This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO Gaussian 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 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.

It has been shown that random beamforming using partial channel state information (CSI) achieves the same throughput scaling as obtained from dirty paper coding for a broadcast (downlink) channel with M transmit antennas and K users where K is large. In this paper, we apply this scheme to wideband MIMO broadcast channels. By using OFDM, an L-tap wideband channel can be decomposed to N parallel narrowband channels (subcarriers), where N > L . Neighboring subcarriers are highly correlated. Therefore, we consider neighboring subcarriers as a cluster and find the closed form solution for the joint characteristic function of SINR values at two subcarriers in a cluster. We show numerically how the knowledge of the quality of the center subcarrier sheds light about the quality of other subcarriers in the same cluster, and address the issue of cluster size. In addition, through complex and asymptotic analysis, we show that for cluster size of order N/L¿(log K) (for large K), users need only feedback the best SINR at the center subcarrier of each cluster in order for the transmitter to perform opportunistic beamforming and maintain the same throughput scaling as when full CSI is available. Using simulation results, we verify our analytical result and show that even fewer feedback can be tolerated, and larger clusters (N/2L) can be implemented for a small throughput hit.

It has recently been shown that significant reduction in the peak to mean envelope power (PMEPR) can be obtained by altering the sign of each subcarrier in a multicarrier system with n subcarriers. However, finding the best sign not only requires a search over 2npossible signs but also may lead to a substantial rate loss for small size constellations. In this paper, we first propose a greedy algorithm to choose the signs based on p-norm minimization and prove that the resulting PMEPR is guaranteed to be less than c log n where c is a constant independent of n for any n. This approach has lower complexity in each iteration compared to the derandomization approach of while achieving similar PMEPR reduction. We further improve the performance of the proposed algorithm by enlarging the search space using pruning. Simulation results show that PMEPR of a multicarrier signal with 128 subcarriers can be reduced to within 1.6 dB of the PMEPR of a single carrier system. In the second part of the paper, we address the rate loss by proposing a block coding scheme in which only one sign vector is chosen for K different modulating vectors. The sign vector can be computed using the greedy algorithm in n iterations. We show that the multi-symbol encoding approach can reduce the rate loss by a factor of K while achieving the PMEPR of c logKn, i.e., only logarithmic growth in K. Simulation results show that the rate loss can be made smaller than %10 at the cost of only 1 db increase in the resulting PMEPR for a system with 128 subcarriers.

A fundamental function performed by a sensory network is the retrieval of data gathered collectively by sensor nodes. The metrics that measure the efficiency of this data collection process are time and energy. In this paper, we study via simple discrete mathematical models, the statistics of the data collection time in sensory networks. Specifically, we analyze the average minimum delay in collecting randomly located/distributed sensors data for networks of various topologies when the number of nodes becomes large. Furthermore, we analyze the impact of various parameters such as size of packet, transmission range, and channel erasure probability on the optimal time performance. Our analysis applies to directional antenna systems as well as omnidirectional ones. This paper focuses on directional antenna systems and briefly presents results on omnidirectional antenna systems. Finally, a simple comparative analysis shows the respective advantages of the two systems.

Network coding and cooperative diversity have each extensively been explored in the literature as a means to substantially improve the performance of wireless networks. Yet, little work has been conducted to compare their performance under a common framework. Our goal in this paper is to fill in this gap. Specifically, we consider a single-hop wireless network consisting of a base station and N receivers. We perform an asymptotic analysis, as N rarr infin, of the expected delay associated with the broadcasting of a file consisting of K packets. We show that if K is fixed, cooperation outperforms network coding, in the sense that the expected delay is proportional to K (and thus within a constant factor of the optimal delay) in the former case while it grows logarithmically with N in the latter case. On the other hand, if K grows with N at a rate at least as fast as (logN)r, for r Gt 1, then we show that the average delay of network coding is also proportional to K and lower than the average delay of cooperation if the packet error probability is smaller than 0.36. Our analytical findings are validated through extensive numerical simulations.

