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The ever-growing demand for higher rates and better quality of service in cellular systems has attracted many researchers to study techniques to boost the capacity and improve the performance of cellular systems. The main candidates to increase the capacity are to use multiple antennas or to increase the bandwidth. This thesis attempts to solve a few challenges regarding scheduling schemes in the downlink of cellular networks, and the implementation of modulation schemes suited for wideband channels. Downlink scheduling in cellular systems is known to be a bottleneck for future broadband wireless communications. Information theoretic results on broadcast channels provide the limits for the maximum achievable rates for each receiver and transmission schemes to achieve them. It turns out that the sum-rate capacity (sum-rate (or throughput) refers to the sum of the transmission rates to all users) of a multi-antenna broadcast channel heavily depends on the availability of channel state information (CSI) at the transmitter. Unfortunately, the dirty paper coding (DPC) scheme which achieves the capacity region is extremely computationally intensive especially in multiuser context. Furthermore, relying on the assumption that full CSI is available from all the n users may not be feasible in practice. In the first part of the thesis, we obtain the scaling law of the sum-rate capacity for large n and for a homogeneous fading MIMO (multiple input multiple output) broadcast channel, and then propose a simple scheme that only requires little (partial) CSI and yet achieves the same scaling law. Another important issue in downlink scheduling is to maintain fairness among users with different distances to the transmitter. Interestingly, we prove that our scheduling scheme becomes fair provided that the number of transmit antennas is large enough. We further analyze the impact of using a throughput optimal scheduling on the delay in sending information to the users.

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.

We consider a single-antenna broadcast block fading channel with n users where the transmission is packetbased. We define the (packet) delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. This is a more stringent notion of delay than average delay and is the worst case (access) delay among the users. A delay optimal scheduling scheme, such as round-robin, achieves the delay of mn. For the opportunistic scheduling (which is throughput optimal) where the transmitter sends the packet to the user with the best channel conditions at each channel use, we derive the mean and variance of the delay for any m and n. For large n and in a homogeneous network, it is proved that the expected delay in receiving one packet by all the receivers scales as n log n, as opposed to n for the round-robin scheduling. We also show that when m grows faster than (log n)^r, for some r > 1, then the delay scales as mn. This roughly determines the timescale required for the system to behave fairly in a homogeneous network. We then propose a scheme to significantly reduce the delay at the expense of a small throughput hit. We further look into the advantage of multiple transmit antennas on the delay. For a system with M antennas in the transmitter where at each channel use packets are sent to M different users, we obtain the expected delay in receiving one packet by all the users.

This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n + M log P/M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n rarr infin. When the channel exhibits some spatial correlation with a covariance matrix R (non-singular with tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n + M log P/M + log det(R) + o(1). We further show that the sum-rate of various beamforming schemes achieves M log log n + M log P/M + M log c + o(1) where c les 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in M. Sharif et al. (2005) and more generally, for random beamforming with preceding in which beams are pre-multiplied by a fixed matrix. Simulation results are presented at the end of the paper.

In this paper we consider the effect of channel estimation error on the capacity region of MIMO Gaussian broadcast channels. It is assumed that the receivers and the transmitter have (the same) estimates of the channel coefficients (i.e., the feedback channel is noiseless). We obtain an achievable rate region based on the dirty paper coding scheme. We show that this region is given by the capacity region of a dual multi-access channel with a noise covariance that depends on the transmit power. We explore this duality to give the asymptotic behavior of the sum-rate for a system with a large number of user, i.e., n rarr infin. It is shown that as long as the estimation error is of fixed (w.r.t n) variance, the sum-capacity is of order M log log n, where M is the number of antennas deployed at the transmitter. We further obtain the sum-rate loss due to the estimation error. Finally, we consider a training-based scheme for block fading MISO Gaussian broadcast channels. We find the optimum length of the training interval as well as the optimum power used for training in order to maximize the achievable sum-rate.

