Políticas juveniles de Formación y Empleo

hl k ˆ hn k hl k hn k hk k Backhaul with delay CSI feedback with delay   ˆ hk k, ˆhnk, ˆhlk

Figure 5.13 CSIfeedback and backhauling concept considered for inter-cell interference nulling (ICIN).

directly applicable to the multi-cell scenario. While theCSIof only one channel is fed back in the single-cell case, cooperative strategies require feedback ofCSI from multipleBSs using the same feedback link. Further, in single-cell transmis- sion, quantized CSI reaches the BS after experiencing a delay in the feedback channel [ZHKA09]. In the multi-cell cooperative framework, however, quantized CSI is subject to an additional source of delay in the backhaul link. The impact of delayed CSI on the performance of non-cooperative systems [ZHKA09] has been investigated extensively. The effect of delayed limited feedback on the per- formance of cooperative systems has received comparatively less attention.

In this section, two different cases are considered: i) a single receive antenna and ii) multiple receive antennas at the user equipment (UE). For the sin- gle receive antenna case, the BSs need to optimize their precoding matri- ces/beamforming vectors to maximize the sum-rate under given constraints but for a multiple receive antenna case, the precoding/postcoding matrices/vectors should be jointly optimized. In Subsection 5.3.2, we describe ICIN, a low- complexity and non-iterative partial cooperative strategy that uses explicit per- base power constraints and yields reasonable gains in the sum-rate, while result- ing in a small burden over the backhaul link. Note thatICINrequires that the total number of antennas perBSbe larger than the number of single-antenna ter- minals considered in one transmission, an aspect we will discuss in detail later. We also describe some limited CSI feedback algorithms for ICIN. In Subsec- tion5.3.3,we further extend the cooperative strategies to the multiple antenna cases and show performance results.

70 CoMPSchemes Based on Interf.-Aware Transceivers or Interf. Coord.

5.3.2

Single Receive Antenna at the Terminal

We now briefly describe ICINfor the setup in Fig. 5.13 for an M cell system. We assume that on a particular observed resource, the BSin each cell serves a single active user. The received signal power of the desired and interfering signals is a function of the user’s location in the cell. A similar approach was adopted in [JTS+_{08a, SSBN}+_{06]. Each user is assumed to face interference from M− 1}

neighboring BSs. We index the users in each cell by the BS they obtain their desired signal from, i.e. the k-thBSservices the k-th user, for k = 1, . . . , K. Note that by assuming that there is a single user in each cell on each resource, we fix

K = M . We assume that all BSs are equipped with Nbs antennas, while each

user supports a single receive antenna.

As defined in Chapter 3, the channel between BS m and UE k is denoted

by hm

k ∈ CNbs×1. The symbol to be transmitted to the k-th user is denoted by

x_k, where the transmit power is E{x_kxH

k} = Es, implying a per-base station

power constraint. The channels are subject to large-scale fading, which includes distance-dependent path-loss and shadowing effects, and small-scale fading. After averaging over the small-scale fading effects, the received SNR of the desired signal is denoted by ρ_k. The interfering signal SNR from a BS m to UE k

is given by αm_kρ_k, where αm

k ∈ [0, 1] (i.e. the interfering signal strength can

at most be equal to that of the desired signal). A similar parameter is used in[JTS+_08a,SSBN+_{06] to model theSNRof the interfering signal with respect}

to the received signal. Note that ρ_k and αm

k are independent of the beamforming

vectors. Observing the transmission of a single frequency-flat sub-carrier of an orthogonal frequency division multiple access (OFDMA) system, and assuming that the channels remain constant over the codeword transmission, the signal- to-interference-and-noise ratio (SINR) of the k-th user is given by

SINR_k= ρ_khk k H_w k 2  j=k αj_kρ_k  hj_{k H} w_j 2 + 1 , (5.24)

where w_k denotes the beamforming vector employed at BS k to transmit to

UE k, which is normalized to have unit-norm. We assume that the BSs have

perfect knowledge of the involvedSNR terms ρ_k and αm k .