Orthogonal Frequency Division Multiplexing (OFDM) is an attractive technique for high data rate transmissions in wireless and wireline systems. However OFDM signals suffer from high peak-to-mean envelope power (PMEPR). In this paper we consider the problem of reducing this high PMEPR using reserved peak reduction subcarriers as considered by Tellado and Cioffi [9]. We analyze the fundamental tradeoff between PMEPR reduction and the rate loss due to reserved subcarriers. We first provide a lower bound on the complementary cumulative distribution of PMEPR using infinitely many reserved subcarriers. We then show that the problem of minimizing the maximum of the absolute value of the signal using reserved subcarriers can be stated as a convex linear matrix inequality problem. While the problem is proved to be convex, its complexity is cubic in the number of OFDM subcarriers n which can be prohibitive when n is large. We then propose a suboptimal Greedy algorithm based on p-norm minimization that chooses only bipolar values for each subcarrier that has less complexity and more PMEPR reduction than the previously proposed algorithm in [8]. Our results provide the best tradeoff possible between PMEPR reduction and the associated rate loss and also leads to a practical algorithm to approach those limits.

We consider the problem of differentiated rate scheduling for the downlink (i.e., multi-antenna broadcast channel), in the sense that the rates required by different users must satisfy certain constraints on their ratios. When full channel state information (CSI) is available at the transmitter and receivers, the problem can be readily solved using dirty paper coding (DPC) and the application of convex optimization techniques on the dual problem which is the multiple access channel (MAC). Since in many practical application full CSI may not be feasible and computational complexity prohibitive when the number of users is large, we focus on other simple schemes that require very little CSI: time-division opportunistic (TO) beamforming where in different time slots (of different lengths) the transmitter performs opportunistic beamforming to the users requiring the same rate, and weighted opportunistic (WO) beamforming where the random beams are assigned to those users having the largest weighted SINR. For single antenna systems we also look at the capacity-achieving superposition coding (SC) scheme. In all cases, we determine explicit schedules to guarantee the rate constraints and show that, in the limit of large number of users, the throughput loss compared to the unconstrained throughput (sum-rate capacity) tends to zero. We further provide bounds on the rate of convergence of the sum-rates of these schemes to the sum-rate capacity. Finally, we provide simulation results of the performance of different scheduling schemes considered in the paper.

We consider a block-fading homogeneous broadcast channel with n users each receiving packets randomly and independently with a rate of lambda. Packets are stored in separate queues to await transmission using an opportunistic scheduling which exploits the multiuser diversity of the channel by serving the user with the most favorable channel condition at each coherence interval. In this paper, we consider a stochastic model in which mean packet transmission time is n-1and establish a convergence result for the occupancy distribution of all n queues under opportunistic scheduling. It is shown that if lambda1/lambdan + O(1) for large n. In order to improve the occupancy distribution while exploiting the multiuser diversity, we also study a scheme that serves the user with the longest queue among the d users with the most favorable channel conditions. It is shown that upper bound on the expected length of the longest queue improves to logd/lambdan + O(1). Simulation results are presented to validate our asymptotic results.

In this paper, we obtain the scaling laws of the sum-rate capacity of a MIMO X-channel, a 2 independent sender, 2 independent receiver channel with messages from each transmitter to each receiver, at high signal to noise ratios (SNR). The X-channel has sparked recent interest in the context of cooperative networks and it encompasses the interference, multiple access, and broadcast channels as special cases. Here, we consider the case with partially cooperative transmitters in which asymmetric side-information (in the form of a codeword) is available at one of the transmitters. It is proved that when there are M antennas at all four nodes, the sum-rate scales like 2M log SNR which is in sharp contrast to lceillfloor4M/3rfloor, 4M/3rceil log SNR for non-cooperative X-channels [M. Maddah-Ali et al., 2006], [S.A. Jafar]. This further proves that, in terms of sum-rate scaling at high SNR, partial side-information at one of the transmitters and full side-information at both transmitters are equivalent in the MIMO X-channel.