In a broadcast channel in which one transmitter serves n receivers, the capacity region highly depends on the amount of channel state information (CSI) at the transmitter. Assuming that the transmitter knows the SNR of all the receivers, opportunistic strategy maximizes the throughput (sum-rate) of the system. It is usually assumed that CSI is accurate, however, evaluating the SNR is basically an estimation problem in the receiver which cannot be done without error. In this paper, we analyze the effect of the noisy estimation of SNR on the throughput of a broadcast channel. We propose a generalization of the opportunistic transmission in which the transmitter still sends to the user with the highest estimated SNR, but backs off on the transmit rate based on the variance of the estimation error. We obtain the optimum amount of back off and compute the throughput for our scheduling scheme. Clearly, the estimation can be improved by using a longer training phase; however, longer training would deteriorate the throughput. In the final part of the paper, we address this trade off and obtain the optimum training strategy that maximizes the throughput of the system.

In this paper, we consider a fading broadcast channel where users have different rate demands. In particular, we assume users are divided into M groups, each group of which requires the same rate, and where the ratio of the rates of the groups are given. The transmitter would like to maximize the throughput (sum of the rates to all users) while maintaining the rational rate constraints. In general, this problem appears to be computationally intractable since the ergodic capacity region is described as the convex hull of (an infinite) set of rates. In this paper, we therefore, focus on the asymptotic regime of many users (large n) where explicit results can be found. In particular, we propose three scheduling schemes to provide the rational rate constraints namely, weighted opportunistic (WO), time division opportunistic (TO), and superposition coding (SC). The WO scheduling is a generalization of the opportunistic scheduling in which we transmit to only the user that has the maximum weighted signal to noise ratio (SNR). In TO, each group has its own time slot in which the transmitter chooses the user with the best SNR from the corresponding group. Superposition coding is the one that achieves the capacity region. For each scheduling we give explicit scheme to guarantee the rational rate constraints. We also analyze the throughput loss due to rate constraints for different schemes. In particular, we show that the throughput loss compared to the maximum throughput (i.e., the sum rate capacity without any rate constraints) tends to zero for large n, and finally, we analyze the convergence rate of all the schemes.

We consider a single-antenna broadcast block fading channel (downlink scheduling) with n users where the transmission is packet-based and all users are backlogged. We define the delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. This is a more stringent notion of delay than average delay and is the worst case delay among the users. A delay optimal scheduling scheme, such as round-robin, achieves the delay of mn. In a heterogeneous network and for the optimal throughput strategy where the transmitter sends the packet to the user with the best channel conditions, we derive the moment generating function of the delay for any m and n. For large n and in a homogeneous network, the expected delay in receiving one packet by all the receivers scales as n log n, as opposed to n for the round-robin scheduling. We also show that when m grows faster than (log n)^r, for some r > 1, then the expected value of delay scales like mn. This roughly determines the time-scale required for the system to behave fairly in a homogeneous network. We then propose a scheme to significantly reduce the delay at the expense of a small throughput hit. We further look into two generalizations of our work: i) the effect of temporal channel correlation and ii) the advantage of multiple transmit antennas on the delay. For a channel with memory of two, we prove that the delay scales again like n log n no matter how severe the correlation is. For a system with M transmit antennas, we prove that the expected delay in receiving one packet by all the users scales like (n log n)/(M +O((M^2)/n) for large n and when M is not growing faster than log n. Thus, when the temporal channel correlation is zero, multiple transmit antenna systems do not reduce the delay significantly. However, when channel correlation is present, they can lead to significant gains by “decorrelating” the effective channel through means such as random beamforming.

It has recently been shown that by altering the sign of each subcarrier in a multicarrier system significant reduction in the peak to mean envelope power (PMEPR) can be obtained. In fact, the PMEPR can even be made a constant independent of the number of subcarriers n. However, finding the best sign requires a search over 2^n possible signs which is computationally prohibitive. In this paper, we first propose a greedy algorithm to choose the signs based on p-norm minimization and we prove that it can achieve a PMEPR of order log n. We further decrease the PMEPR by enlarging the search space considered by the greedy algorithm. By ignoring peaks with probability less than l0^-3, simulation results show that the PMEPR of a multicarrier system with 128 subcarriers each one modulated by 64QAM constellations is reduced to 3.4. This implies that at the cost of one bit of information per subcarrier (i.e., not sending information over the sign of each subcarrier) and modest computational complexity in the transmitter, the PMEPR can be reduced from 12.5 to 3.4 which is within 1.6 dB of the PMEPR of a single carrier system with 64QAM modulation.

