We consider a wireless communication scenario with K source-destination pairs communicating throu... more We consider a wireless communication scenario with K source-destination pairs communicating through several half-duplex amplify-and-forward relays. We design the relay beamforming matrices by minimizing the total power transmitted from all the relays subject to quality of service constraints on the received signal to interference-plus-noise ratio at each destination node. We propose a novel method for solving the resulting nonconvex optimization problem in which the problem is decomposed into a group of second-order cone programs (SOCPs) parameterized by K real parameters. Grid search or nested bisection can be used to search for the optimal values of these parameters. We provide numerical simulations showing the superior performance of the proposed algorithms compared to earlier suboptimal approximations and their ability to approach the globally optimal solution of the non-convex problem.
The downlink frame of a cellular relay network is considered, where a shared MIMO decode-and-frow... more The downlink frame of a cellular relay network is considered, where a shared MIMO decode-and-froward relaying is used to serve the users at the edge of the cell. The relay employs zero-forcing beamforming to manage the interference among the mobile stations (MSs) at the edge of the cell. A non-cooperative scheme is considered where there is no coordination between the base stations (BSs) and the relay station (RS), and a power control algorithm for the RS is developed that maximizes the rate of the relayed users. A cooperative setting which allows the coordination of a power allocation between BSs and RSs is also considered. For this setting, based on the proposed achievable scheme, an optimization formulation is derived to maximize the total throughput of the MSs subject to a constraint on the total power of the system. The problem is solved iteratively as a sequence of geometric programs. Simulation results are provided showing that a significant increase in the network throughput can be achieved via the proposed schemes compared to a conventional cellular system with no relays.
Knee flexion deformity can cause marked physical disability. Acute correction, whether nonoperati... more Knee flexion deformity can cause marked physical disability. Acute correction, whether nonoperative or operative, may lead to serious complications. We treated 50 patients (71 knees) between 1994 and 2002 with the Ilizarov external fixator. The deformity was gradually corrected using Ilizarov principles. Of the 50 patients, 29 were affected unilaterally and 21 bilaterally. In 15 patients, there were associated deformities. In no patient did we surgically release soft tissues; in two patients with arthrodesed or congenitally fused knees, we performed osteotomy before distraction. All patients were assessed clinically and radiographically. We assessed knee flexion angle, range of motion, stability, presence of pain, and healing index. After a minimum followup of 1 year (mean 3.7 years; range, 1–8 years), 18 of 20 of the preoperatively nonambulatory patients having bilateral surgery could walk at last followup. Complications included pin tract infection in all patients, knee subluxation in three patients, and fracture related to treatment in seven patients. We believe gradual correction using a circular frame an effective method to treat flexion knee contractures. In patients with bilateral deformities, improvement in functional activity may be expected in most patients. Level of Evidence: Level IV, therapeutic study. See the Guidelines for Authors for a complete description of levels of evidence.
The Taylor spatial frame uses the slow correction principles of the Ilizarov system but adds a si... more The Taylor spatial frame uses the slow correction principles of the Ilizarov system but adds a six-axis deformity analysis incorporated within a computer program. To evaluate its use in our community, we used it in lengthening and deformity correction of the lower limbs to treat 22 cases from 1999 to 2001. There were 14 females and eight males (average age 16.5 years). Our target was lengthening in eight cases, correction of deformities in eight and both in six. The results were excellent in 18 cases, good in two, and fair in two. Despite the cost, patient profile and a steep learning curve, our results were encouraging but less favorable than with the Ilizarov external fixator. Le Cadre Spatial de Taylor utilise les principes de la correction progressive du système Ilizarov mais ajoute une analyse de la difformité selon six axes, incorporée dans un programme informatique. Pour évaluer son usage nous l’avons utilisé dans notre institution, dans 22 cas, de 99 à 2001 pour allonger et corriger des déformations des membres inférieurs. Il y avait 14 femmes et 8 hommes (âge moyen 16.5 années). Notre but était l› allongement dans 8 cas, la correction de difformités dans 8 cas, et les deux dans 6 cas. Les résultats étaient excellents dans 18 cas, bon dans 2, et juste dans 2. En dépit du coût, du profil des patients, et de la courbe d’apprentissage, nos résultats étaient encourageant, mais moins favorables qu’avec le fixateur externe d’Ilizarov.