This paper re-examines the well-known fundamental tradeoffs between rate and reliability for the multi-antenna, block Rayleigh fading channel in the high signal to noise ratio (SNR) regime when (i) the transmitter has access to (noiseless) one bit per coherence-interval of causal channel state information (CSI) and (it) soft decoding delays together with worst-case delay guarantees are acceptable. A key finding of this work is that substantial improvements in reliability can be realized with a very short expected delay and a slightly longer (but bounded) worst-case decoding delay guarantee in communication systems where the transmitter has access to even one bit per coherence interval of causal CSI. While similar in spirit to the recent work on communication systems based on automatic repeat requests (ARQ) where decoding failure is known at the transmitter and leads to re-transmission, here transmit side-information is purely based on CSI. The findings reported here also lend further support to an emerging understanding that decoding delay (related to throughput) and codeword blocklength (related to coding complexity and delays) are distinctly different design parameters which can be tuned to control reliability.

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 parameters, 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.

In this letter, we derive the scaling laws of the sum rate for fading multiple-input multiple-output 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. Throughout the letter, we assume a fix average transmit power and consider a block-fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like MloglognN 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)loglogn. Therefore, the asymptotic gain of DPC over time sharing for the sum rate is (M/min(M,N)) when M and N are fixed. It is also shown that if M grows as logn, 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 Nloglogn

This correspondence deals with the outage capacity of relay networks in the low signal-to-noise ratio (SNR) regime. This work is motivated by the fact that in relay channels, unlike multi-antenna point-to-point links, the transmitters, i.e., source and relays, may not be co-located and therefore their channel statistics can be quite different. It has been recently shown that bursty amplify and forward (BAF) is outage optimal when all the links have a Rayleigh distribution. In this correspondence, it is shown that BAF is in fact outage optimal for a wide class of independent channels with smooth distribution functions. Optimality of BAF is further generalized to a special class of dependent channels, namely, the case where we opportunistically use only the best relay (out of N relays). It turns out that relative to the strategy where all the N relays are used, this opportunistic best relay strategy uses significantly smaller average power (independent of ) while suffering negligible increase in outage. This holds out potential for significant gains in an ad hoc network scenario where minimizing interference to possibly other users as well as conserving power are important considerations.

We consider a single-antenna broadcast block fading channel with n users where the transmission is packet- based. 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 nlogn, 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 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 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.

We consider the diversity-multiplexing tradeoff in half duplex relay channels. In recent work by Azarian et al. [2], it was shown that Dynamic Decode and Forward (DDF) strictly dominates all the other schemes in the high SNR (HSNR) regime, with the inherent assumption that all the links have the same average SNR p. In this work, we introduce geometry into the problem by letting the SNR of different links scale differently with p. We exhaustively identify the tradeoff for DDF and Non- Orthogonal Amplify and Forward (NAF) when the SNRs are different. We show that, even when geometry is included, the dominance behavior of DDF still holds. In some regions, NAF can at most do as well as DDF. We also show that when the multiplexing gain exceeds the exponential order of the SNR of either source to relay or relay to destination channels, the tradeoff curve of DDF reduces to that of direct transmission.

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

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 this letter, we consider the problem of constructing high-rate codes with low peak-to-mean-envelope power ratio (PMEPR) for multicarrier signals. Assuming coefficients of the multicarrier signal are chosen from a symmetric q-ary constellation, we construct codes with rate 1-(1/r)logq2 and PMEPR of less than crlogn for any r and n, where n is the number of subcarriers and c is a constant independent of n and r. The construction is based on dividing n subcarriers into n/r groups of r subcarriers and choosing a sign for each group to minimize the PMEPR. The signs are chosen using a variation of the algorithm proposed by the authors in previous papers. For large n, we can, in fact, construct a code with a rate of 1-O(1/logn) and PMEPR of less than clog2n. For binary phase-shift-keying-modulated signals, this partially solves the problem posed by Litsyn and implies a construction of 2n/2codewords with PMEPR less than 2clogn

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 logn, as opposed to n for the round-robin scheduling. We also show that when m grows faster than (logn)/sup 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 logn 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/sup 2//n)) for large n when M is not growing faster than logn. 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.