We consider the problem of differentiated rate scheduling for the fading MIMO Gaussian broadcast channel, in the sense that the rates required by different users must satisfy certain rational rate constraints. When full channel state information (CSI) is available at the transmitter, the problem can be readily solved using dirty paper coding (DPC) and con- vex optimization techniques on the dual multiple-access channel (MAC). However, since in many practical applications full CSI is not feasible, and since the computational complexity may be prohibitive when the number of users is large, we focus on two simple schemes that require very little CSI: time-division opportunistic (TO) beamforming where in different time-slots the transmitter performs opportunistic beamforing only to users requiring the same rate, and weighted opportunistic (WO) beamforing where the random beams are assigned to those users having the largest weighted SINR. In both cases we determine explicit schedules to guarantee the rate constraints and show that, in the limit of a large number of users, the throughput loss compared to the unconstrained sum-rate capacity tends to zero. As a side result, we show that, in this regime, the sum-rate of opportunistic beamforming converges to the optimal sum-rate achieved by DPC, which is a stronger result than the order-optimal results of (10, 13).

In this paper, we propose a method to reduce the peak to mean envelope power ratio (PMEPR) of multicarrier signals by modifying the constellation. For MPSK constellations, we minimize the maximum of the multicarrier signal over the sign and amplitude of each subcarrier. In order to find an efficient solution to the aforementioned non-convex optimization problem, we present a suboptimal solution by first optimizing over the signs using the result of [1], and then optimizing over the amplitudes given the signs. We prove that the minimization of the maximum of a multicarrier signal over the amplitude of each subcarrier can be written as a convex optimization problem with linear matrix inequality constraints. We also generalize the idea to other constellations such as 16QAM. Simulation results show that by an average power increase of 0.21 db and not sending information over the sign of each subcarrier, PMEPR can be decreased by 5.1 db for a system with 128 subcarriers.

We consider a single-antenna broadcast fading channel with n backlogged users. Assuming the transmission is packet-based, we define the delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. A delay optimal strategy such as round-robin achieves the delay of mn. For the optimal throughput strategy (i.e. transmitting to the user with the best channel condition at each channel use), we derive the mean and variance of the delay for any m and n. For large n, it is proved that the expected delay in receiving the first packet in all users scales like n log n as opposed to n for the round-robin scheduling.

We derive the scaling laws of the sum rate throughput for MIMO Gaussian broadcast channels using time-sharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Assuming a fixed total average transmit power, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nN for DPC and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of time-sharing to the strongest user scales like min(M,N) log log n. It is also shown that if M grows as log n, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of time-sharing scales like N log log n.

In this letter, we consider the achievable average power reduction of multiple subcarrier modulated optical signals by using optimized reserved carriers. Based on Nehari's result we present a lower bound for the maximum average power of the signal after adding the reserved carriers. Simulations show that the mean value of the average required power behaves very close to /spl radic/(2nloglogn) for binary phase-shift keying (BPSK) constellations where n is the number of subcarriers. We further remark on evaluating optimum values for reserved carriers using convex optimization and Nehari's result.

This paper presents the data collection function in sensory networks. Specifically we derive relationships between data collection time and transmission range, data packet size and channel noise in the simple line scenario. To develop intuition these relationships are studied in the limit case where the number of sensor nodes becomes large.

It has been shown that with probability one the peak to mean envelope power ratio (PMEPR) of any random codeword chosen from a symmetric QAM/PSK constellation is log n where n is the number of subcarriers [1]. In this paper, the existence of codes with nonzero rate and PMEPR bounded by a constant is established.

Multicarrier signals often exhibit large peak to mean envelope power ratios (PMEPR) which can be problematic in practice. In this paper, we study adjusting the sign of each subcarrier in order to reduce the PMEPR of a multicarrier signal with n subcarriers. Considering that any randomly chosen codeword has PMEPR of log n with probability one and for large values of n [1], randomly choosing signs should lead to the PMEPR of log n in the probability sense. Based on the derandomization algorithm suggested in [2], we propose a deterministic and efficient algorithm to design signs such that the PMEPR of the resulting codeword is less than c log n for any n where c is a constant independent of n. By using a symmetric q-ary constellation, this algorithm in fact constructs a code with rate 1 - logq 2, PMEPR of c log n, and with simple encoding and decoding. We then present simulation results for our algorithm.