Between December 1993 and 1999 we treated 34 open tibial diaphyseal fractures. Thirty patients we... more Between December 1993 and 1999 we treated 34 open tibial diaphyseal fractures. Thirty patients were available for evaluation with a mean follow-up after fracture union of 40.5 (24–80) months. Patient average age was 33.1 (15–71) years. Two fractures were grade I, 16 grade II, six grade IIIA, five grade IIIB and one grade IIIC. The wound was debrided and the bone fixed with Ilizarov device. Soft-tissue healing was achieved through Z-plasty, delayed primary closure, split-thickness skin grafting, pedicle flaps and skin traction, and all fractures united with an average 5.6 (3–15.4) months. In 28 patients the results were excellent and good, in one fair and in one poor. Despite numerous complications the use of Ilizarov external fixator provides initial and definitive fracture stability. Entre décembre 1993 et 1999 nous avons traité 34 fractures diaphysaires tibiales ouvertes. Trente malades étaient disponibles pour l'évaluation avec un suivi moyen après consolidation de 40.5 (24–80) mois. L'âge moyen des malades était 33.1 (15–71) années. Deux fractures étaient de grade 1, 16 de grade II, 6 de grads IIIA, 5 de grade IIIB et 1 de grade IIIC. La blessure était débridée et l'os fixé avec l'appareil d'Ilizarov. La cicatrisation des parties molles a été obtenue avec des plasties en Z, des fermetures différées, des greffes de peau, des lambeaux pédiculés et des tractions cutanées. Toutes les fractures ont consolidé avec un délai moyen de 5.6 (3–15.4) mois. Pour 28 malades les résultats étaient excellents et bons, un était juste, et un mauvais. En dépit de nombreuses complications l'usage du fixateur externe d'Ilizarov fournit une stabilité initiale et définitive de la fracture.
Traditional methods of correcting foot deformities may be difficult to apply in some conditions, ... more Traditional methods of correcting foot deformities may be difficult to apply in some conditions, especially in presence of other lower limb problems. This study discusses the versatility of Ilizarov external fixator (IEF) in such cases. It was performed in 34 foot deformities in 33 patients, treated with IEF between 1997 and 1999. The average age of the patients was 15 years. The aetiology of foot deformity was recurrent congenital talipes equinovarus (n=10), neglected congenital talipes equinovarus (n=3), poliomyelitis (n=9), post-traumatic deformity (n=6), post-burn deformity (n=1), arthrogryposis multiplex congenita (n=2), and cerebral palsy, fibular hemimelia and tibial hemimelia (1 case each). Unconstrained IEF was applied for the foot in all cases. The leg construct was applied according to the target: foot deformity alone or associated with other leg problems. IEF construct was extended to the femur in cases with flexion knee deformity and hinges were added. Follow-up continued until overcorrection was maintained for the same period of correction followed by an appropriate cast for 8 weeks. The mean time for deformity correction and Ilizarov stabilisation was 16 weeks, and follow-up period was 23.1 months. The results were good in 31, fair in 2 and bad in 1. Additional procedures were performed, most often in the same operating time. Primary arthrodesis was done for 5 feet and for one revision of failed previous arthrodesis. Open corrective osteotomy for arthrodesis was performed in 2 cases. Two females were treated for flexion knee with bloodless technique. Wire-site infections, wire cut-through a calcaneum and metatarsals and fracture post-IEF removal were observed. Although it is technically difficult, IEF can be considered an effective and versatile way of treating foot and other associated lower limb problems through one-reconstruction attack.