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

In this letter, we propose a method to reduce the peak-to-mean-envelope-power ratio (PMEPR) of multicarrier signals by modifying the constellation. For M-ary phase-shift keying 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 nonconvex optimization problem, we present a suboptimal solution by first optimizing over the signs, and then optimizing over the amplitudes given the signs. We prove that the minimization of the maximum of a continuous 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 16-quadrature amplitude modulation. 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.

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.

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 M. Sharif et al. (2003), 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.

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.

This paper derives 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 nTV 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 TV 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 logn, 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.

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.

Multicarrier signals exhibit a large peak-to-mean envelope power ratio (PMEPR). In this correspondence, without using a Gaussian assumption, we derive lower and upper probability bounds for the PMEPR distribution when the number of subcarriers n is large. Even though the worst case PMEPR is of the order of n, the main result is that the PMEPR of a random codeword C=(c/sub 1/,...,c/sub n/) is logn with probability approaching one asymptotically, for the following three general cases: i) c/sub i/'s are independent and identically distributed (i.i.d.) chosen from a complex quadrature amplitude modulation (QAM) constellation in which the real and imaginary part of c/sub i/ each has i.i.d. and even distribution (not necessarily uniform), ii) c/sub i/'s are i.i.d. chosen from a phase-shift keying (PSK) constellation where the distribution over the constellation points is invariant under /spl pi//2 rotation, and iii) C is chosen uniformly from a complex sphere of dimension n. Based on this result, it is proved that asymptotically, the Varshamov-Gilbert (VG) bound remains the same for codes with PMEPR of less than logn chosen from QAM/PSK constellations.

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, randomly choosing signs should lead to the PMEPR of log n in the probability sense. Based on the derandomization algorithm suggested in Spencer (1994), 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 - log/sub q/ 2, PMEPR of c log n, and with simple encoding and decoding. We then present simulation results for our algorithm.

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 in 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 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 /spl radic/(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 PMEPR of multicarrier signals, we show the existence of very high rate codes with average power of O(/spl radic/(n log n)) for large values of n, and furthermore the existence of codes with non-vanishing to zero rate and the average power of O(/spl radic/n) asymptotically.

Orthogonal frequency-division multiplexing (OFDM) introduces large amplitude variations in time, which can result in significant signal distortion in the presence of nonlinear amplifiers. We introduce a new bound for the peak of the continuous envelope of an OFDM signal, based on the maximum of its corresponding oversampled sequence; it is shown to be very tight as the oversampling rate increases. The bound is then used to derive a closed-form probability upper bound for the complementary cumulative distribution function of the peak-to-mean envelope power ratio of uncoded OFDM signals for sufficiently large numbers of subcarriers. As another application of the bound for oversampled sequences, we propose tight relative error bounds for computation of the peak power using two main methods: the oversampled inverse fast Fourier transform and the method introduced for coded systems based on minimum distance decoding of the code.

In this paper, we introduce a new bound for the peak of the continuous envelope of an OFDM signal based on the maximum of its corresponding oversampled sequence, that is considerably tighter than the recent results presented in Sharif and Khalaj (2001). The proposed bound is then used as the basis of our study in two parts. In the first part, we find an upper bound for the regrowth of the peak of the digitally clipped oversampled sequence after discrete to continuous conversion. We also show that for oversampling rates greater than /spl pi///spl radic/2, the peak regrowth percentage depends only on oversampling rate, regardless of the number of subcarriers. In the second part, we propose new and tight relative error bounds for computation of the peak power using two main methods: the oversampled inverse fast Fourier transform (IFFT) and the method introduced for coded systems by Tarokh and Jafarkhani (2000).

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.