When full and instantaneous CSI is available at all BSs, the k-th BS has instantaneous knowledge of not only its own desired channel toUEk, hk_k, but also of the interference caused to neighboring cells, i.e. hk

j, j = 1, . . . , K, j= k. T he

k-thBSthen computes the beamforming vector, w_k, as[ZA10,JLD08,LKL09]

w_k = a_k, where A_k = [a1. . . aK] = . ˜ hk1, . . . , ˜hkK /_† , (5.25)

where (.)†refers to the pseudo-inverse and ˜hm_k = hm_k/"hm_k" denotes the normal-

5.3 Downlink Coordinated Beamforming 71

Nbs≥ K,(5.25) ensures perfect interference nulling in most cases, i.e. hj_kwj= 0,

for k, j = 1, . . . , K, j = k. Note that while ICIN is a simple, non-iterative and distributed coordinated beamforming strategy, it suffers from the dimensionality constraints imposed from computing the pseudo-inverse, i.e. Nbs≥ K. For the more practical case where the number of users in the system is greater than Nbs, scheduling can be employed to enforce Nbs≥ K. This implies that there exists a trade-off between increasing the number of users for simultaneous transmission in the cells and perfect interference cancelation. Clustering can also be employed to group cells into clusters of size ≤ Nbs each and use intra-cell time division multiple access (TDMA)or a comparable orthogonal transmission strategy, to make sure that Nbs≥ K.

Limited Feedback

Practical feedback channels are bandwidth-limited and have delays associated with them. Hence, it is important to investigate the performance of ICINwith delayed limited feedback[BH10]. The channel directions ˜hm

k[t] are quantized to

the unit-norm vectors given by ˆhm

k [t] at the k-th user, where we now introduce

variable t to capture the time instant, for example a transmit time interval (TTI). We assume that each user can utilize Btot bits for feedback, and that

B_k and B_kj bits are used to quantize ˜hk

k[n] and ˜h j

k[t], j= k respectively, where

B_k+_j=kB_kj = Btot. The delay associated with quantizing ˜hk_k[t] to ˆhk_k[t] and feeding back the latter to the k-th BS is denoted by D_k. T he k-th user also quantizes the interfering channels, ˜hj_k[t], j= k to ˆhj_k[t], j= k and feeds back the latter to the k-th BS, which then forwards this information to the j-th BS over the backhaul link, incurring an overall delay of Dj_k. The limited feedback model is also shown in Fig.5.13.

At the time instant t, the k-thBShas knowledge of ˆhk

k[t− Dk] and ˆhkj[t− Dkj],

for all j= k. The beamforming vector at the t-th time instant, w_k[t], is designed using the delayed and quantizedCSIof the desired channels and the interference caused to other cells[BH10]

w_k[t] =a_k where (5.26) A = . ˆ hk1[t−Dk1]..ˆhkk−1[t−Dkk−1], ˆhkk[t−Dk], ˆhkk+1[t−Dk+1k ]..ˆhkK[t−DkK] /_† .

When Nbs≥ K, the beamforming vector lies in the Nbs− (K − 1) dimensional null-space of the K− 1 interfering channels. Hence, when Nbs= K, wk[t] will

lie in a one-dimensional sub-space, independent of ˆhk_k. T his implies that if we have Nbs= K, it is not necessary to feedback the quantized desired channel back to the BS, i.e. B_k = 0. In contrast, when Nbs> K, knowledge on ˆhk_k is desirable to determine the best w_k[t] in the Nbs− (K − 1) dimensional sub- space. By assuming that hk

k[t] and hkj[t], j= k are constant throughout the

72 CoMPSchemes Based on Interf.-Aware Transceivers or Interf. Coord.

Markov block fading autoregressive model[TJMW01]

hk_k[t] = η_khk_k[t− D_k] + 0 1− η2 kehk k[t], and (5.27) hk_j[t] = ηk_jhk_j[t− Dk_j] + 0 1− (ηk j)2ehk j[t], (5.28) where e_hk

k[t] and ehkj[t] denote the channel knowledge uncertainties, which are

uncorrelated with hk_k[t− D_k] and hk

j[t− Dkj], respectively. The entries of ehk k[t]

and e_hk

j[t] are distributed byNC(0, 1). The correlation coefficients for the desired

and interfering channels are denoted by η_k and η_jk, respectively. Clarke’s auto- correlation model is used to determine η_k and ηk

j as [ZHKA09]

η_k = J0(2πDkfdTs), and ηjk = J0(2πD_jkfdTs), (5.29)

where J0 is the zeroth order Bessel function of the first kind, fd is the Doppler

spread and T_sis the symbol duration. The Doppler spread is given as f_d= νf_c/c,

where ν is the relative velocity of the transmitter-receiver pair, f_c the carrier frequency, and c the speed of light. The mean loss in sum-rate due to delayed limited feedback is bounded in[BH10], as a function of delays, signal strengths, and can be minimized choosing B_k and B_kj as per Theorems5.1-5.3.