We consider a wireless communication scenario with K source-destination pairs communicating throu... more We consider a wireless communication scenario with K source-destination pairs communicating through several half-duplex amplify-and-forward relays. We design the relay beamforming matrices by minimizing the total power transmitted from all the relays subject to quality of service constraints on the received signal to interference-plus-noise ratio at each destination node. We propose a novel method for solving the resulting nonconvex optimization problem in which the problem is decomposed into a group of second-order cone programs (SOCPs) parameterized by K real parameters. Grid search or nested bisection can be used to search for the optimal values of these parameters. We provide numerical simulations showing the superior performance of the proposed algorithms compared to earlier suboptimal approximations and their ability to approach the globally optimal solution of the non-convex problem.
The downlink frame of a cellular relay network is considered, where a shared MIMO decode-and-frow... more The downlink frame of a cellular relay network is considered, where a shared MIMO decode-and-froward relaying is used to serve the users at the edge of the cell. The relay employs zero-forcing beamforming to manage the interference among the mobile stations (MSs) at the edge of the cell. A non-cooperative scheme is considered where there is no coordination between the base stations (BSs) and the relay station (RS), and a power control algorithm for the RS is developed that maximizes the rate of the relayed users. A cooperative setting which allows the coordination of a power allocation between BSs and RSs is also considered. For this setting, based on the proposed achievable scheme, an optimization formulation is derived to maximize the total throughput of the MSs subject to a constraint on the total power of the system. The problem is solved iteratively as a sequence of geometric programs. Simulation results are provided showing that a significant increase in the network throughput can be achieved via the proposed schemes compared to a conventional cellular system with no relays.
Knee flexion deformity can cause marked physical disability. Acute correction, whether nonoperati... more Knee flexion deformity can cause marked physical disability. Acute correction, whether nonoperative or operative, may lead to serious complications. We treated 50 patients (71 knees) between 1994 and 2002 with the Ilizarov external fixator. The deformity was gradually corrected using Ilizarov principles. Of the 50 patients, 29 were affected unilaterally and 21 bilaterally. In 15 patients, there were associated deformities. In no patient did we surgically release soft tissues; in two patients with arthrodesed or congenitally fused knees, we performed osteotomy before distraction. All patients were assessed clinically and radiographically. We assessed knee flexion angle, range of motion, stability, presence of pain, and healing index. After a minimum followup of 1 year (mean 3.7 years; range, 1–8 years), 18 of 20 of the preoperatively nonambulatory patients having bilateral surgery could walk at last followup. Complications included pin tract infection in all patients, knee subluxation in three patients, and fracture related to treatment in seven patients. We believe gradual correction using a circular frame an effective method to treat flexion knee contractures. In patients with bilateral deformities, improvement in functional activity may be expected in most patients. Level of Evidence: Level IV, therapeutic study. See the Guidelines for Authors for a complete description of levels of evidence.
The Taylor spatial frame uses the slow correction principles of the Ilizarov system but adds a si... more The Taylor spatial frame uses the slow correction principles of the Ilizarov system but adds a six-axis deformity analysis incorporated within a computer program. To evaluate its use in our community, we used it in lengthening and deformity correction of the lower limbs to treat 22 cases from 1999 to 2001. There were 14 females and eight males (average age 16.5 years). Our target was lengthening in eight cases, correction of deformities in eight and both in six. The results were excellent in 18 cases, good in two, and fair in two. Despite the cost, patient profile and a steep learning curve, our results were encouraging but less favorable than with the Ilizarov external fixator. Le Cadre Spatial de Taylor utilise les principes de la correction progressive du système Ilizarov mais ajoute une analyse de la difformité selon six axes, incorporée dans un programme informatique. Pour évaluer son usage nous l’avons utilisé dans notre institution, dans 22 cas, de 99 à 2001 pour allonger et corriger des déformations des membres inférieurs. Il y avait 14 femmes et 8 hommes (âge moyen 16.5 années). Notre but était l› allongement dans 8 cas, la correction de difformités dans 8 cas, et les deux dans 6 cas. Les résultats étaient excellents dans 18 cas, bon dans 2, et juste dans 2. En dépit du coût, du profil des patients, et de la courbe d’apprentissage, nos résultats étaient encourageant, mais moins favorables qu’avec le fixateur externe d’Ilizarov.
