epis) and monomorphisms (monos) in bigraphs. These notions are defined in a precategory just as in a category, as follows:

Definition 5.1 (epi, mono) An arrow f in a precategory is epi if g ° f = h ° f implies g = h. It is mono if f ° g = f ° h implies g = h. 〉

Proposition 5.2 (epis and monos in concrete bigraphs)A concrete place graph is epi iff no root is idle; it is mono iff no two sites are siblings. A concrete link graph is epi iff no outer name is idle; it is mono iff no two inner names are siblings.

A concrete bigraph G is an epi (resp. mono) iff its place graph GPand its link graph GLare so.

EXERCISE 5.1 Prove the above proposition, at least for the case of epi link graphs. Hint: Make the following intuition precise: if G and H differ then, when composed with F, the difference can be hidden if and only if F has an idle name. 〉

The proposition fails for abstract bigraphs, suggesting that concrete bigraphs have more tractable structure. We shall now provide further evidence for this by constructing RPOs for them.