In this paper we show that "separation"-based approaches in wireless networks do not necessarily give good performance in terms of the capacity of the network. Therefore in optimal design of a wireless network, its total structure should be considered. In other words, achieving capacity on the subnetworks of a wireless network does not guarantee globally achieving capacity. We will illustrate this fact by considering some examples of multistage Gaussian wireless relay networks. We will consider a wireless Gaussian relay network with one stage in both fading and nonfading environment. We show that as the number of relay nodes, n, grows large, the capacity of this network scales like log n. We then show that with the "separation"-based scheme, in which the network is viewed as the concatenation of a broadcast and a multiaccess network, the achievable rate scales as log log n and as a constant for fading and nonfading environment, respectively, which is clearly suboptimal.

Multicarrier signals exhibit a large peak to mean envelope power ratio (PMEPR). In this paper, we derive the lower and upper probability bounds for the PMEPR distribution when entries of the codeword, C, are chosen independently from a symmetric q-ary PSK or QAM constellation, C /spl isin/ /spl Qscr/;/sup nq/, or C is chosen from a complex n dimensional sphere, /spl Omega//sup n/ when the number of subcarriers, n, is large and without any Gaussian assumption on either the joint distribution or any sample of the multicarrier signal. Even though the worst case PMEPR is of the order of n, the main result is that the PMEPR of a random codeword C chosen from /spl Qscr/;/sup nq/ or /spl Omega//sup n/ is log n with probability one, asymptotically. A Varsharmov-Gilbert (VG) style bound for the achievable rate and minimum Hamming distance of codes chosen from /spl Qscr/;/sup nq/, with PMEPR of less than log n is obtained. It is proved that asymptotically, the VG bound remains the same for the codes chosen from /spl Qscr/;/sup nq/ with PMEPR of less than log n.

Multiple subcarrier modulation (MSM) is an attractive technique for optical wireless communication for high speed applications. The main disadvantage of this scheme is its low average power efficiency which is an analogous problem to the high peak to mean envelope power ratio (PMEPR) of multicarrier signals. In this paper, we consider the achievable average power reduction of MSM signals by using optimized reserved carriers and coding methods. Based on Nehari’s result we present a lower bound for the maximum average power of the signal after adding the reserved carriers. It is shown that the mean value of the average required power behaves very close to √2n log log n for a BPSK constellation where n is the number of subcarriers. We then consider finding the optimum values for the carriers and the effect of having finite bandwidth for reserved carriers. In the next section, mainly based on recent coding results for the PMEPR of multicarrier signals, we show the existence of very high rate codes with average power of O(√n log n) for large values of n, and furthermore the existence of codes with non-vanishing to zero rate and average power of O(√n) asymptotically.

Clipping the OFDM signals in the digital part of the transmitter is one of the simplest methods to reduce the peak factor. However, it suffers from additional clipping distortion, peak regrowth after digital to analog conversion, and out-of-band radiation in the case of oversampled sequence clipping. We use oversampled sequence clipping to combat the effect of peak regrowth and propose a method to reconstruct the clipped samples and mitigate the clipping distortion in the presence of channel noise at the expense of bandwidth expansion. We show through extensive simulations that by slightly increasing the bandwidth of the system, we can significantly improve the performance while limiting the maximum amplitude of the analog signal.

Orthogonal frequency division multiplexing (OFDM) has a large peak to mean envelope power ratio (PMEPR), which can result in significant signal distortion in the presence of nonlinear amplifiers. We show that the peak of the continuous envelope of the OFDM signal can be bounded by the maximum of the corresponding oversampled sequence. This fact is then used as the cornerstone of our two-part study. In the first part, statistical analysis is used to find the probability upper bound for the complementary cumulative distribution function of PMEPR. It is also proven that for a large number of subcarriers, only one redundant bit is necessary to limit the PMEPR within 10% of its maximum value. In the second part, PMEPR estimation using oversampling and the fast Fourier transform is revisited. Here, we introduce a novel measure on the estimation error using an oversampled OFDM signal.