Between December 1993 and 1999 we treated 34 open tibial diaphyseal fractures. Thirty patients we... more Between December 1993 and 1999 we treated 34 open tibial diaphyseal fractures. Thirty patients were available for evaluation with a mean follow-up after fracture union of 40.5 (24–80) months. Patient average age was 33.1 (15–71) years. Two fractures were grade I, 16 grade II, six grade IIIA, five grade IIIB and one grade IIIC. The wound was debrided and the bone fixed with Ilizarov device. Soft-tissue healing was achieved through Z-plasty, delayed primary closure, split-thickness skin grafting, pedicle flaps and skin traction, and all fractures united with an average 5.6 (3–15.4) months. In 28 patients the results were excellent and good, in one fair and in one poor. Despite numerous complications the use of Ilizarov external fixator provides initial and definitive fracture stability. Entre décembre 1993 et 1999 nous avons traité 34 fractures diaphysaires tibiales ouvertes. Trente malades étaient disponibles pour l'évaluation avec un suivi moyen après consolidation de 40.5 (24–80) mois. L'âge moyen des malades était 33.1 (15–71) années. Deux fractures étaient de grade 1, 16 de grade II, 6 de grads IIIA, 5 de grade IIIB et 1 de grade IIIC. La blessure était débridée et l'os fixé avec l'appareil d'Ilizarov. La cicatrisation des parties molles a été obtenue avec des plasties en Z, des fermetures différées, des greffes de peau, des lambeaux pédiculés et des tractions cutanées. Toutes les fractures ont consolidé avec un délai moyen de 5.6 (3–15.4) mois. Pour 28 malades les résultats étaient excellents et bons, un était juste, et un mauvais. En dépit de nombreuses complications l'usage du fixateur externe d'Ilizarov fournit une stabilité initiale et définitive de la fracture.
Traditional methods of correcting foot deformities may be difficult to apply in some conditions, ... more Traditional methods of correcting foot deformities may be difficult to apply in some conditions, especially in presence of other lower limb problems. This study discusses the versatility of Ilizarov external fixator (IEF) in such cases. It was performed in 34 foot deformities in 33 patients, treated with IEF between 1997 and 1999. The average age of the patients was 15 years. The aetiology of foot deformity was recurrent congenital talipes equinovarus (n=10), neglected congenital talipes equinovarus (n=3), poliomyelitis (n=9), post-traumatic deformity (n=6), post-burn deformity (n=1), arthrogryposis multiplex congenita (n=2), and cerebral palsy, fibular hemimelia and tibial hemimelia (1 case each). Unconstrained IEF was applied for the foot in all cases. The leg construct was applied according to the target: foot deformity alone or associated with other leg problems. IEF construct was extended to the femur in cases with flexion knee deformity and hinges were added. Follow-up continued until overcorrection was maintained for the same period of correction followed by an appropriate cast for 8 weeks. The mean time for deformity correction and Ilizarov stabilisation was 16 weeks, and follow-up period was 23.1 months. The results were good in 31, fair in 2 and bad in 1. Additional procedures were performed, most often in the same operating time. Primary arthrodesis was done for 5 feet and for one revision of failed previous arthrodesis. Open corrective osteotomy for arthrodesis was performed in 2 cases. Two females were treated for flexion knee with bloodless technique. Wire-site infections, wire cut-through a calcaneum and metatarsals and fracture post-IEF removal were observed. Although it is technically difficult, IEF can be considered an effective and versatile way of treating foot and other associated lower limb problems through one-reconstruction attack.
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Papers by Mohamed Fadel